An approach to new physics at LHCb: study of penguin pollution to ΦS(BS⁰ → J/ΨΦ) using BS⁰ → J/ΨK*⁰ decays, and search for a light A01 Higgs boson in the NMSSM

UNIVERSIDADE DE SANTIAGO DE COMPOSTELA Departamento de F´ısica de Part´ıculas An approach to new physics at LHCb: study of penguin pollution to φs(B0 s→J/ψφ) using B0 s→J/ψK∗0decays, and search for a light A0 1Higgs boson in the NMSSM Carlos V´azquez Sierra Tese de Doutoramento Programa de Doutoramento en F´ısica Nuclear e de Part´ıculas M´aximo Pl´o Casas´us, Catedr´atico de Universidade do Departamento de F´ısica de Part´ıculas da Universidade de Santiago de Compostela, Juan Jos´e Saborido Silva, Profesor Titular de Universidade do Departamento de F´ısica de Part´ıculas da Universidade de Santiago de Compostela, Diego Mart´ınez Santos, Investigador Asociado do Departamento de F´ısica de Part´ıculas da Universidade de Santiago de Compostela, INFORMAN: Que o presente traballo, titulado “An approach to new physics at LHCb: study of penguin pollution to φs(B0 s→J/ψφ) using B0 s→J/ψK∗0decays, and search for a light A0 1Higgs boson in the NMSSM”, foi realizado por Carlos V´azquez Sierra baixo a s´ua direcci´on no Departamento de F´ısica de Part´ıculas da Universidade de Santiago de Compostela e no experimento LHCb do CERN. As´ı mesmo, expresan a s´ua conformidade co mesmo eautorizan a s´ua presentaci´on diante da Comisi´on Examinadora do Programa de Doutoramento en F´ısica Nuclear e de Part´ıculas, constitu´ındo as´ı a Tese de Doutoramento do seu autor para optar ´o Grao de Doutor en F´ısica. E para que as´ı conste, asinan en Santiago de Compostela, a 2 de setembro de 2016, M´aximo Pl´o Casas´us Juan Jos´e Saborido Silva Diego Mart´ınez Santos Carlos V´azquez Sierra Author: Carlos V´azquez Sierra Supervisor: M´aximo Pl´o Casas´us Supervisor: Juan Jos´e Saborido Silva Supervisor: Diego Mart´ınez Santos Inform for European Mention: Paula ´ Alvarez Cartelle Inform for European Mention: Greig Cowan Acknowledgements First of all, I would like to thank my supervisors for their dedication, time, and patience. Without Diego, Juan and M´aximo, this work would not be possible. I’m sincerely grateful. I would like to express my gratitude to my colleagues of the LHCb Collaboration, especially the VELO Upgrade group (the first people whom I worked with when I arrived at CERN for the first time as a summer student), the B decays to charmonia (B2CC) working group (where I spent most of my time as a PhD student), and the stripping group where I belonged to for a two-years period as the stripping liaison of the B2CC working group. Most of the knowledge I acquired during the last four years was obtained from fruitful discussions with their integrants. I also want to thank two of my Spanish LHCb colleagues, Pablo and Vicente. One can meet not only fellow scientists but also friends when working at such a big collaboration as LHCb. Special thanks to Vincenzo, Olivier, Yasmine, Cibr´an, Martino and Veronika, for kindly accepting being members of my thesis jury, and to Paula and Greig, for accepting the hard task of reading this work as referees for the European Mention. Of course I want to thank my colleagues here at Santiago, as part of the Grupo de F´ısica de Altas Enerx´ıas (GAES). An special word for Xabi and his invaluable help during the analysis of A0 1→µ+µ−decays, and for my fellow PhD and postdoc students: ´ Alvaro, Brais, Mar´ıa, Juli´an, To˜no, Miguel, Miriam, Martino, Jessica and Veronika. I thank the financial support provided by the Ministerio de Econom´ıa y Competitividad (MINECO) and by the European Research Council (ERC). ii Agradecimientos No pod´ıa faltar el m´as sincero agradecimiento a mi padre Carlos, a mi madre Mar´ıa Isabel y a mi t´ıa ´ Angeles, por su apoyo, sus consejos y un cari˜no que no se puede describir con palabras. Gracias por haberme ayudado a llegar a ser lo que soy hoy en d´ıa. Tambi´en quiero agradecer a aquellos que son pr´acticamente parte de mi familia, Fran, Camilo y Xabier, a los que conozco ya hace m´as de una d´ecada y con los que he compartido buenos y malos momentos, aunque siempre con un denominador com´un y es el de haber sido memorables. Dentro de este grupo podr´ıa inclu´ır tambi´en a aquellos que conoc´ı cuando comenc´e la Licenciatura, y que a´un conservo ya no s´olo como compa˜neros de biblioteca sino como buenos amigos: Aar´on, Alexis y Yago. Agradezco tambi´en la amistad y apoyo de aquellos que no conoc´ı al comienzo pero s´ı durante mis primeros a˜nos en la Universidad, y que a´un conservo: ´ Alvaro, Vila, Arribi, Alex, Tato, Yasser, Aida, Santiago, Adri´an... Por ´ultimo, ser´ıa hip´ocrita por mi parte no dar las gracias a los que tambi´en son mis amigos, y que, tanto por su apoyo como por las noches de rock & roll que hemos vivido juntos, han ayudado de una forma u otra a conservar mi salud mental y han contribuido al ´exito de mi per´ıodo como estudiante de doctorado: Brais, Gonzalo, Hugo, Colinas, Hermida, Xos´e... Y por supuesto, una especial nota de cari˜no y agradecimiento a mis tres grandes templos nocturnos de preferencia, Curruncho, Maycar y Ulises. Espero no olvidarme de nadie, y de hacerlo, mis m´as sinceras disculpas: la memoria es, a veces, muy cruel de no tener en consideraci´on a aquellos que de verdad se lo merecen. iii Elementary particles are terribly boring, which is one reason why we are so interested in them. Steven Weinberg The imagination of nature is far, far greater than the imagination of man. Richard Feynman Homines, dum docent discunt. Lucius Annaeus Seneca iv Abstract This thesis presents the analysis of B0 s→J/ψK∗0decays, using 3 fb−1of data collected by the LHCb experiment during 2011 and 2012, from LHC pp collisions at centre-of-mass energies of 7 TeV and 8 TeV, respectively. The purpose of this analysis is to estimate the second order (penguin) contributions, which may be confused as possible new physics, to the CP-violating phase φsmeasured in B0 s→J/ψφ decays. First steps of the analysis of the A0 1→µ+µ−decay mode, using 2.97 fb−1of Run I LHCb pp data, are also reported, along with the characterisation of silicon pixel detectors using SPS test beams consisting of charged hadrons with a momentum of 180 GeV/c, in the context of the upgraded LHCb VELO R&D programme. The excellent performance of the LHCb detector during 2011 and 2012, especially the muon and trigger systems, crucial for the reconstruction of muon tracks, has been also reported. Some details about the on-going upgrade of LHCb subsystems have been reviewed as well. v Chapter 1 Introduction The Standard Model (SM) of Particle Physics, based on strong, weak and electromagnetic (electroweak) interactions, is a very powerful and self-consistent model which has led to many successes in providing accurate descriptions of experimental measurements. As of today this theory is considered the benchmark model to classify subatomic particles and explain their interactions, except gravitation, which is not incorporated in the SM. However, as the scientific community knows very well, being successful is still far from being perfect: some tensions between results from several experiments and SM predictions have arisen in the previous years, such as the inability to find a proper SM candidate for dark matter in the Universe, the existence of neutrino masses, or the necessary imbalance between matter and antimatter in the Universe, among others. The SM is not able to explain these phenomena, which are intensively investigated in several High Energy Physics (HEP) experiments. Searching for both direct or indirect evidence of possible New Physics (NP), which may lead to the establishment of a new benchmark model able to explain all these tensions, can be considered as the avant-garde of HEP. A more detailed theory overview is given in Chapter 2. Regarding indirect searches of possible NP, the violation of a certain discrete symmetry, the CP violation, is one of the ingredients necessary to explain the imbalance between matter and antimatter in the Universe, also known as the problem of the baryogenesis. However, experimental results have shown that the amount of CP violation predicted by the SM is not enough to satisfy the conditions needed to solve that baryogenesis puzzle: a search for new NP sources of CP violation is mandatory. The study of CP violation in the neutral B0 smeson system offers an excellent opportunity to detect possible deviations from SM predictions. A study of second order (penguin) contributions to the mixing-induced CP-violating phase φsin b→c¯cs processes, which may be confused as a signal of NP, is presented in Chapter 4, while the results are discussed in Chapter 5. My contribution to this analysis is focused in the construction of the data samples, the event selection, the treatment of peaking backgrounds and the measurement of branching fractions. As for direct searches of possible NP, one way to complement the SM are its supersymmetric extensions. Direct searches of possible new particles predicted by those extensions, such as in the Next-to-Minimal-Supersymmetric-SM (NMSSM), constitute a direct way 1 to test the robustness of the SM, where the observation of possible NP particles predicted by alternative candidate models, might be achieved. A search of the A0 1→µ+µ−decay mode, where A0 1is the light CP-odd Higgs boson in the NMSSM, is presented in Chapter 6, where the construction of the data samples, event selection and multivariate studies are my main contribution to this analysis. The work of this thesis has been done using data recorded by the LHCb experiment, dedicated to Heavy Flavor (HF) physics at the Large Hadron Collider (LHC), which is located at CERN and is the most powerful hadron accelerator and collider ever built by humankind. The primary goal of the experiment is to look for indirect evidence of NP in CP violation and rare decays of beauty and charm hadrons. As of June 2016, the LHCb experiment is driven by a collaboration of 1199 members, from 69 institutes in 16 countries around the world. A 2% of the collaboration are part of the University of Santiago de Compostela, while 1.45% is the average contribution per institute. Data used for the studies described in this thesis were taken during 2011 and 2012, as part of the first LHC run period, named Run I. At the present moment, the LHCb experiment is taking data as well, as part of the second LHC run period, named Run II, which started at 2015 and will last until 2018. A more detailed description of the LHC and the LHCb experiment can be found in Chapter 3. However, the LHCb experiment is now going through an upgrade of its subdetectors and online infrastructure, the LHCb Upgrade, which will end after the second LHC long technical stop, the Long Shutdown 2 (LS2), with the start of Run III planned for 2021. Characterisation studies for a certain type of silicon pixel sensors, based on Medipix3 technology, in the context of the upgrade of the LHCb Vertex Locator are presented at the end of Chapter 3.3. My contribution to these studies is focused in the measurements performed with irradiated assemblies. Apart from the contributions described in the previous paragraphs, during my PhD period at LHCb, I also worked as a piquet of the Silicon Tracker subdetector (see Chapter 3.2.1.2), and with the LHCb stripping team as the stripping liaison of the Bmeson to charmonia working group. Details about what the “stripping” is are given in Chapter 3.2.6. In summary: after this brief introduction, a theory overview is presented in Chapter 2, a detailed description of the LHC machine and the LHCb experiment is given in Chapter 3, Chapter 4contains the analysis of B0 s→J/ψK∗0decays while the results are discussed in Chapter 5, in Chapter 6the study of the A0 1→µ+µ−decay mode is presented, and finally, Chapter 7gives the conclusions and Chapter 8(Chapter 9) contains a summary of this thesis in English (Galician). 2 Chapter 2 Theory overview The Standard Model is a Quantum Field Theory (QFT) based on strong and ElectroWeak (EW) interactions [1–4]. It is characterised by a huge predictive power, leading to continued successes in providing accurate descriptions of experimental measurements. Due to this fact and to the theoretical self-consistency of the model itself, as of today this theory is considered the benchmark model to classify subatomic particles and explain their interactions, except gravitation, which is not incorporated in the SM. However, some phenomena are not incorporated in the SM, such as the possible presence of Dark Matter (DM) in the Universe, or the non-zero masses of the neutrinos [4]. The CP transformation combines charge conjugation C, which means that this operation changes one particle into its anti-particle, with parity P. If CP were an exact symmetry, the laws of Nature would be the same for matter and for antimatter [5]. It is observed that most phenomena are indeed CP-symmetric. In particular, this symmetry is respected by electromagnetic and strong interactions. The weak interactions, on the other hand, violate C,P[6,7], and also CP [8]. This phenomenon of CP violation, discovered more than 50 years ago, is one of the three essential ingredients to explain the imbalance between matter and anti-matter in the Universe [9]. The existence of CP violation, along with the existence of B(baryonic number) violation and with the existence of interactions out of thermal equilibrium, are known as the “Sakharov conditions” (named after the Russian nuclear physicist and Nobel Peace Prize Andrei D. Sakharov) for the baryon asymmetry in the baryogenesis [10]. In the SM, CP violation arises in the Yukawa-sector via quark mixing and it is described by a complex parameter in the Cabibbo-Kobayashi-Maskawa (CKM) matrix [11,12]. Current results in CP violation from various experiments do not contradict the unitarity of the CKM matrix [13], resulting in the statement that this single complex phase of the CKM is currently sufficient to describe the multitude of CP-violating phenomena observed by experiments [14]. However, CP violation in the Yukawa-sector is not sufficient to cope with the previously stated problem of the baryogenesis in the Universe [15]. This demands the existence of additional sources of CP violation Beyond the SM (BSM): finding such a source may not only fulfill one of the “Sakharov conditions”, but also result in the detection of New Physics itself. The study of CP violation in the B0 ssystem offers an excellent opportunity to detect 3 possible deviations from SM predictions. The current SM estimation for CP violation effects due to the intereference between mixing and decay in b→c¯cs processes, taking only into account tree-level topologies, is [16] −2βs=−0.0376+0.0008 −0.0007 rad,(2.1) where βsis defined in terms of the Wolfenstein parametrisation of the CKM matrix (see Chapter 2.2). However, due to the outstanding precision of this estimation, contributions due to second-order topologies have to be taken into account to avoid confusing any possible significative deviation as an unambiguous signal of NP. These contributions, socalled “penguin pollution”, are studied in Chapter 4as a central part of this work. The latest experimental world average for the CP-violating phase φs(see Chapter 2.2 and Chapter 2.3), taking into account the results from several experiments, is [13] φs=−0.033 ±0.033 rad.(2.2) As stated in Chapter 3, search for indirect evidence of NP in CP violation and rare decays of beauty and charm hadrons is the main objective of the LHCb experiment, which is an ideal laboratory for these kind of studies. In Chapter 2.1, a phenomenological introduction to CP violation in the B0 ssystem is presented. In Chapter 2.2, the introduction in previous chapter is particularised to the measurement of CP violation due to the interference between mixing and decay for the B0 s→J/ψφ channel. Phenomenological characterisation of penguin pollution to previous case is explained in Chapter 2.3. Finally, a brief discussion about potential sources and searches of NP in these measuremrents is presented in Chapter 2.4. 2.1 CP violation in the B0 ssystem In the system of neutral B0 smesons, the quantum mechanical time evolution of a decaying B0 smeson, with mass and lifetime mB0 sand τB0 s= 1/ΓB0 s, respectively, is given by |B0 s(t)i=e−i2mB0 s−iΓB0 st 2|B0 s(0)i,(2.3) where ΓB0 sdenotes the total decay rate of the B0 smeson. The time evolution of these states is governed by the Schr¨odinger equation id dt |B0 s(t)i |B0 s(t)i=M−iΓ 2|B0 s(t)i |B0 s(t)i,(2.4) where Mand Γare 2×2 hermitian matrices. In the SM, B0 s−B0 soscillations are induced due to the flavour changing weak interaction described by the so-called “box diagrams” (see Figure 2.1). An initially produced B0 sor B0 smeson evolves in time into a superposition of both states, causing off-diagonal elements of Mand Γmatrices to be non-zero. Due 4 Figure 2.1: “box diagrams” related to B0 s−B0 smixing. to the CPT theorem, their diagonal elements are equal, representing the mass MB0 sand the decay rate ΓB0 s, respectively, of B0 sand B0 smesons. These mass eigenstates are |BLi=p|B0 si+q|B0 si, |BHi=p|B0 si−q|B0 si,(2.5) with |p|2+|q|2= 1. Once the mass eigenstates |BLi(light) and |BHi(heavy) are defined, the mass difference ∆MB0 sand the decay rate difference ∆ΓB0 scan be written as ∆MB0 s=MH−ML,∆ΓB0 s= ΓL−ΓH,(2.6) followed by the time evolution of the flavour eigenstates as |B0 s(t)i=g+(t)|B0 si+q pg−(t)|B0 si, |B0 s(t)i=p qg−(t)|B0 si+g+(t)|B0 si,(2.7) with the coefficients g±(t) = 1 2e−iMLte−1 2ΓLt±e−iMHte−1 2ΓHt.(2.8) The decay amplitude describing the transition of the flavour eigenstate B0 sinto the final state f(being ¯ fits CP-conjugated state) is denoted by Af(A¯ f); for the decay of a B0 sstate into f(¯ f) the notation ¯ Af(¯ A¯ f) is used, Af=hf|H|Bi, A ¯ f=h¯ f|H|Bi, ¯ Af=hf|H|Bi,¯ A¯ f=h¯ f|H|Bi,(2.9) being the flavour changing weak transitions described by an effective Hamiltonian H=M−iΓ 2.(2.10) 5 The amplitudes Afand ¯ Afare typically affected by hadronic effects and very difficult to be calculated reliably in theory. However, CP-symmetries are governed by a single complex quantity, λf, given by λf=q p ¯ Af Af ,(2.11) whose argument is usually written as φs=−arg(λf).(2.12) Defining the following abbreviations for direct, mixing-induced and ∆Γ-correctioninduced CP asymmetries, respectively, Adir CP =1−|λf|2 1 + |λf|2,Amix CP =2=(λf) 1 + |λf|2,A∆Γ =2<(λf) 1 + |λf|2,(2.13) which satisfy the closing relation (Adir CP )2+ (Amix CP )2+ (A∆Γ)2= 1,(2.14) the time dependent asymmetry due to the interference of both decay rates Γ[B0 s→f] and Γ[B0 s→f] can be written as ACP,f(t)=Γ[B0 s→f] −Γ[B0 s→f] Γ[B0 s→f] + Γ[B0 s→f] =Adir CP cos(∆MB0 st) + Amix CP sin(∆MB0 st) cosh ∆ΓB0 st/2−A∆Γ sinh ∆ΓB0 st/2.(2.15) From these considerations, three main cases can be studied: CP violation appearing in in the mixing (|q/p| 6= 1), in the decay (|¯ A¯ f/Af| 6= 1), and induced due to the interference between the mixing and the decay. The latter case, which is the only relevant for the purpose of this work, is explained in detail in Chapter 2.2. A more detailed discussion about CP violation in the B0 ssystem can be found in [14], from where most of the details described here were extracted. 2.2 The φsphase in the B0 s→J/ψφ mode As previously stated at the beginning of Chapter 2,CP violation due to the interference between mixing and decay in b→c¯cs processes can be computed in the SM with high precision, constituting an excellent probe for the search of sources of possible NP. The golden mode for the measurement of this CP-violating phase −2βsis the B0 s→J/ψφ channel, which is mediated by a b→c¯cs process. In this section, the formalism described in Chapter 2.1 will be particularised for this case. For this purpose, the following considerations should be made: 1. The final state fis a CP eigenstate: since in B0 s→J/ψφ decays, the final state f=J/ψφ is a CP eigenstate, the relation f≡fCP =ηCP ¯ fCP (2.16) 6 is satisfied. Consequently, to a good approximation, hadronic uncertainties cancel out in the ratio of decay amplitudes, only remaining a pure weak CKM phase φCKM j, and being the ratio given by ¯ Af Af =−ηCP e−2iφCKM j,(2.17) thus the parameter λf, given by (2.11), is now written as λf=q p ¯ Af Af =−VtsV∗ tb V∗ tsVtb −ηCP e−2iφCKM j=ηCP VtsV∗ tb V∗ tsVtb e−2iφCKM j,(2.18) where the CKM elements responsible for the mixing are explicitly shown. 2. Only one type of weak process contributes to the decay amplitude: the decay mode B0 s→J/ψφ is governed on quark-level by a b→c¯cs transition, with a large treelevel contribution and a suppressed penguin contribution. Hence, it can be considered that |λf|= 1, and consequently, Adir CP = 0, Amix CP = sin φsand A∆Γ =−cos φs. Then, the general expression of the time dependent asymmetry as given in (2.15), can be written as ACP,f(t)≈sin(φs) cos(∆MB0 st) cos(φs) sinh ∆ΓB0 st/2−cosh ∆ΓB0 st/2.(2.19) Since only one CKM process b→c¯cs is contributing, the parameter |λf|can be completely written in terms of elements of the CKM matrix and the corresponding CP eigenvalue. Hence, its argument φspreviously written in (2.12) is, in the SM and considering only tree-level topologies, given by φSM s=−arg ηCP VtsV∗ tb V∗ tsVtb VcbV∗ cs V∗ cbVcs .(2.20) Following previous considerations, and using a convention which leads to a positive value of βs, a positive CP eigenvalue ηCP = +1 is adopted. Therefore, the phase given by (2.20) can be finally re-written as φSM s= 2 arg −VtsV∗ tb VcbV∗ cs =−2βs,(2.21) where βsis defined, using the Wolfenstein parametrisation of the CKM matrix, as βs= ηλ2+O(λ4) [16–18]. Hereafter, the CP-violating phase φsin this particular case where φSM s=−2βs, will be simply referred to as φs. The final state of the B0 s→J/ψφ decay mode is an admixture of CP eigenstates because of the relative angular momentum between J/ψ and φmesons. Since both particles are spin-1 vector mesons, the angular momentum eigenvalue can run over three possible values, 0, 1 or 2. In other words, there are three possible linear polarisation states: 7 longitudinal (0), parallel (1,k) and perpendicular (2,⊥). Of course, each one of these polarisation states corresponds to a CP eigenstate with an associated CP eigenvalue. Hence, it is neccesary to disentangle this admixture in order to distinguish among eigenstates, where parallel and longitudinal states are CP-even, and perpendicular state is CP-odd. CP-violating effects in the time-dependent angular distribution of the B0 s→J/ψφ decay products play a key role for the search of NP. Within the SM, these effects are expected to be small: a hypothetical discovery of CP-violating effects significantly larger than zero could lead to clear evidences of NP. But penguin topologies in the B0 s→J/ψφ channel (see Figure 2.2), which are doubly Cabibbo-suppressed and hence assumed to be negligible [19–22], cannot be calculated reliably from QCD [23] and could mimic CP-violating effects which might be misinterpreted as signals of NP in B0 s−B0 smixing with a small but sizeable CP-violating NP phase. This limits the theoretical accuracy of the benchmark for the search of NP and pollutes the efforts, probably leading to false evidences of NP. Latest LHCb results from time-dependent tagged analysis of B0 s→J/ψK+K−decays [24] show the following measurement for the CP-violating phase φsin this mode, φs(B0 s→J/ψK+K−) = −0.058 ±0.049 (stat) ±0.006 (syst),(2.22) where the first uncertainty is statistical and the second is systematic. This value is in good agreement with the SM tree-level predicted value in (2.1). But this result could be affected by penguin pollution, leading to an avoidable imprecision in the systematic uncertainties. In consequence, it is strongly recommended to estimate this pollution in order to disentangle SM effects from possible NP and to obtain more precise values by decreasing statistical errors. Theoretically, penguin effects are expected to interfere constructively with mixinginduced CP violation, leading to CP asymmetries significantly large. These effects can be controlled by means of an analysis of the angular distribution of the B0 s→J/ψK∗0channel (see Figure 2.3) and its CP-conjugate: applying SU(3) flavour-symmetry arguments and neglecting penguin annihilation and exchange topologies (probed through B0→J/ψφ decays), the relevant hadronic parameters entering the B0 s→J/ψφ observables can be determined and taken into account in the extraction of φs. Using the B0 s→J/ψK∗0 channel as a control channel for this purpose is possible because relevant hadronic parameters which can be used to estimate the penguin pollution in the extraction of φsfrom the B0 s→J/ψφ channel are not suppressed. A direct measurement of these hadronic parameters in the same B0 s→J/ψφ channel is almost impossible because they are strongly suppressed, around a 95% [19–22]. The formalism used in this work for the estimation of this penguin pollution is described in Chapter 2.3. 8 B0 s J/ψ φ W ¯ b s s ¯c c ¯s (a) B0 s J/ψ φ W ¯ b s s ¯s ¯c c ¯u, ¯c, ¯ t Colour singlet exchange (b) Figure 2.2: Tree-level (a) and penguin (b) diagrams (SM) contributing to B0 s→J/ψφ. B0 s J/ψ K∗0 W ¯ b s s ¯c c ¯ d (c) B0 s J/ψ K∗0 W ¯ b ss ¯ d ¯c c ¯u, ¯c, ¯ t Colour singlet exchange (d) Figure 2.3: Tree-level (c) and penguin (d) diagrams (SM) contributing to B0 s→J/ψK∗0. 2.3 Contribution to φsdue to penguin diagrams For neutral B0 smeson decays, the transition amplitudes Afand ¯ Afdefined in Chapter 2.1, can be written in the following form [20,21], Af=Nf[1 −bfeρfe+iγ],(2.23) ¯ Af=ηfNf[1 −bfeρfe−iγ],(2.24) where ηfis the CP eigenvalue of the final state f,Nfis a CP-conserving normalisation factor representing the dominant tree-level topology, bfparametrises the relative contribution from the penguin topologies, ρfis the CP-conserving phase difference between the tree and penguin contributions, whereas their relative weak phase is given by the Unitary Triangle (UT) angle γ.1The parameters Nfand bfdepend both on CKM factors and on 1Defined as γ= arg −Vud V∗ ub VcdV∗ cb [25]. 9 are crucial. After the description of the different subsystems of the LHCb detector, enumerated in more detail in Chapter 3.2, its DAta acQuisition (DAQ) sequence is described in Chapter 3.2.4, along with the simulation framework, in Chapter 3.2.5. A summary of the detector performance is presented in Chapter 3.2.6, followed by a description of the experimental conditions of LHCb Run I on Chapter 3.2.7. A final chapter describing the on-going upgrade of the LHCb detector in order to be able to cope with higher luminosities and higher centre-of-mass energies due to the upgrade of the LHC machine, can be found in Chapter 3.3. Some paragraphs and sentences in the following pages may be literally extracted from other LHCb theses, such as refs. [40–44], and also from certain technical design reports and performance publications, but appropriately cited in the latter case. 3.1 The Large Hadron Collider The Large Hadron Collider, operating at CERN since September 2008, is the most powerful hadron accelerator and collider ever built by humankind. Installed in the 27 km circular tunnel built to house the Large Electron Positron (LEP) collider, it is located between 45 m and 170 m underneath surface at the French-Swiss border. The LHC machine was designed to accelerate proton beams up to an energy of 7 TeV per beam and to collide them with a centre-of-mass energy of 14 TeV [37]. Protons, obtained from hydrogen gas, are progressively accelerated up to 450 GeV through the chain of pre-accelerators shown in Figure 3.1. First, the LINear ACCelerator 2 (LINAC2) up to 50 MeV; second, the BOOSTER up to 1.4 GeV; third, the Proton Synchrotron up to 26 GeV; and finally, the Proton Synchrotron (SPS) up to 450 GeV. After being accelerated up to 450 GeV, each beam is injected in the LHC and accelerated using 16 radiofrequency (RF) cavities to the final collision energy. At these energies, 1232 superconducting Nb-Ti dipole magnets, cooled down to 1.9 K using super-fluid He, create a very intense magnetic field (8.33 T at a nominal centre-of-mass energy of 7 TeV) to bend and keep the two proton beams in opposite orbits around the LHC ring. The two beams are accomodated in the same cryostat with a common yoke, which provides the opposite magnetic fields. To focus the nominal proton beams, composed of bunches of 1.2 to 1.4×1011 protons with a separation of 25 ns (40 MHz of bunch crossing frequency), 392 quadrupole magnets are also located around the ring. A schematic of the cross-section of a LHC cryodipole, where all these elements are mecanically fit together, is shown in Figure 3.2. The LHC was operated during 2011 and 2012 at centre-of-mass energies of 7 and 8 TeV (3.5 TeV and 4 TeV per beam), respectively, with bunches separated in time by 50 ns (20 MHz of bunch crossing frequency). Beams are collided in four interaction points (IPs) along the LHC ring. A total of seven detectors share these four IPs, as shown in Figure 3.3, to study the physics produced by the unprecedented high energy collisions at the TeV scale. The two General Purpose Detectors (GPDs) ATLAS (A Toroidal LHC ApparatuS) [47] 16 Fig. 2.1: Representation of the di↵erent steps, within the CERN accelerator complex, necessary to bring protons at 7 TeV. Protons are extracted from an H source and then progressively accelerated through the LINear ACCelerator 2 (LINAC 2) up to 50 MeV, the BOOSTER up to 1.4 GeV, the Proton Synchroton (PS) up to 26 GeV and the Super Proton Synchroton (SPS) up to 450 GeV. Then, they are injected in the LHC where they reach the final collision energy. (Figure adapted from CERN-DI-0606052 c CERN Geneva) from BSM physics. The other experiments being operated at the LHC are: LHCb [95](whichis described in detail in Section 2.2), ALICE [96], TOTEM [97], LHCf [98]and MoEDAL [99]). 34 Figure 3.1: CERN accelerator complex layout (2008) [45]. On the left, the step-by-step acceleration sequence is shown. and CMS (Compact Muon Solenoid) [48] are based on large central detectors, located at IPs 1 and 5 respectively, and designed to study collisions producing high tranverse momentum (pT) particles. Both experiments develop a wide physics programme, which includes direct searches of NP particles, band tquark physics, and the fundamental objective of the detection of the Higgs boson. The latter was reported to be successfully observed for the first time in 2012, in the mass region around 125 GeV [49,50]. One year later, the Nobel Prize in Physics was awarded jointly to Fran¸cois Englert and Peter Higgs.3Now, a large part of ATLAS and CMS physics programme is devoted to a precision measurement of the properties of this recently discovered scalar boson. Located at IP 2, ALICE (A Large Ion Collider Experiment) [51] is a dedicated heavy–ion experiment which studies quark-gluon plasma with data resulting from nucleus–nucleus collision. For this purpose, LHC is filled in with dedicated runs of heavy ions (Pb) instead of protons. Finally, the LHCb (Large Hadron Collider beauty) [52] experiment (described more in 3The Nobel Prize in Physics 2013: Fran¸cois Englert and Peter Higgs (a,b,c) 17 Figure 3.2: Cross-section of a LHC cryodipole [37]. Lengths are in mm. detail in Chapter 3.2) at IP 8 was originally designed for the study of CP violation and rare decays focused in band cquark physics. However, due to the excellent performance of the detector during the past years, the LHCb collaboration has been able to develop a wider physics programme obtaining successful results, such as the first observation of an exotic five-quark [53] and the observation of several exotic four-quark [54–56] hadronic structures, and studies of proton-nucleus collisions [57–61]. Because of these improvements, in the present years the LHCb detector started to be considered a forward GPD. Other experiments as TOTEM (TOTal Elastic and diffractive cross section Measurement) [62], LHCf (Large Hadron Collider forward) [63] and MoEDAL (Monopole and Exotics Detector at the LHC) [64] are also being operated at the LHC. The LHCf experiment studies energy distributions of particles in the very forward region, and is placed at roughly ∼140 m from the ATLAS IP. TOTEM is designed to measure the total elastic and diffractive cross section as its name indicates, and shares IP 5 with CMS. The MoEDAL, deployed at the opposite side of the LHCb detector at IP 8, is a pioneering 18 Figure 3.3: Detailed schematic of the LHC ring, adapted from ref. [46], showing the different interaction points, sectors and experiments. experiment designed to search for highly ionizing avatars of new physics, such as magnetic monopoles or massive (pseudo)stable charged particles. 3.2 The LHCb detector The LHCb detector is a single-arm spectrometer with a forward angular coverage, focused on the high rapidity region on one side of the IP. It approximately covers an angular range from 10 to 300 mrad in the bending plane. The angular coverage is smaller in the nonbending plane, from 10 to 250 mrad [52]. As shown in Figure 3.4,4the polar distribution of the b¯ bpair production at the LHC justifies this design, because at high energies these pairs are predominantly produced in the same forward or backward cone. The IP 8 of the LHC, previously used by the DELPHI experiment during the LEP time, has been allocated to the LHCb detector. A modification to the LHC optics, 4These plots were created using PYTHIA8 [65] and CTEQ6 NLO [66] by Christian Elsasser ([email protected]). 19 0 /4π /2π /4π3 π 0 /4π /2π /4π3 π [rad] 1 θ [rad] 2 θ 1 θ 2 θ b b z LHCb MC = 14 TeVs 1 η -8 -6 -4 -2 0 2 4 6 8 2 η -8 -6 -4 -2 0 2 4 6 8 LHCb acceptance GPD acceptance = 14 TeV s LHCb MC Figure 3.4: Angular b¯ bproduction plots, from LHCb simulation, at a centre-of-mass energy of 14 TeV. Left: Polar distribution of the b¯ bpair production in the forward region. Right: pseudorapidity distribution of the b¯ bpair production, where one axis refers to one of the b-quarks and the other axis refers to the remaining one in the pair. A comparison between LHCb acceptance (defined as 1.8< η < 4.9) and other GPDs acceptance (defined as |η|<2.4) is overlayed over the right plot, manifestly showing the forward design of the LHCb detector. displacing the interaction point by 11.25 m from the centre, has permitted maximum use of the existing cavern for the LHCb detector components. With a low occupancy and low radiation damage due to a modest luminosity of 2 ×1032cm−2s−1, an amount of 1012 b¯ bpairs would be produced in 107s. Due to this lower luminosity, tuned independently from the other IPs, events are dominated by a single pp interaction per bunch crossing and hence simpler to analyse [52]. The layout of the LHCb spectrometer is shown in Figure 3.5. The right-handed coordinate system adopted has the z axis along the beam, and the y axis along the vertical. With an overall dimension of approximately 6 m ×5 m ×20 m, the detector is composed by the following main parts: the beam pipe, the magnet, the tracking and vertexing systems: VErtex LOcator, Silicon Tracker and Outer Tracker; and the particle identification systems: Ring Imaging CHerenkov detectors, the calorimeter system, and the muon system. Also, because of the high interaction rate and the low branching ratio of those rare decays of interest (as addressed at the beginning of Chapter 3), an efficient rejection of data needs to take place. For this purpose a trigger system is built, consisting of a hardware based system (Level 0 or L0) and a pure software based trigger (High Level Trigger or HLT). The beam pipe [52] is 19 m long and is divided in four conical sections, including the forward window of the VELO and covering the full LHCb acceptance. This design is 20 Figure 3.5: Schematic two-dimensional view of the LHCb detector [67]. The right-handed coordinate system adopted has the z axis along the beam, and the y axis along the vertical. particularly delicate since the LHCb experiment is focused on the high rapidity region, where the particle density is high: the mass of the beam pipe and the presence of flanges and bellows have a direct influence on the occupancy, in particular for the tracking system and the RICH detectors. The momentum of charged particles is measured using a a dipole magnet, covering the forward acceptance of ±250 mrad vertically and of ±300 mrad horizontally. This dipole is composed by a Fe yoke surrounded by two identical coils of conical saddle shape produced of the metal alloy Al 99.7 [42,68]. In average, the LHCb magnet has an integrated magnetic field of 4 T ×m. The relative precision obtained after a field mapping is about 4×10−4, enough to achieve the required momentum resolution for charged particles. Figure 3.6 shows on the left a picture of the dipole installed at the LHCb experimental site, while on the right the Bymagnetic field component as a function of the zcoordinate is presented. For the measurement of CP asymmetries, it is important to control the systematic effects of the detector, by changing periodically the direction of the magnetic field. As stated at the beginning of Chapter 3, without an appropriate vertex reconstruc21 Figure 3.6: LHCb magnet dipole. Left: picture of the dipole installed at the LHCb experimental site (2004). Right: Bymagnetic field component as a function of the z coordinate [52]. tion and particle identification, and an efficient rejection of background data, the physical studies described in this work could not be done. Hence, tracking and vertexing systems, particle identification systems and trigger systems are described in the following paragraphs with more detail, followed by a description of the LHCb DAQ sequence, the simulation framework and a summary of the detector performance during the Run I. 3.2.1 Tracking and vertexing systems The LHCb tracking and vertexing systems consists of the VErtex LOcator system, the Tracker Turicensis (TT) and the Inner Tracker (IT) developed as a common project called the Silicon Tracker (ST), and the Outer Tracker (OT) located at the outer region of the IT. Each one of the ST and OT stations has four detection layers in a x-u-v-x arrangement with vertical strips in each of the two xlayers, and strips rotated by ±5oin the uand v layers, in order to get a stereo-view of the particle trajectory. 3.2.1.1 VErtex LOcator The VErtex LOcator, has a critical importance for the experiment purposes: in order to study different b-hadron decays like those involving short-lived resonances, a precise vertex reconstruction which allows to distinguish between primary and secondary vertices (see Chapter 3.2.6.1) is imperative. As a consequence, high background rejection and a precise measurement of lifetimes (not only required to resolve short-lived resonances but also to resolve the fast oscillation of the B0 smeson system) are achieved. LHCb VELO contains 21 stations, positioned along and perpendicular to the beam axis with an r-φgeometry: with this design, forward-going tracks with a high impact 22 parameter with respect to the production vertex are easily identified. It covers the pseudorapidity range 1.6 < η < 4.9 for particles coming from primary vertices in the range -10.6 cm <z<10.6 cm. Each disc, with a radius of ∼42 mm, is composed of two types of half-disc silicon sensors: r-type sensors (circular strips centered around the beam axis, measuring the rpolar coordinate) and φ-type sensors (straight and almost radial strips, measuring the φpolar coordinate). These half-disc sensors, are arranged in pairs of r-type and φ-type, mounted back-to-back to reduce thickness. At innermost radius, the minimum strip pitch in the sensors is 38 µm, increasing up to 101.6 µm. The sensitive area of the sensors starts at 8 mm from the beam axis, such that the first measurement of the track is as close to the primary vertex as possible: the shorter the extrapolation of a track from its first measurement to the interaction region, the smaller is the error on the reconstructed position of the vertex [52,69]. A modelled view of the VELO, and a real picture of one of the modules, are shown in Figure 3.7. Figure 3.7: LHCb VErtex LOcator. Left: modelled view of the VELO. Right: a VELO module [52]. 3.2.1.2 Silicon Tracker The Silicon Tracker is composed by two detectors: the Tracker Turicensis [70] and the Inner Tracker [71]. Both use silicon microstrip sensors with a strip pitch size (or distance between the centre-of-mass of neighboring strips) of about 200 µm. Housed in separated light tight, thermally and electrically insulated detector volumes, both detectors are mantained at a temperature below 5 oC, being these volumes continuously flushed with nitrogen to avoid condensation on cold surfaces. Design choices for the ST were mainly driven by considerations of spatial resolution, hit occupancy, signal shaping time, single hit-efficiency and radiation damage, among others. An important contribution5 5Grupo de F´ısica de Altas Enerx´ıas (GAES): LHCb Silicon Tracker Construction (a) 23 from the University of Santiago de Compostela to the construction of the ST has to be remarked. The four detection layers of the TT are located upstream of the LHCb magnet dipole (see Figure 3.5) covering the full acceptance of the experiment. The TT has a width of 150 cm and a height of 130 cm, with a total active area of 8.4 m2. The IT, composed by four detector boxes arranged around the beam pipe and located downstream of the magnet, is 120 cm wide and 40 cm high. It has an active area of 4.0 m2[52]. Figure 3.8 shows the layouts of a TT layer and a IT module, as described before. 132.4 cm 7.74 cm 138.6 cm 7.4 cm Figure 3.8: LHCb Silicon Tracker. Left: schematic layout of one of the TT layers. Right: view (top) and schematic (bottom) layout of an IT module [52,70,71]. 3.2.1.3 Outer Tracker The Outer Tracker [72] is a drift-time detector, designed for the tracking of charged particles and the measurement of their momentum over a large acceptance area. An excellent momentum resolution is required for a precise determination of the invariant mass of reconstructed b-hadrons. High tracking efficiency (95%) and a low fraction of wrongly reconstructed tracks (≤15%) is demanded by the reconstruction of high multiplicity B decays. This detector is designed as an array of individual, gas (70% Argon, 20% CO2) strawtube modules (see Figure 3.9), arranged in three stations (as the external part of T1, T2 and T3 in Figure 3.5) of four layers each one. Rigidity, electrical shielding and radiation hardness were main requirements during its design [52]. 24 Figure 3.9: LHCb Outer Tracker. Left: cross section of a straw-tubes module. Right: overview of a straw-tubes module design [52,72]. 3.2.2 Particle identification system The particle identification systems consists of three well-separated parts: the RICH detectors, the calorimeter system, and the muon system. 3.2.2.1 Ring Imaging CHerenkov detectors It is essential for the goals of the experiment to separate pions from kaons in selected B hadron decays (see Chapter 4.2). This task is performed by the RICH detectors: this system consists of two RICH (RICH1 and RICH2) detectors to cover the full momentum range. The upstream RICH1 covers the full LHCb angular acceptance, from ±25 mrad to ±300 mrad (horizontal) and ±250 mrad (vertical), and the low momentum charged particle range, from ∼1 to 60 GeV/c, using aerogel and C4F10 radiators. The downstream RICH2 covers a limited angular acceptance, from ±25 mrad to ±120 mrad (horizontal) and ±100 mrad (vertical), and the high momentum charged particle range, from ∼15 GeV/c up to and beyond 100 GeV/c, using a CF4radiator. Both RICH detectors [73] (see Figure 3.10) are composed by a combination of spherical and flat mirrors which reflect and focus Cherenkov light out of the spectrometer acceptance, and Hybrid Photon Detectors (HPDs) to detect Cherenkov photons in the wavelength range from 200 to 600 nm, surrounded by external iron shields. 3.2.2.2 Calorimeter system The calorimeter system [74] provides the identification of electrons, photons and hadrons as well as the measurement of their energies and positions. This system is essential for the study of Bmeson decays. It selects the transverse energy of hadron, electron and photon candidates for the first trigger level (L0), too (see Chapter 3.2.3). This system is composed by a Scintillator Pad Detector (SPD) and a PreShower (PS) detector, followed by an Electromagnetic CALorimeter (ECAL) and a Hadron CALorimeter (HCAL). The 25 2. Data selected by the trigger, pure electronic signals recorded by the different subdetectors, are transformed by different mathematical algorithms in an ensemble of tracks and vertices. Tracks correspond to the charged particles trajectories produced in the collisions (or from decays of other particles) and which go through the detector, while vertices correspond to the point where the collisions (Primary Vertices, PVs) or the decay of a particle in two or more daughter tracks (Secondary Vertices, SVs) took place. In practice, vertices are built from the crossing point of two or more tracks. The reconstruction of tracks and vertices is mainly done by the tracking and vertexing system (see Chapter 3.2.1). The information from the particle identification system (see Chapter 3.2.2) is then added to identify the nature of the tracks, distinguishing, for instance, muons from other particles. This whole process is called reconstruction. Figure 3.14 displays a LHCb B0 s→J/ψφ reconstructed event using the Panoramix12 application. 3. Once all the triggered events have been reconstructed, it becomes mandatory to separate them according to their physics content. This is done by selecting the different decays using their particular features. For instance, B0 s→µ+µ−or A0 1→µ+µ−decays, with the same final state, have different mass and decay time of the parent particle. With these selections, the splitting of the data is performed, with a procedure called “stripping” in the framework of LHCb.13 Thus, each one of these selections is embedded in a “stripping line”. These selections, performed with the data already on tape, are called “offline”. 4. The triggered, reconstructed and stripped dataset has to be then distributed to a series of computing centers spread worldwide. A copy of the raw data from detectors is also saved, with the idea of allowing a later re-reconstruction and stripping once the relevant algorithms have been improved. The process of distributing the data has a double intention. On the one hand, it ensures that the data cannot be lost, regardless any possible technical problem appearing. On the other hand, it allows physicists an easy access to a distributed computing system of huge power. This distributed system is called Grid [87], used via the DIRAC framework [88]. Details about the performance of tracking and vertexing, particle identification and trigger systems are given in Chapter 3.2.6.1, Chapter 3.2.6.2 and Chapter 3.2.6.3, respectively. 3.2.6.1 Tracking and vertexing As already stated, one of the key points for the reconstruction of events at LHCb is the determination of the trajectories of all charged particles (tracks) and the position where they were generated (vertices) both if this was a collision (PVs) or the decay point of some other particle (SVs). During the event reconstruction stage, the following types of tracks, as shown in Figure 3.15, are considered [89]: 12The Panoramix project (a). 13The Stripping project (a). 32 Figure 3.14: Event reconstruction of a LHCb simulated B0 s→J/ψφ event. •Long tracks: tracks traversing the full tracking system. They have hits in both the VELO and the T-stations of the OT, and optionally in the TT. As they traverse the full magnetic field they have the most precise momentum estimate and therefore are the most important set of tracks for physics analyses. •Upstream track: tracks passing only through the VELO and TT stations. In general their momentum is too low to traverse the magnet and reach the T-stations. However, they pass through the RICH1 detector and may generate Cherenkov photons if they have p > 1 GeV/c2. They are therefore also used to understand backgrounds in the particle identification algorithm of the RICH. •Downstream tracks: tracks passing only through the TT and T-stations. They are important for the reconstruction of long lived particles, such as K0 sand Λ, that decay outside the VELO acceptance. •VELO tracks: tracks passing only through the VELO and are typically large-angle or backward tracks, which are useful for the primary vertex reconstruction. •T tracks: tracks passing only through the T-stations. They are typically produced 33 in secondary interactions, but are still useful during the treatment of RICH2 data for particle identification. Figure 3.15: Various types of tracks considered for the event reconstruction [52]. The capability of assigning a track to the right vertex and of distinguishing secondary vertices is given by the resolution on the Impact Parameter (IP), or the distance of closest approach of a track to a vertex. The VELO detector provides very good IP resolution (see Figure 3.16) thanks to thin silicon strips placed as close as 8 mm from the beam axis. The LHCb tracking system gave very good performances as well: a relative momentum resolution below 0.5% at low momenta and 0.9% at 100 GeV/c2, and as a consequence, a very good di-muon relative mass resolution of about 5 per mille all the way up to the masses of the Υ resonances (see Figure 3.17). Thus, the best performances in terms of momentum resolution for long tracks are achieved. 3.2.6.2 Particle identification The particle identification is the last step of the LHCb event reconstruction. Once all the tracks have been built, the information from the particle identification system (RICH, calorimeter and muon systems) is added in order to establish hypotheses about the nature of the particles (pion, kaon, proton, muon or electron). Similarly, the energy deposited at the calorimeters may be related to photons, even if these particles cannot be associated to tracks since they are neutral (see Figure 3.18). As previously stated in Chapter 3.2.5, differences in particle identification efficiencies between simulated and real data samples may appear and therefore need to be corrected for: a software package developed by the LHCb global PID team, PIDCalib [91], is used by LHCb physicists for this task. The LHCb PID information from the different subdetectors is linearly combined in a common likelihood to maximise the efficiency and minimise the mis-identification rate, 34 Figure 3.16: Performance of the LHCb VELO detector. Left: PV resolution as a function of the number of tracks composing the vertex. The x(red) and y(blue) resolutions are separately shown while the overlayed histogram (grey) shows the distribution of number of tracks per reconstructed primary vertex for events passing the high level trigger. Right: impact parameter in xresolution as a function of 1/pT. Both plots are made using LHCb data collected in 2012 [89,90]. Figure 3.17: Left: relative momentum resolution versus momentum for long tracks from J/ψ →µ+µ−events. Right: mass distribution for the Υ resonances, showing the excellent relative mass resolution of LHCb of about 5 per mille [89]. ∆LLxy, being this variable the likelihood of the considered particle to be x, with respect to the hypothesis of being yinstead (this “normalisation” hypothesis yis chosen by default to be the pion hypothesis). However, another approach which takes into account correlations between subdetectors and additional information is replacing (or used with) the previous likelihood: the output of a MultiLayer Perceptron Neural Network (MLPNN) named ProbNNx, which is simply the probability of the studied particle to be x. However, the identification of each particle is typically dominated by one of the subdetectors. The PID 35 Figure 3.18: Energy deposition on the different elements of the calorimeter system, depending on the nature of the considered particle, where h refers to hadrons. algorithms for RICH, calorimeter and muon systems, together with their performances, are presented next. The RICH PID is based on the difference in the expected Cherenkov angle [92] (angle of the radiated photons) between protons, kaons and pions. The low mass difference between pions and muons makes the Cherenkov angle very similar in both of these particles, so RICH PID is not efficient separating them (see Figure 3.19). Using the RICH information, PID variables can be built for tracks in order to establish the probabilities of different particle hypotheses [52]. Figure 3.20 shows the kaon efficiency (kaons identified as kaons) and pion mis-identification (pions mis-identified as kaons) fraction on 2012 data, as a function of momentum and for one of the LHCb dipole magnet polarities. Proton efficiency and pion mis-identification fraction as a function of momentum for the complementary LHCb magnet polarity and for 2012 data are also shown. The calorimeter system (or simply CALO) PID uses the energy deposited in the different regions (see Figure 3.18) of the LHCb calorimeter to identify the particles having gone through its different parts. As muons are Minimum Ionizing Particles (MIPs), they are capable of going through the detector losing a characteristic energy on it which can also help on their identification. Similarly to the RICH case, but using the energy deposited in the different calorimeter elements, these algorithms use the information to obtain PID variables for the different particle hypotheses. Efficiency and mis-identification rate for electrons in 2011 data as a function of track momentum are shown in Figure 3.21. Muon identification uses the fact that muons are the only particles (except for punchthrough hadrons, which are rather unlikely) able to go through the calorimeter and hit the muon system stations. For any reconstructed track, a field of interest at the muon stations is built and muon hits are searched for. The identity and location of these hits allows the calculation of a muon PID variable that is later used to discriminate between muons and other particles [94]. Figure 3.22 shows the muon PID efficiency 36 Figure 3.19: Reconstructed Cherenkov angle as a function of track momentum in the C4F10 radiator [93]. Figure 3.20: LHCb RICH system performance. Left: kaon efficiency and pion misidentification fraction on 2012 data, as a function of track momentum and for LHCb magnet down polarity. Right: proton efficiency and pion mis-identification fraction on 2012 data, as a function of track momentum and for LHCb magnet up polarity. and mis-identification probabilities for protons, pions and kaons as a function of the particle momentum [52]. A di-muon invariant mass reconstruction after imposing trigger requirements, showing the excellent performance of LHCb muon and trigger systems, is presented in next Chapter 3.2.6.3. 37 Figure 3.21: LHCb CALO electron identification performances on 2011 data. Left: electron efficiency as a function of the track momentum. Right: electron mis-identification rate as a function of track momentum [89]. Figure 3.22: Muon efficiency (a) and misidentification probabilities for protons (b), pions (c) and kaons (d) as a function of particle momentum [94]. 38 3.2.6.3 Trigger performance For the analyses described in this thesis, of B0 s→J/ψK∗0(see Chapter 4) and A0 1→µ+µ− (see Chapter 6) decay modes, the most relevant LHCb trigger lines are those related to the reconstruction of single muons and di-muon resonances. A reconstruction of the di-muon invariant mass of LHCb data taken during Run I is presented in Figure 3.23, showing the excellent performance of the LHCb combined muon and trigger systems in the context of muon searches. In the LHCb trigger context, an event is classified as TOS (Trigger On Signal) if the trigger objects that are associated with the signal are sufficient to trigger the event. TOS efficiencies for L0, HLT1 and HLT2 muon trigger lines are presented in Figure 3.24. The integrated efficiency for both L0 single muon and di-muon triggers combined is evaluated to be 89%, while for HLT1, single muon and di-muon trigger efficiencies are 90% and 69%, respectively. The total output rate of all single muon and di-muon trigger lines is about 1 kHz [77,95]. Trigger efficiencies obtained for the analysis of B0 s→J/ψK∗0decays are calculated in Appendix D.2. ] 2 Dimuon mass [GeV/c 0.2 12 3 4 5 10 20 100 200 2 Dimuons per GeV/c 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 Single muon Charmonium Bottomonium Other triggers LHCb Preliminary 2011+12 data ω/ρφ ψJ/ (2S)ψ (nS)Υ Z ] 2 Dimuon mass [GeV/c 9 9.5 10 10.5 11 2 Dimuons per GeV/c 10 20 30 40 6 10× (1S)Υ (2S)Υ(3S)Υ Figure 3.23: Di-muon mass distribution divided by trigger groups of LHCb Run I data. An inset plot with a zoom on the bottomonium region is shown on the top right corner [96]. 39 [GeV/c] T p 0 5 10 15 20 / 100% TOS ∈ 0 0.2 0.4 0.6 0.8 1 L0Muon L0DiMuon L0Muon OR L0DiMuon LHCb preliminary [GeV/c] T p 0 5 10 15 20 / 100% TOS ∈ 0 0.2 0.4 0.6 0.8 1 1.2 Hlt1TrackMuon Hlt1DiMuonHighMass Hlt1DiMuonLowMass LHCb preliminary [GeV/c] T p 0 5 10 15 20 / 100% TOS ∈ 0 0.2 0.4 0.6 0.8 1 1.2 Hlt2DiMuonJPsiHighPT Hlt2DiMuonJPsi Hlt2DiMuonDetachedJPsi LHCb preliminary Figure 3.24: TOS efficiencies of L0 (top), HLT1 (middle) and HLT2 (bottom) muon trigger lines, calculated using B+→J/ψK+candidates, and as a function of the B+ pT[77]. 40 3.2.7 Run I experimental conditions The evolution of the LHCb operating conditions during LHC Run I is shown in Figure 3.25. Starting with luminosities of approximately 1028cm−2s−1and almost no pile-up, the luminosity reached 1032cm−2s−1[89], leading to world-best measurements published by the LHCb collaboration [97]. Figure 3.25: Average number of visible interactions per bunch crossing, “pile-up” (top) and instantaneous luminosity (bottom) at the LHCb interaction point during the Run I period. The dotted lines show the design values [89]. Despite the fact that the data taken during that year is not used for the analyses described in this thesis, it is worth to mention that LHCb recorded 38 pb−1of data during 2010, under a constantly changing set of run conditions, being this small dataset the very first part of the data taken during the Run I period. During 2011, with a target luminosity of L= 3.5 ×1032 cm−2s−1and a measured b¯ bcross section of σ(pp →b¯ bX) = (284 ±20 ±49) µb at √s= 7 TeV [98], a total amount of the order of 1012 b¯ bpairs was produced in 107s, approximately corresponding to the canonical one year of data taking. That year, a luminosity levelling procedure was introduced at the LHCb interaction point. By adjusting the transverse overlap of the beams at LHCb, the instantaneous luminosity could be kept stable to within about 5% during a fill, as illustrated in Figure 3.26. In 2012, the LHC beam energy was increased to 4 TeV. LHCb took data at a luminosity of 4 ×1032 cm−2s−1, twice the LHCb design luminosity. The LHC delivered stable beams for about 30% of the operational year. An effort was made in 2012 to use more efficiently the processing power available in the Event Filter Farm (EFF, see Chapter 3.2.4), which otherwise would have been idle during 70% of the time. The mechanism put in operation defers a fraction of the HLT processing to the inter-fill time, typically several hours, between the LHC collision periods. In this approach about 20% of the L0 accepted events during data-taking are temporarily saved on the local disks of the EFF nodes and 41 ii 1 Introduction As part of the upgrade of the LHCb experiment, scheduled for the second long shutdown of the LHC in 2018/19, the present microstrip-based Vertex Locator (VELO) is foreseen to be replaced by a silicon hybrid pixel detector [1] with an ASIC dubbed “VeloPix” which will be derived from the Medipix family of ASICs. Like its predecessors Medipix2, Timepix, Medipix3, and Timepix3, the VeloPix chip will feature a matrix of 256 × 256 square pixels with a pitch of 55 µ m. Prior to the arrival of the Timepix3 ASIC, Timepix and Medipix3 were the most suitable devices for the qualification of prototype sensors for the VELO upgrade. Until the end of lifetime of the upgraded experiment, the pixels closest to the beam line ( r = 5 . 1 mm) accumulate a fluence of up to 8 × 10 15 1 MeV n eq cm −2 . Qualifying silicon sensors in terms of radiation hardness is therefore a key element of the VELO upgrade R&D programme. Timepix silicon detectors have been characterised extensively in terms of chargedparticle tracking performance [2]. Since the ASIC has per-pixel information on the collected charge in terms of a time-over-threshold (ToT) value, a direct measurement of the charge deposition spectrum is possible. Medipix3 [3,4] on the other hand is a pure counting chip which was designed primarily for photon imaging applications. In order to measure the deposited charge in the sensor one therefore has to resort to indirect methods (Section 3). Among the large-scale ASICs in the high-energy physics community, Medipix3 has been the first to be based on IBM 130 nm CMOS technology. Compared to the Timepix (which was fabricated in 250 nm technology), it is expected to be more radiation tolerant [5] and thus lends itself for testing irradiated sensors. In this work, we report on measurements with irradiated and non-irradiated Medipix3 assemblies carried out in 2012 at the H8 beamline of the CERN North Area facility, using positively charged hadrons with a momentum of 180 GeV/ c . These measurements are intended to provide a validation of the chip functionality and performance complementary to characterisation measurements using photon sources. In addition, they also represent a first step towards a comprehensive evaluation of the radiation hardness of silicon pixel sensors with the “Medipix footprint” of 55 ×55 µm2pixels. 2 Setup The Timepix telescope, described in Ref. [6], was used for reconstructing the tracks of particles crossing the Medipix3 device under test (DUT). In order to minimise the pointing error, the DUT was placed in the centre of the telescope. For reading out the Medipix3 chip, the “Merlin” data acquisition system [7] developed at the Diamond Light Source facility was used. The synchronisation of Timepix and Medipix3 is straightforward, as both ASICs work in a “camera-style” frame-based readout mode. An external circuit implemented using NIM modules was used for sending shutter opening and closing signals to the telescope and the device under test. The coincident firing of two scintillators located upstream and downstream of the telescope was used for counting the number of beam 1 Figure 1: DUT mount and cooling setup. A Peltier cooler (not visible in the photograph) is clamped between the cooling block and the TPG sheet onto which the chip is glued. particles traversing the telescope and the duration of a shutter was adjusted such that 50 scintillator triggers were accumulated in one frame. During one spill (9.6 s) typically about 500 frames were recorded. The temperature of the irradiated samples was controlled using a combination of thermoelectric and CO 2 cooling, the latter being provided by a portable cooling plant [8]. As can be seen on the photograph in figure 1, the chip was glued onto a tape of Thermal Pyrolytic Graphite (TPG) the other end of which was attached to the cold side of a Peltier cooler. The hot side of the Peltier cooler was put in contact with an aluminium cooling block through which CO 2 was circulating. With the chip switched off, a temperature of approximately − 20 ◦ C was reached, rising to − 15 ◦ C with the chip in operation. The setup was placed in a light-tight aluminium case which was flushed with nitrogen. The non-irradiated assemblies were measured at room temperature. In all measurements discussed below, the DUTs were n -onp silicon sensors bumpbonded to Medipix3.1 ASICs. The ASICs were operated in single-pixel high-gain mode and only one threshold (DAC THL) was used. Before taking data, a threshold equalisation was performed using the front-end noise as reference. The equalisation procedure consists of optimising the DAC values of two global current sources (ThresholdN and DACpixel) and the threshold adjustment bits of each pixel, such that the THL value corresponding to the noise floor lies within a certain window for all pixels. For the non-irradiated assemblies a target window of 5 <THL <25 was used. Prior to the beam test, calibration measurements using testpulses were performed to determine the relation between THL DAC and injected charge. To verify the viability of the testpulse method, data were taken with a 241 Am source for the two non-irradiated assemblies discussed below, and – after applying the calibrations obtained from the testpulse scan – the signal peaks were found to match within 2% between the two assemblies. These measurements were however made with a different readout system [9] and equalisation 2 mask than used in the testbeam (at that time the testpulse functionality was not yet implemented in Merlin). Where possible 1 , calibration measurements using test pulses were later (after the beam test) made also using the Merlin system. These calibration curves are used in the following for a relative comparison of the signals measured with different sensors. 3 Measurements For each track reconstructed in the telescope, the intercept with the DUT plane is calculated. In order to suppress fake tracks a requirement on the track quality is applied and the tracks are required to include hits on all telescope planes. If an unused cluster with a centre of gravity within a radius rw = 110 µ m around the track intercept is found, it is associated to the track and tagged as used. In case of multiple candidate clusters, the closest one is selected. The hit efficiency (or cluster finding efficiency) ε is then given by the fraction of tracks with an associated cluster on the DUT. The pointing resolution of the telescope ( ∼ 1 . 5 µ m in the present configuration) allows one to probe the hit efficiency as function of the track intercept within a pixel cell. In the analysis we divide the pixel cell in 9 ×9 bins and calculate separate efficiencies for each bin. The most probable value (MPV) of the deposited charge can be estimated by scanning the hit efficiency as function of threshold. Assuming that the distribution of the collected charge can be described by a Landau distribution fL convoluted with a Gaussian distribution fG, the hit efficiency as a function of the threshold Qis given by ε(Q) = ∞ Z Q dxfL⊗fG(x).(1) By fitting the measured efficiency with Eq. (1) , the MPV and width of the Landau distribution and the σ of the Gaussian can be determined (the mean of the Gaussian is fixed to zero). This method requires that the entire charge deposited by a track is collected by a single pixel. We therefore use the hit efficiency in the central bin of the 9 × 9 matrix for this measurement. To determine the spatial resolution, the distributions of the residuals between the x, y coordinates of the track intercepts and the associated clusters are calculated. The standard deviation of the residual distribution is used as a resolution metric (the pointing error of the telescope represents only a small correction when subtracted in quadrature). 3 THL 50 100 150 200 Efficiency 0 0.2 0.4 0.6 0.8 1 MPV 0.4± 111.2 L σ 0.3± 10.3 G σ 0.8± 12.5 MPV 0.4± 111.2 L σ 0.3± 10.3 G σ 0.8± 12.5 THL 0 100 200 300 Probability [a. u.] 0 0.005 0.01 0.015 THL 50 100 150 200 Efficiency 0 0.2 0.4 0.6 0.8 1 MPV 0.3± 71.6 L σ 0.1± 4.4 G σ 0.3± 11.6 MPV 0.3± 71.6 L σ 0.1± 4.4 G σ 0.3± 11.6 THL 0 50 100 150 200 Probability [a. u.] 0 0.005 0.01 0.015 0.02 Figure 2: Hit efficiency (for tracks crossing the centre of a pixel cell) in non-irradiated Medipix3 assemblies with 100 µ m thick n -onp sensors as function of threshold, for (left) assembly W20 B6 and (right) assembly W20 J9. The insets show the distribution of the charge deposition in units of THL. The error bars represent the statistical uncertainty of the measurements. For several points the error bars are smaller than the symbols. 4 Results 4.1 Non-irradiated assemblies The measurements before irradiation were carried out using n -onp active-edge sensors with a nominal thickness of 100 µ m manufactured by VTT 2 . The MPV of the charge deposition spectrum is thus expected to be around 7000 −7500 electrons. Two assemblies, W20 B6 and W20 J9, were tested with beam. After the beam test, part of the backside metallisation was removed from the sensor on W20 B6, and by injecting laser pulses the depletion voltage Vdep was determined to be approximately − 15 V. In the beam test, both sensors were operated at a bias voltage of − 60 V, and were oriented perpendicularly to the beam. For each point in the threshold scan, a data set comprising typically 1 −2×105reconstructed telescope tracks was recorded. From the hit efficiency in the centre of the pixel cell as function of threshold (figure 2), the most probable value of the charge deposition spectrum is determined to correspond to THL ∼ 111 . 2 for assembly W20 B6 and THL ∼ 71 . 6 for assembly W20 J9. The statistical errors of the fit values are given in figure 2. Uncertainties due to tracking cuts, alignment, non-linearity of the THL DAC give rise to a systematic error on the MPV of ∼ ± 2 . 5%. The MPVs in terms of THL DAC values differ significantly between the two devices. This 1One of the assemblies (W20 B6) was accidentally damaged after the beam test. 2VTT Technical Research Centre of Finland, Espoo, Finland 4 m]µ [x 0 20 40 m]µ [y 0 10 20 30 40 50 0.97 1 1 1 1 1 1 1 0.98 0.99 1 1 1 1 1 1 1 0.99 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0.99 1 1 1 1 1 1 1 0.99 1 1 1 1 1 0.97 1 0.99 0.99 0.99 1 1 1 0.97 m]µ [x 0 20 40 m]µ [y 0 10 20 30 40 50 0.91 0.97 0.98 0.97 0.98 0.97 0.97 0.97 0.89 0.96 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.95 0.97 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.95 0.96 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.96 0.97 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.95 0.97 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.95 0.97 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.95 0.96 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.94 0.86 0.95 0.96 0.96 0.96 0.96 0.96 0.94 0.83 Figure 3: Hit efficiency in non-irradiated Medipix3 assemblies with 100 µ m thick sensors as function of the track intercept within a pixel cell, for (left) assembly W20 B6 at THL/MPV ∼ 0 . 45 and (right) assembly W20 J9 at THL/MPV∼0.56. can be attributed to non-optimised settings of the DAC “Vcas” (for voltage cascode), which sets the reference voltage for some transistors in the pixel circuit and, if not tuned properly, can have an impact on the operating point of the circuit. As discussed in section 2, testpulse calibration measurements using the Merlin readout system could only be made for assembly W20 J9. To facilitate the comparison between the devices, the results discussed below are therefore presented as function of the threshold-tosignal ratio, i. e. the applied THL DAC normalised to the respective MPV. Figure 3 (left) shows the hit efficiency as function of the track intercept within a pixel cell for the lowest threshold-to-signal ratio (THL/MPV ∼ 0 . 45) covered by the threshold scan. At this threshold – which is high compared to a typical operational threshold of 1000 electrons – the detector can be seen to be fully efficient ( ε > 0 . 99), except at the corners. With increasing threshold – as illustrated in figure 3 (right) – a drop in efficiency becomes noticeable at the borders of the pixel cell. This is a consequence of charge sharing due to diffusion, as can be seen from figure 4 which shows the average cluster size as function of the track intercept within the pixel cell. Figure 5 (left) shows the average cluster size as function THL/MPV. At the lowest threshold, an average cluster size of 1 . 103 ± 0 . 001 is found, with single-pixel clusters constituting ∼ 91 . 3% and two-pixel clusters ∼ 7 . 7% of all associated clusters. The cluster size as function of threshold/signal follows the same shape for both sensors, exhibiting a minimum around THL/MPV ∼ 0 . 9 and a subsequent maximum around THL/MPV ∼ 1 . 6. With increasing threshold, an increasing fraction of the observed clusters is produced by primary particles which suffer collisions with large energy loss. These collisions give rise to energetic electrons which further ionise along their path and produce electron-hole pairs 5 m]µ [x 0 20 40 m]µ [y 0 10 20 30 40 50 1.3 1.2 1.17 1.18 1.17 1.19 1.19 1.18 1.29 1.23 1.04 1.06 1.05 1.05 1.06 1.05 1.05 1.21 1.21 1.05 1.04 1.05 1.05 1.06 1.05 1.04 1.17 1.18 1.05 1.05 1.05 1.04 1.04 1.04 1.06 1.18 1.18 1.05 1.05 1.05 1.04 1.05 1.04 1.06 1.16 1.19 1.05 1.03 1.06 1.04 1.04 1.04 1.06 1.16 1.2 1.05 1.04 1.07 1.04 1.04 1.04 1.05 1.17 1.21 1.07 1.05 1.06 1.06 1.05 1.04 1.07 1.22 1.28 1.22 1.19 1.19 1.19 1.19 1.2 1.23 1.29 Figure 4: Average cluster size as function of the track intercept within a pixel cell for assembly W20 B6 (100 µ m thick sensor) at THL/MPV ∼ 0 . 45. Multi-pixel clusters are found predominantly at the edges and corners of the pixel cell. away from the trajectory of the primary particle. The residual distributions (in the x direction) at low threshold for one-pixel and two-pixel clusters are shown in figure 6. Averaged over all cluster sizes, the standard deviation of the residual distribution is found to be ∼ 15 . 7 µ m in both x and y . As expected from the dominance of one-pixel clusters, this value is close to the binary limit (55 µ m /√12 ∼ 15 . 9 µ m). Figure 5 (right) shows the σ of the residual distribution in x as function of threshold/signal. The resolution can be seen to deteriorate significantly after the threshold crosses the MPV. Figure 5 also includes results obtained with a Timepix ASIC bump-bonded to a 100 µ m thick n -onp sensor from the same batch. The Timepix assembly was measured in the same beam test campaign and was operated at a threshold of 1000 electrons and a bias voltage of − 60 V. The data were taken in ToT mode, but the values shown in figure 5 were calculated with the ToT values set to one to mimic the Medipix3 behaviour. The results for the Timepix assembly are in agreement with the extrapolated results from the Medipix3 assemblies. To understand better the observed shapes of resolution and cluster size as function of threshold, a simple simulation using the Garfield++ toolkit [10] was used. The primary ionisation process is calculated using the Heed program [11], which in addition to the energy loss by the traversing charged particle also simulates the ionisation cascade from high-energy (“delta”) electrons produced in the interactions of the charged particle with the silicon medium as well as the spatial distribution of the resulting electron-hole pairs. Each electron is subsequently transported through the sensor, based on the drift velocity and diffusion coefficient as function of the electric field. A one-dimensional approximation 6 THL / MPV 0 0.5 1 1.5 2 2.5 Average cluster size 1 1.05 1.1 1.15 1.2 1.25 THL / MPV 0 0.5 1 1.5 2 2.5 m]µ [ x σ 0 5 10 15 20 25 Figure 5: Average cluster size (left) and standard deviation of the x -residual distribution (right) at perpendicular track incidence as function of threshold-to-signal ratio for assemblies W20 B6 (empty circles) and W20 J9 (full circles). Results for a Timepix assembly with the same type of sensor are shown with full squares. The error bars represent the statistical uncertainty of the measurements. For most points the error bars are smaller than the symbols. for the electric field is used3. As can be seen from figure 7, the features in the measured cluster size and resolution as function of threshold-to-signal ratio are reproduced by the simulation, provided that the spatial extent of the ionisation pattern is taken into account. This corroborates the conclusion that these features are due to “delta” electrons. 4.2 Irradiated assemblies A set of Medipix3.1 assemblies, with VTT n -onp active-edge sensors from the same batch as the non-irradiated sensors discussed above, were irradiated at the Ljubljana TRIGA reactor [12] to a 1 MeV neutron equivalent fluence of 5 × 10 14 cm −2 and subsequently annealed for 80 minutes at 60 ◦ C. From lab measurements with a laser, the effective depletion voltage Vdep of these sensors after irradiation was measured to be between − 85 and − 105 V. One of the assemblies, W20 H5, was characterised in the beam test. The sensor, which has a pixel-to-edge distance of 100 µ m, was operated at a bias voltage of − 100 V as operation at higher bias was inhibited by the onset of electrical breakdown (figure 8). In general, the irradiated assemblies exhibited a higher dark count rate compared to the non-irradiated ones, which was attributed to electrons from the β -decay of 182 Ta 3 The electric field is assumed to vary linearly between E = (V−Vdep)/d at the sensor backside and E= (V+Vdep)/d at the implants, where dis the sensor thickness. 7 m]µ [ track x - cluster x -40 -20 0 20 40 mµEntries / 2 0 2000 4000 m]µ [ track x - cluster x 40−20−0 20 40 mµEntries / 2 0 500 1000 Figure 6: Residual distribution for (left) one-pixel and (right) two-pixel clusters extending over two columns in a non-irradiated 100 µ m thick sensor (assembly W20 B6, at THL/MPV ∼ 0.45). THL / MPV 0 0.5 1 1.5 2 2.5 Average cluster size 1 1.05 1.1 1.15 1.2 1.25 THL / MPV 0 0.5 1 1.5 2 2.5 m]µ [ x σ 0 5 10 15 20 25 Figure 7: Simulated average cluster size (left) and standard deviation of the x -residual distribution (right) at perpendicular track incidence as function of threshold-to-signal ratio. Full (empty) symbols show the results with (without) the spatial extent of the ionisation pattern being included in the simulation. produced by neutron activation during the irradiation of the ASIC 4 . This – presumably in combination with other radiation effects – resulted in problems during the equalisation 4 The presence of 182 Ta in the irradiated assemblies was confirmed by gamma spectroscopy measurements performed by the CERN radioprotection group. 8 Reverse bias [V] 0 50 100 A]µCurrent [ 1 10 2 10 Figure 8: Leakage current as function of reverse bias voltage at T = − 13 ◦ C after irradiation to 0 . 5 × 10 15 1 MeV n eq cm −2 (100 µ m thick n -onp active-edge sensor with 100 µ m pixel-to-edge distance). procedure for some assemblies, as well as a larger threshold dispersion. The optimised values of the DACs which control the global currents (ThresholdN and DACpixel) were larger (by a factor 2 – 3) compared to the non-irradiated assemblies. As can be seen from figure 9, the MPV of the charge deposition spectrum corresponds to a THL DAC of ∼ 53 . 9. After correcting for the differences in gain and offset using testpulse calibration curves, this value is found to be approximately 8.5% lower than the MPV of the non-irradiated sensors. As in the non-irradiated case, the cluster size spectrum is dominated by single-pixel clusters. Cluster size and σ of the x -residual distribution as function of threshold-to-signal ratio (figure 10) follow closely the corresponding curves for the non-irradiated assemblies (figure 5). Figure 11 shows the hit efficiency as function of the track intercept within a pixel cell at the lowest measured threshold ( THL = 40). In the centre of the pixel cell, an efficiency of 0 . 93 ± 0 . 01 is found, compared to 0 . 97 ± 0 . 01 for the non-irradiated assemblies at the same threshold-to-signal ratio (∼0.74). A further beam test measurement was performed with a Medipix3.1 ASIC bumpbonded to a 200 µ m thick n -onp sensor manufactured by CNM 5 . The sensor featured two guard rings and was diced at a distance of 400 µ m from the border of the pixel matrix. The assembly (W20 D6) was also irradiated at Ljubljana, but to a higher fluence, 2 . 5 × 10 15 1 MeV n eq cm −2 . During the equalisation procedure, a large threshold dispersion was observed, such that the upper limit of the equalisation target window needed to be increased to THL = 40. In addition, a significant fraction ( ∼ 10%) of the pixels needed 5Centro Nacional de Microelectr´onica, Barcelona, Spain 9 4.1 Event selection and data samples Real data (Chapter 4.1.1) and simulated data (Chapter 4.1.2) samples used for this analysis are presented in this section, among with the requirements from the offline selection (Chapter 4.1.3) as well. The offline selection consists of two parts: a “cut-based” set of requirements to reduce the size of the real data sample to a manageable level, followed by the use of Boosted Decision Trees with Gradient boosting (BDTG) [116] to reject as much combinatorial background as possible while keeping a high signal efficiency. The J/ψ meson is reconstructed from µ+µ−and the K∗0hadron from K−π+, as well as their charge conjugated decays. A very large B0→J/ψK∗0component is present in the data and taken into account, also used as a control channel (see Chapter 4.5.3). 4.1.1 Real data samples Real data events for this analysis are selected from two LHCb datasets with a total integrated luminosity of 3.0 fb−1of pp collision data: •Reco14-Stripping20r1: corresponding to 1 fb−1of integrated luminosity, collected during 2011 at a centre-of-mass energy of √s= 7 TeV, and analysed with DaVinci v32r2p3. •Reco14-Stripping20r0p1: corresponding to 2 fb−1of integrated luminosity, collected during 2012 at a centre-of-mass energy of √s= 8 TeV, and analysed with DaVinci v32r2p5. Both datasets have been reconstructed using Brunel v43r2p6, Condition DataBase (CondDB) and Detector Description DataBase (DDDB) tags cond-20130114 and dddb-20130111, respectively.1 4.1.2 Simulated samples Three sets of simulated samples are used in this analysis, containing B0 s→J/ψK∗0, B0→J/ψK∗0and B0 s→J/ψφ simulated decays each one. Four samples per set, containing approximately the same number of simulated events all of them, are considered: one pair is representative of the data taken during 2011 (Reco14a-Stripping20r1, flagging mode, TCK 0x40760037), whilst the other pair is representative of the data taken during 2012 (Reco14a-Stripping20, flagging mode, TCK 0x409f0045). The only difference between members of a same pair is the polarity of the LHCb dipole magnet considered during the simulation. In summary, four samples (one per year and magnet polarity) per considered decay mode (B0 s→J/ψK∗0,B0→J/ψK∗0and B0 s→J/ψφ) are used: 2 (polarity) ×2 (year) ×3 (decay mode). The total number of simulated events per mode are approximately 1 M, 2 M and 10 M, respectively. This information is summarized in 1LHCb database tags: CondDB (a) and DDDB (b). 64 Table 4.1: Simulated samples used in the analysis of B0 s→J/ψK∗0decays. Approximately half of the simulated events per each sample correspond to one of the two LHCb magnet polarities, while the other half corresponds to the opposite. Decay mode Simulated events Sim pass TCK (year) Stripping version B0 s→J/ψK∗0509 500 Sim08c 0x40760037 (2011) Stripping20r1 531 498 Sim08a 0x409f0045 (2012) Stripping20 B0→J/ψK∗01 016 249 Sim08b 0x40760037 (2011) Stripping20r1 1 019 996 Sim08a 0x409f0045 (2012) Stripping20 B0 s→J/ψφ 5 028 485 Sim08a 0x40760037 (2011) Stripping20r1 5 114 480 Sim08a 0x409f0045 (2012) Stripping20 Table 4.1. Information about the software packages used to simulate these samples can be found in Chapter 3.2.5, where Table 3.2 summarizes their corresponding versions. 4.1.3 “Cut-based” requirements The “cut-based” set of requirements consists of two subsets: a first subset of cuts, applied once by the LHCb computing team to the triggered LHCb data immediately before the data sample is re-constructed, called “stripping line” (see Chapter 3.2.5); followed by a second subset of offline cuts tuned for the present analysis. The stripping line used for this analysis is named StrippingBetaSBs2JpsiKstarWideLine. The analysis is not restricted to any particular trigger line, i.e. an event should just pass at least one of the LHCb trigger lines. Table 4.2 lists the final “cut-based” selection criteria (already taking into account both subsets of cuts). For J/ψ →µµ candidates, a mass window of 150 MeV/c2around the reconstructed J/ψ peak is imposed, along with good vertex and DOCA (or minimum distance between the two daughter muon tracks) reconstruction criteria (χ2 vtx/ndof <16, χ2 DOCA/ndof <20). For daughter muon tracks, a threshold cut in the pTof 0.5 GeV/c, good muon identification by the muon system and a cut in the χ2of the reconstructed impact parameter (∆LLµπ > 0, χ2 IP >16), are imposed. For K∗0→K−π+candidates, a mass window in the K−π+invariant mass of 70 MeV/c2around the measured K∗0mass, along with good vertex and DOCA reconstruction criteria (χ2 vtx/ndof <25, χ2 DOCA/ndof <30), are required. For daughter hadron (h) candidates, threshold cuts in the pTof 0.5 GeV/c and in the χ2of the reconstructed impact parameter are required as well. A requirement of the hadron candidates to not be a ghost (fake) track is also imposed (Probghost(track) <0.8). Good pion (∆LLKπ < 0, ProbNNK <0.01) and kaon (∆LLKπ > 0, ProbNNK >0.21) identification by the RICH system, are also part of the requirements. Finally, for B0 s→J/ψK∗0candidates, a mass window in the four-body invariant mass, along with a good vertex reconstruction criterion and a threshold cut in the DIRA (angle between the direction of the momentum of the B0 scandidate and the direction defined by the difference between the secondary and the primary vertex) of the 65 B0 smeson (M∈[5150,5650] MeV/c2,χ2 vtx/ndof <10, DIRA >0.999) are required. A threshold cut in the VS variable (separation between a vertex w.r.t. its associated primary vertex) of 1.5 mm is imposed as well. A final veto cut of B+→J/ψK+three-body decays, as the removal of the mass window defined 60 MeV/c2around the B+measured mass in the J/ψK+spectrum is also required. Table 4.2: Selection criteria for B0 s→J/ψK∗0decays. Cut variable Cut value J/ψ →µµ |M(µ+µ−)−M(J/ψ)|<150 MeV/c2 χ2 vtx/ndof(J/ψ)<16 χ2 DOCA/ndof(J/ψ)<20 ∆LLµπ(µ)>0 χ2 IP(µ)>16 pT(µ)>0.5 GeV/c IsMuon(µ) true K∗0→K−π+|M(K−π+)−896|<70 MeV/c2 χ2 vtx/ndof(K∗0)<25 χ2 DOCA/ndof(K∗0)<30 pT(h)>0.5 GeV/c Probghost(track)(h)<0.8 χ2 IP(h)>2 ∆LLKπ(π)<0 ProbNNK(π)<0.01 ∆LLKπ(K)>0 ProbNNK(K)>0.21 B0 s→J/ψK∗0M(B0 s)∈[5150,5650] MeV/c2 χ2 vtx/ndof(B0 s)<10 DIRA(B0 s)>0.999 VS >1.5 mm B+→J/ψK+veto |M(J/ψ, K)−5279|>60 MeV/c2 4.1.4 BDTG requirements As previously stated at the beginning of this section, most of the combinatorial background is rejected from data using a MultiVariate Analysis (MVA) method, consisting of Boosted Decision Trees with Gradient boosting. In order to obtain a cut value optimised separately for each data-taking year conditions, this BDTG is trained, tested and optimised separately for both 2011 and 2012 samples; but following a common procedure. Henceforth, the procedure described in the following paragraphs is assumed to be performed in parallel for 2011 and 2012 samples. Thus, for this purpose, a signal sample from B0 s→J/ψK∗0simulated decays and a background sample extracted from real data are 66 constructed. For both samples, a common selection, which consists of the same requirements as in Table 4.2 but excepting the ProbNN particle identification cuts for kaons and pions, is applied. For the signal sample, true MC-truth for B0 ssimulated candidates and a mass window constraint of 25 MeV/c2around the B0 speak, are required. Here, MC-truth is a boolean variable associated to each simulated event which is true only when the corresponding event has a particle TRUEID equal to its corresponding ID defined in the PDG Monte Carlo numbering scheme [117]. Hereafter, referring to “true MC-truth” and simply “MC-truth” will be equivalent. For the background sample, candidates from the high mass sideband with invariant masses between 5401.3 MeV/c2and 5700 MeV/c2are selected (this is the region 35 MeV/c2away from the B0 speak in the high mass sideband, since σB0 sis estimated to be approximately 10 MeV/c2as shown in Chapter 4.3.2). A requirement on the RICH particle identification ProbNN variables of kaons and pions, complementary to those shown in Table 4.2 in order to use different real data samples during the MVA procedure and further steps of the analysis avoiding possible bias, is imposed too (ProbNNK(K)<0.21 kProbNNK(π)>0.01). All these requirements which define signal and background samples, are summarised in Table 4.3. Table 4.3: Signal and background sample definitions for samples used in MVA studies. Decay mode Cut variable Cut value Signal sample B0 s→J/ψK∗0|M(J/ψK−π+)−5366.3|<25 MeV/c2 MC-truth true Background sample B0 s→J/ψK∗0M(J/ψK−π+)−5366.3>35 MeV/c2 K∗0→K−π+ProbNNK(K)kProbNNK(π)<0.21 k>0.01 TMVA toolkit [116] was used for this MVA procedure. After their preparation, each sample is split in two halves: 50% of the sample is used for training while the other 50% used for testing. A BDTG method is trained and tested over those samples using the following kinematic variables as discriminating variables for the MVA procedure (B0 s meson variables are named here as B0): •max DOCA: maximum of all distances between pairs of tracks from daughter particles. •B0 LOKI DTF CTAU: time of flight ct of the B0 smeson candidate, where tis the decay time of the B0 smeson candidate measured in its proper reference frame. •lessIPS: minimum of all significances on the impact parameter of a daughter particle (kaons, muons and pions) with respect to the B0 smeson candidate. •B0 PT: transverse momentum of the B0 smeson candidate. •B0 IP OWNPV: impact parameter of the B0 smeson candidate with respect to its best own parent vertex. 67 •B0 ENDVERTEX CHI2: reconstruction significance of a reconstructed decay vertex of the B0 smeson candidate. Signal and background distributions for discriminating variables are presented in Figure 4.2 and Figure 4.3, among with the BDTG method response in Figure 4.1, for both 2011 and 2012 conditions separately. No overtraining is observed in Figure 4.1, showing a good discrimination power for the chosen BDTG method between both signal and background distributions. BDTG response -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 dx / (1/N) dN 0 2 4 6 8 10 12 14 16 Signal (test sample) Background (test sample) Signal (training sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = 0.119 (0.406) U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% TMVA overtraining check for classifier: BDTG BDTG response -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 dx / (1/N) dN 0 2 4 6 8 10 12 14 16 Signal (test sample) Background (test sample) Signal (training sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = 0.432 ( 1) U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% TMVA overtraining check for classifier: BDTG Figure 4.1: BDTG response to signal and background distributions for 2011 (left) and 2012 (right) conditions. max_DOCA [units] 0.5 1 1.5 2 2.5 0.0711 units / (1/N) dN 0 2 4 6 8 10 12 Signal Background U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.3)% Input variable: max_DOCA B0_LOKI_DTF_CTAU [units] 1 2 3 4 5 0.129 units / (1/N) dN 0 0.5 1 1.5 2 2.5 3 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.4)% Input variable: B0_LOKI_DTF_CTAU lessIPS [units] 10 20 30 40 50 60 70 80 90 2.4 units / (1/N) dN 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 U/O-flow (S,B): (0.0, 0.0)% / (0.1, 0.0)% Input variable: lessIPS B0_PT [units] 50001000015000200002500030000350004000045000 1.14e+03 units / (1/N) dN 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 -3 10× U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: B0_PT B0_IP_OWNPV [units] 0.1 0.2 0.3 0.4 0.5 0.014 units / (1/N) dN 0 5 10 15 20 25 30 U/O-flow (S,B): (0.0, 0.0)% / (0.1, 0.3)% Input variable: B0_IP_OWNPV B0_ENDVERTEX_CHI2 [units] 10 20 30 40 50 1.28 units / (1/N) dN 0 0.02 0.04 0.06 0.08 0.1 0.12 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: B0_ENDVERTEX_CHI2 Figure 4.2: Distributions for MVA discriminating variables under 2011 conditions. 68 max_DOCA [units] 1 2 3 4 5 0.131 units / (1/N) dN 0 1 2 3 4 5 6 7 8 9Signal Background U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.3)% Input variable: max_DOCA B0_LOKI_DTF_CTAU [units] 1 2 3 4 5 0.139 units / (1/N) dN 0 0.5 1 1.5 2 2.5 3 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.2)% Input variable: B0_LOKI_DTF_CTAU lessIPS [units] 10 20 30 40 50 60 70 80 2.04 units / (1/N) dN 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 U/O-flow (S,B): (0.0, 0.0)% / (0.2, 0.0)% Input variable: lessIPS B0_PT [units] 500010000150002000025000300003500040000 1.08e+03 units / (1/N) dN 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 -3 10× U/O-flow (S,B): (0.0, 0.0)% / (0.1, 0.0)% Input variable: B0_PT B0_IP_OWNPV [units] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0227 units / (1/N) dN 0 5 10 15 20 25 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.2)% Input variable: B0_IP_OWNPV B0_ENDVERTEX_CHI2 [units] 10 20 30 40 50 1.28 units / (1/N) dN 0 0.02 0.04 0.06 0.08 0.1 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: B0_ENDVERTEX_CHI2 Figure 4.3: Distributions for MVA discriminating variables under 2012 conditions. After training and testing it, a cut on the BDTG is applied: the purpose of this cut is to suppress as much combinatorial background contribution as possible from data. Since background and signal distributions are well discriminated (see Figure 4.1), it is possible to find an optimal cut value on the BDTG where most of the combinatorial background contribution on data with the same properties as the background sample used should be removed. The cut value, henceforth called also “optimal point”, is chosen so that it maximises the figure of merit (FoM) [118] F(sWeights) = (Pwi)2 Pw2 i ,(4.1) where wiare the sWeights associated to each event, and calculated with the sPlot technique [113], considering B0 scandidate events as signal yield. This FoM can be understood as an effective signal value, which is proportional to the number of events of a signal-only sample with the same statistical power as the sample used to compute F(sWeights). For these calculations, a mass model consisting of two Crystal-Ball [119] (signal parametrisation) and an exponential function (background parametrisation) is used. As previously noted, since the optimal point may be different for 2011 and for 2012 conditions, the optimisation as well is performed separately for 2011 and 2012 samples. After applying the requirements described in Table 4.2, these fits are performed in a single M(J/ψKπ) bin. For a range of cut values applied on the BDTG, an sPlot can be performed and a value for the FoM can be obtained. A pair of plots, one per data-taking year condition, containing the value of F(sWeights) versus the cut value applied on the BDTG, are shown in Figure 4.4. Optimal BDTG cut values are chosen as those that maximise 69 Cut applied on BDTG -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 F(sWeights) 0 100 200 300 400 500 BDTG optimisation (2011 data conditions) Optimal cut value: 0.2 BDTG optimisation (2011 data conditions) Cut applied on BDTG -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 F(sWeights) 0 200 400 600 800 1000 BDTG optimisation (2012 data conditions) Optimal cut value: 0.12 BDTG optimisation (2012 data conditions) Figure 4.4: BDTG optimisation for 2011 (left) and 2012 (right) conditions. F(sWeights). These values are BDTG >0.2 for 2011 conditions and BDTG >0.12 for 2012 conditions. For more details about the whole MVA procedure, see Appendix A. 4.1.5 Selection efficiencies Signal efficiency and background rejection values are calculated separately for both 2012 and 2011 data samples. Signal and background samples used for these calculations are defined in Table 4.3, except the ProbNN particle identification cut for the background sample. Three different subsets of cuts are considered, resulting in three individual signal efficiencies (background rejections) values: a first set, corresponding to the requirements presented in Table 4.2, used to obtain εsel (rsel). A second set, corresponding to the optimal BDT cut value obtained in Chapter 4.1.4, used to calculate εMVA (rMVA). A third set, composed of RICH particle identification cuts for pions (ProbNNπ/ProbNNp >21.9) and kaons (ProbNNK/ProbNNp >0.99) to suppress Λ0 bpeaking backgrounds (implemented a posteriori and described in Chapter 4.2.3), used to obtain εΛ0 b(rΛ0 b). Each one of these individual efficiencies (rejections) are calculated w.r.t. the corresponding previous set of cuts, in an inclusive way. Finally, a total efficiency (rejection) value is obtained, containing the information from all the efficiencies (rejections) computed in previous steps, εtot (rtot). These efficiencies and rejections are shown in Table 4.4. Values related to cuts on RICH particle identification variables are corrected using the PIDCalib package [91,93,120]. This package is used in this analysis to correct ProbNN and ∆LL distributions for daughter hadrons in simulation using real data samples. After applying the final selection cuts (which includes those cuts described in Table 4.2, the optimal BDTG cut value, and the cuts devoted to the Λ0 bbackgrounds suppression), 147760 events are selected in the 2012 data sample and 68100 events are selected in the 2011 data sample. From all the cuts in the RICH particle identification variables included in the previously defined final selection requirements, those used to suppress Λ0 bpeaking backgrounds have a small effect on the other background components. As explained in Chapter 4.2.3, 70 Table 4.4: Signal efficiencies and background rejections for 2011 and 2012 conditions. εsel (rsel)εMVA (rMVA)εΛ0 b(rΛ0 b)εtot (rtot) Signal efficiency, 2011 54.58 ±0.23 92.73 ±0.27 93.35 ±0.20 47.25 ±0.30 ε(%) 2012 54.56 ±0.23 93.38 ±0.28 93.41 ±0.22 47.59 ±0.31 Background rejection, 2011 99.12 ±0.01 92.97 ±0.35 21.22 ±2.11 99.951 ±0.003 r(%) 2012 99.30 ±0.01 92.59 ±0.23 23.69 ±1.39 99.960 ±0.002 the Λ0 bcontributions are treated separately with respect to the rest of the peaking backgrounds present in the final data sample. In order to properly estimate the rejection level of Λ0 b→J/ψpK−(Λ0 b→J/ψpπ−) peaking backgrounds after the final selection, specific background samples where an MC-truth condition for protons and kaons (pions) is required, are used instead. After their calculation, the corresponding rejections are corrected using the PIDCalib package as done in the previous step. Table 4.5 gives the Λ0 b→J/ψpK−and Λ0 b→J/ψpπ−background overall rejections as well as the ones from the specific cuts implemented to reduce the Λ0 bpeaking backgrounds: equivalent percentages as in Table 4.4 are presented but using different background samples. These cuts result in a rejection of ∼7% of signal events (see Table 4.4) while rejecting ∼90% and ∼38% of Λ0 b→J/ψpK−and Λ0 b→J/ψpπ−backgrounds, respectively. Table 4.5: Background rejections over specific Λ0 bsamples, for 2011 and 2012 conditions. rsel & MVA (%) rΛ0 b(%) rtot (%) Λ0 b→J/ψpK−sample 2011 97.78 ±0.032 91.89 ±0.66 99.82 ±0.0093 2012 97.38 ±0.036 87.80 ±1.00 99.68 ±0.013 Λ0 b→J/ψpπ−sample 2011 97.98 ±0.031 37.54 ±2.06 98.74 ±0.025 2012 98.06 ±0.031 38.02 ±5.81 98.80 ±0.024 4.2 Treatment of peaking backgrounds In addition to the signal and combinatorial background, extensive studies of fully simulated samples show contributions from several specific backgrounds, such as B0 s→J/ψK+K−,B0 s→J/ψπ+π−and B0→J/ψπ+π−decay modes. The invariant mass distribution of misidentified B0→J/ψπ+π−and B0 s→J/ψπ+π−decays peaks near the B0 s→J/ψKπ signal peak, as shown in Figure 4.5, whilst the misidentified B0 s→J/ψK+K−events are located almost under the B0→J/ψKπ signal peak, see Figure 4.6. This behaviour makes the invariant mass of the J/ψ Kπ system not to be a discriminating variable, and hence those misidentified backgrounds cannot be added as extra species to the mass model used for the fit with the sPlot technique [113], see Chapter 4.3.1. Instead, and in the same way as sWeights are applied such that sideband events cancel out the likelihood contribution from background events underneath 71 the peak, simulated events with negative weights are used to cancel out the likelihood contribution from these peaking background events present in the real data. In Chapter 4.2.1, raw yields of expected backgrounds using simulated samples are calculated. As a next step, in Chapter 4.2.2, a per-event weighting to correct those samples to look like real data is assigned. There are also contributions from misidentified Λ0 b→J/ψpK−and Λ0 b→J/ψpπ−peaking backgrounds. Only the latter is treated separately, added as an extra specie to the mass model, as shown in Chapter 4.2.3. ] 2 ) [MeV/cπ KψM(J/ 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 0 0.05 0.1 0.15 0.2 0.25 signal 0 s B signal 0 B (PHSP) - π + π ψ J/→ 0 B (770) 0 ρ ψ J/→ 0 B (PHSP) - π + π ψ J/→ 0 s B (980) 0 fψ J/→ 0 s B ] 2 ) [MeV/cπ KψM(J/ 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 0 0.05 0.1 0.15 0.2 0.25 signal 0 s B signal 0 B (PHSP) - π + π ψ J/→ 0 B (770) 0 ρ ψ J/→ 0 B (PHSP) - π + π ψ J/→ 0 s B (980) 0 fψ J/→ 0 s B Figure 4.5: Invariant mass distributions from simulation of misidentified B0 s→J/ψπ+π− and B0→J/ψπ+π−peaking backgrounds, in comparison with invariant mass distributions from MC of B0 s→J/ψKπ and B0→J/ψKπ signal. MC-truth for kaons and pions is imposed, together with the offline requirements described in Chapter 4.1.3. Distributions are normalised to the same area. Left: Simulated data for 2011 conditions. Right: Simulated data for 2012 conditions. 4.2.1 Raw yields from simulated samples The yields of the peaking backgrounds are estimated from simulated data as Nexp = 2 ×σb¯ b×P(b→Bq)×Bvis ×ε×L,(4.2) being P(b→Bq) the hadronisation fraction (henceforth fq), εthe total efficiency (reconstruction, offline selection and trigger), Lthe integrated luminosity of the real data, σb¯ bthe b¯ bproduction cross section [121], and Bvis the visible branching fraction (taking into account not only the branching fraction of Bqbut also the branching fractions of the daughter resonances) of the corresponding peaking background mode [117]. It is very convenient to just calculate the effective luminosity of the simulated samples and scale the yields to the luminosity of the data. The efficiencies of the particle identification (PID) requirements obtained in simulation are corrected using the PIDCalib package [91]. The angular and mh+h−properties of the B0 (s)→J/ψh+h−decays are also corrected using a weighting procedure (as described in Chapter 4.2.2). Hadronisation 72 ] 2 ) [MeV/cπ KψM(J/ 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 0 0.05 0.1 0.15 0.2 0.25 signal 0 s B signal 0 B (PHSP) - K + Kψ J/→ 0 s B (1020)φ ψ J/→ 0 s B ] 2 ) [MeV/cπ KψM(J/ 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 0 0.05 0.1 0.15 0.2 0.25 signal 0 s B signal 0 B (PHSP) - K + Kψ J/→ 0 s B (1020)φ ψ J/→ 0 s B Figure 4.6: Invariant mass distributions from simulation of misidentified B0 s→J/ψK+K− peaking background, in comparison with invariant mass distributions from MC of B0 s→ J/ψKπ and B0→J/ψKπ signal. MC-truth for kaons and pions is imposed, together with the offline requirements described in Chapter 4.1.3. Distributions are normalised to the same area. Left: Simulated data for 2011 conditions. Right: Simulated data for 2012 conditions. factors [122,123] are obtained (see Appendix G) under the assumptions fd=fuand fd+fu+fs+fΛ= 1, giving fd=fu= 0.370 ±0.016, fs= 0.0959 ±0.0068, fΛ0 b= 0.163 ±0.042.(4.3) The raw expectations found for the most relevant backgrounds are shown in Table 4.6. The predictions are shown for two assumptions of the decay model: only phase-space (PHSP), and that of the main resonance of the hh spectrum. In Chapter 4.2.2, events are weighted according to the latest measurements of their differential decay rates, in order to get more precise predictions. 4.2.2 Physical reweighting of simulated samples The events from full simulation are generated in PHSP and hence do not contain the proper physical amplitudes. This can cause the yield estimations of Chapter 4.2.1 not to be accurate and cause the simulated events to be distributed in the decay angles and Kπ mass space, (Ω, mKπ), in a different way than the actual peaking background of the data. The amplitude analysis of B0→J/ψπ+π−,B0 s→J/ψπ+π−, and B0 s→J/ψK+K− decay modes has been performed in refs. [124], [125], and [126], respectively. Simulated events are weighted with wMC =PDAT A(Ω, mhh|Ai) PMC(Ω, mhh),(4.4) where the above PDFs are normalised to the phase space where cos θK∈[−1,1], cos θµ∈ [−1,1] and φ∈[−π, π], and where mhh is inside the kinematical thresholds [2×mh, mB− 73 where the first uncertainties are statistical and obtained from the quadratic sum of the ones in each fitting category, and the second uncertainties correspond to systematics. The correlations between the B0and B0 syields in each fitting category are found to be smaller than 4%. Neglecting these correlations, the ratio NB0 s NB0 = (8.66 ±0.24+0.18 −0.16)×10−3(4.9) obtained for the entire data sample is computed, where the first uncertainty is statistical and the second uncertainties correspond to systematics. Figure 4.11 shows the sum of the fit projections of each bin overlaid to the m(J/ψK+π−) mass spectrum for the entire data sample. Figure 4.12 shows the µµ spectrum and the mKπ spectrum. While the B0 sor B0di-muon sPlots have very similar shape, the mKπ weighted spectrums exhibit different shapes. The B0 smKπ sPlot seems to be slightly distorted. This could be due to the presence of interference between the Kπ S-wave and the K∗0, which would appear to be stronger in the B0 sdecays compared to the B0. In order to check the validity of this hypothesis, two additional studies are performed. First, it is checked if the peaking background treatment propagated to the sWeights is responsible for this behavior. No significant difference between the B0 smKπ spectrum using sWeights computed with and without MC data injection is found. An additional study looking at the mKπ structure after correcting for efficiency effects using the normalisation weights coming from the angular acceptance study, is performed. The interference between the Kπ S-wave and the K∗0P-wave vanishes, since an integration over the helicity angles is done. Figure 4.10 gives the efficiency corrected B0 sand B0mKπ spectra using the nominal sets of sWeights. It is observed that the B0 smKπ distribution is closer to the one of the B0after applying the efficiency correction. This is a clear indication of the presence of stronger interference in the B0 scase compared to the B0one. The effect of allowing the mean and sigma of the B0 sand B0Hypatia functions to share common values over the 20 bins from a simultaneous fit is checked. No significant gain was observed. The corresponding results are presented in Appendix B.3. Table 4.11: Results of the fit to the invariant mass of each individual mKπ bin category for −1.0≤cos(θµ)<−0.6. 826 ≤mKπ ≤861 861 < mKπ ≤896 896 < mKπ ≤931 931 < mKπ ≤966 MeV/c2MeV/c2MeV/c2MeV/c2 kbkg −0.0043 ±0.0014+0.0003 −0.0003 −0.0007 ±0.0016+0.0008 −0.0007 −0.0042 ±0.0011+0.0004 −0.0004 −0.0043 ±0.0009+0.0004 −0.0004 µB05 280.95 ±0.15+0.00 −0.00 5 281.00 ±0.07+0.03 −0.04 5 281.44 ±0.08+0.02 −0.02 5 281.72 ±0.14+0.01 −0.01 µB0 s5 370.17 ±2.48+0.33 −0.40 5 369.05 ±0.87+0.55 −0.16 5 368.38 ±1.17+0.50 −0.51 5 367.68 ±1.72+0.19 −0.30 σB010.03 ±0.16+0.18 −0.14 10.26 ±0.08+0.07 −0.06 9.91 ±0.08+0.07 −0.07 10.37 ±0.14+0.15 −0.12 σB0 s12.23 ±3.15+0.36 −0.34 9.07 ±0.95+0.38 −0.83 12.67 ±1.51+1.48 −1.48 9.02 ±2.06+0.84 −0.79 NB04008.8±66.1+5.4 −5.015964.8±127.4+12.6 −12.614664.2±122.2+29.7 −29.64842.2±70.9+15.7 −15.4 NB0 s31.9±7.7+1.1 −0.8132.2±13.2+3.6 −12.1138.0±14.4+16.9 −16.742.0±8.8+4.3 −4.2 NBkg 87.2±22.4+6.4 −7.366.7±19.7+11.0 −11.797.6±19.5+10.9 −11.2116.6±17.6+9.6 −9.7 NΛpπ 1.8±0.6+0.0 −0.02.0±0.6+0.0 −0.02.0±0.6+0.0 −0.02.3±0.7+0.0 −0.0 80 Table 4.12: Results of the fit to the invariant mass of each individual mKπ bin category for −0.6≤cos(θµ)<−0.2. 826 ≤mKπ ≤861 861 < mKπ ≤896 896 < mKπ ≤931 931 < mKπ ≤966 MeV/c2MeV/c2MeV/c2MeV/c2 kbkg −0.0028 ±0.0014+0.0002 −0.0002 −0.0045 ±0.0008+0.0001 −0.0002 −0.0030 ±0.0011+0.0002 −0.0002 −0.0071 ±0.0014+0.0010 −0.0010 µB05 281.06 ±0.11+0.01 −0.01 5 281.08 ±0.06+0.00 −0.00 5 281.59 ±0.06+0.01 −0.01 5 281.52 ±0.12+0.01 −0.01 µB0 s5 367.44 ±1.60+0.07 −0.05 5 369.35 ±0.87+0.17 −0.09 5 368.16 ±0.73+0.30 −0.32 5 368.78 ±1.46+0.08 −0.11 σB08.42 ±0.12+0.15 −0.12 8.69 ±0.06+0.05 −0.05 8.58 ±0.07+0.06 −0.06 9.04 ±0.12+0.12 −0.14 σB0 s7.74 ±1.89+0.31 −0.25 7.90 ±1.07+0.33 −0.28 8.58 ±0.85+0.67 −0.65 10.33 ±1.69+0.65 −0.46 NB05012.9±72.8+7.9 −7.917416.8±133.4+11.0 −10.915481.1±125.6+26.4 −26.35016.5±72.2+17.1 −15.8 NB0 s33.2±7.1+1.0 −0.8105.1±12.3+2.9 −2.8152.3±14.1+10.9 −10.763.9±10.0+5.2 −4.0 NBkg 78.4±19.8+10.1 −10.2169.9±24.0+12.3 −11.695.9±19.6+13.9 −13.995.6±16.5+12.3 −10.9 NΛpπ 1.8±0.6+0.0 −0.02.0±0.6+0.0 −0.02.0±0.6+0.0 −0.02.3±0.7+0.0 −0.0 Table 4.13: Results of the fit to the invariant mass of each individual mKπ bin category for −0.2≤cos(θµ)<0.2. 826 ≤mKπ ≤861 861 < mKπ ≤896 896 < mKπ ≤931 931 < mKπ ≤966 MeV/c2MeV/c2MeV/c2MeV/c2 kbkg −0.0017 ±0.0011+0.0002 −0.0002 −0.0040 ±0.0008+0.0002 −0.0002 −0.0049 ±0.0008+0.0003 −0.0003 −0.0040 ±0.0009+0.0003 −0.0003 µB05 281.11 ±0.10+0.01 −0.01 5 281.00 ±0.05+0.16 −0.39 5 281.67 ±0.06+0.01 −0.01 5 281.45 ±0.11+0.02 −0.01 µB0 s5 370.94 ±2.72+0.27 −0.27 5 369.72 ±0.82+0.45 −0.11 5 368.59 ±0.76+0.11 −0.11 5 370.61 ±1.12+0.10 −0.20 σB07.97 ±0.11+0.15 −0.11 8.01 ±0.06+0.11 −0.11 7.95 ±0.06+0.06 −0.05 8.35 ±0.11+0.12 −0.09 σB0 s14.59 ±4.91+1.11 −1.09 7.53 ±0.89+0.50 −0.46 8.88 ±0.92+0.50 −0.50 8.08 ±1.20+0.49 −0.36 NB05470.4±75.2+9.2 −8.718252.7±136.3+12.2 −11.515713.0±126.3+26.7 −26.25102.4±72.8+15.5 −13.5 NB0 s38.1±9.0+1.8 −2.0110.1±12.1+3.6 −2.9144.9±13.8+8.8 −8.867.2±9.8+3.4 −3.2 NBkg 86.6±17.7+10.0 −9.9146.8±22.2+11.9 −11.3143.2±19.6+15.3 −14.9114.3±17.0+11.4 −9.8 NΛpπ 1.8±0.6+0.0 −0.02.0±0.6+0.1 −1.12.0±0.6+0.0 −0.02.2±0.7+0.0 −0.0 Table 4.14: Results of the fit to the invariant mass of each individual mKπ bin category for 0.2≤cos(θµ)<0.6. 826 ≤mKπ ≤861 861 < mKπ ≤896 896 < mKπ ≤931 931 < mKπ ≤966 MeV/c2MeV/c2MeV/c2MeV/c2 kbkg 0.0000 ±0.0067+0.0001 −0.0003 −0.0018 ±0.0011+0.0002 −0.0002 −0.0054 ±0.0009+0.0004 −0.0004 −0.0038 ±0.0008+0.0003 −0.0003 µB05 281.06 ±0.11+0.01 −0.01 5 281.00 ±0.06+0.01 −0.01 5 281.64 ±0.06+0.02 −0.02 5 281.57 ±0.11+0.01 −0.01 µB0 s5 371.86 ±2.05+0.12 −0.12 5 368.07 ±0.96+0.11 −0.12 5 367.91 ±0.91+0.32 −0.32 5 367.50 ±1.07+0.08 −0.18 σB08.37 ±0.12+0.15 −0.12 8.70 ±0.06+0.06 −0.05 8.50 ±0.06+0.06 −0.06 8.80 ±0.12+0.12 −0.14 σB0 s11.60 ±2.60+0.29 −0.28 9.54 ±1.04+0.24 −0.23 11.25 ±1.07+0.75 −0.75 7.11 ±1.33+0.53 −0.32 NB04904.6±70.6+5.4 −5.017315.8±132.7+10.7 −10.715528.2±125.6+26.4 −26.24993.6±72.0+15.5 −14.9 NB0 s36.6±7.5+0.8 −0.8127.3±13.0+2.9 −2.8169.6±15.1+12.8 −12.757.0±9.5+3.8 −3.2 NBkg 53.2±11.0+7.2 −6.4103.9±20.2+11.3 −11.1135.8±19.8+11.6 −11.6129.4±17.7+10.9 −10.4 NΛpπ 1.8±0.6+0.0 −0.02.0±0.6+0.0 −0.02.0±0.6+0.0 −0.02.3±0.7+0.0 −0.0 81 Table 4.15: Results of the fit to the invariant mass of each individual mKπ bin category for 0.6≤cos(θµ)≤1.0. 826 ≤mKπ ≤861 861 < mKπ ≤896 896 < mKπ ≤931 931 < mKπ ≤966 MeV/c2MeV/c2MeV/c2MeV/c2 kbkg −0.0057 ±0.0014+0.0005 −0.0006 −0.0014 ±0.0015+0.0004 −0.0003 −0.0017 ±0.0013+0.0002 −0.0003 −0.0042 ±0.0012+0.0005 −0.0005 µB05 280.90±+0.00 −0.00 5 280.85 ±0.07+0.01 −0.01 5 281.48 ±0.08+0.12 −0.11 5 281.41 ±0.14+0.01 −0.01 µB0 s5 371.26 ±1.99+0.11 −0.20 5 368.80 ±0.97+0.04 −0.08 5 368.36 ±0.93+0.20 −0.20 5 368.01 ±1.72+0.49 −0.26 σB010.05 ±0.16+0.18 −0.14 10.23 ±0.08+0.06 −0.06 9.80 ±0.08+0.08 −0.09 10.28 ±0.15+0.15 −0.12 σB0 s10.56 ±2.78+0.54 −0.52 10.06 ±1.06+0.40 −0.38 10.67 ±1.07+0.97 −0.97 10.02 ±2.36+1.18 −1.04 NB04046.6±65.3+6.5 −6.015804.8±126.5+12.7 −11.114422.5±120.9+30.3 −29.74693.7±69.8+14.1 −14.1 NB0 s32.8±7.5+1.0 −0.9129.9±13.1+4.3 −3.5145.9±13.9+24.4 −14.049.6±9.5+6.0 −5.2 NBkg 71.7±17.9+8.9 −9.863.1±17.2+9.8 −12.462.0±15.5+13.2 −13.680.2±16.5+7.8 −7.7 NΛpπ 1.8±0.6+0.0 −0.02.0±0.6+0.0 −0.02.0±0.6+0.1 −1.92.3±0.7+0.0 −0.0 ) [MeV/c^2]πM(K 850 900 950 Candidates / (4.7 MeV/c^2) 0 20 40 60 80 100 120 (b) Figure 4.10: Efficiency corrected Kπ invariant mass spectra using the B0 s(red markers) and B0(black markers) sWeights computed from the maximum likelihood fit to the Kπµ+µ−invariant mass spectrum. 82 ] 2 ) [MeV/cπ KψM(J/ 5200 5300 5400 5500 5600 ) 2 Candidates / (11.1 MeV/c -2 10 -1 10 1 10 2 10 3 10 4 10 5 10 LHCb (a) ] 2 ) [MeV/cπ KψM(J/ 5200 5300 5400 5500 5600 ) 2 Candidates / (11.1 MeV/c 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Data Total PDF signal d 0 B signal s 0 B Combinatorial bkg π pψ J/→ b Λ LHCb (b) Figure 4.11: Sum of the fit projections in the 20 bins with a linear (a) and logarithmic scale (b) on the y-axis. The legend displayed in (b) also applies to (a). 83 ] 2 ) [MeV/cπM(K 850 900 950 ) 2 Candidates / (4.7 MeV/c 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 (a) ] 2 ) [MeV/c - µ + µM( 3050 3100 3150 ) 2 Candidates / (2.6 MeV/c 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 (b) Figure 4.12: Weighted Kπ (a) and µ+µ−(b) invariant mass spectra using the B0 s(red markers) and B0(black markers) sWeights computed from the maximum likelihood fit to the Kπµ+µ−invariant mass spectrum. The vertical dashed lines in (a) describe the four mKπ bins. 84 4.3.3 Fit validation In order to test the robustness of the fit model, before extracting the parameters of interest in the data, validation tests are performed by means of “toy MC” studies, using generated pseudoexperiments. These allow, using “pull” distributions, to estimate the potential biases that can arise from the model. In order to get a realistic estimation of these biases, each toy sample must be statistically equivalent to the real data sample. In other words, the different categories present in the fit model must have yields and characteristics corresponding to these expected in data. The pull of a free parameter ain the i-th pseudoexperiment is defined as pulli=af i−at i σf i ,(4.10) where af iand σf icorrespond to the fitted value of a parameter and its fit error, respectively, and at iis the generated value. In case the parameter is unbiased, the corresponding pull distribution may be considered as a gaussian of zero mean and unity width. Otherwise, the pull distribution gives the bias in units of the statistical error. The pull definition in (4.10) is only valid in the case of symmetric fitted errors. In the case of asymmetric errors, the pull is now defined as pulli= ξaf i−at i eσf iaf i< at i⇒ξ= +1 ; eσf i=σf,+ i af i≥at i⇒ξ=−1 ; eσf i=σf,− i ,(4.11) where σf,+ iand σf,− icorrespond to the positive and negative errors returned by the fit, when using MINOS. Two types of toy studies will be considered: pure and embedded. Pure toys consist in generating pseudoexperiments using the fit model itself. They allow to determine which PDF parameters can be varied in the fit, and are sensitive for instance to biases due to small number of events. Embedded toy studies use reconstructed simulation events for as many as possible event categories, which are embedded within generated samples for the other categories. They are sensitive to reconstruction effects, such as correlations between variables. It is ensured that for each embedded category, a simulation event does not appear twice, and thus the limitation of these studies is the number of statistically independent simulation samples that can be used to construct the pull distribution. Significant biases observed in these studies could then be corrected in the fit to data. Here the B0 s,B0signals and combinatorial backgrounds are generated from their nominal PDFs, while the various peaking backgrounds are embedded from simulation samples. Since in the present analysis a fit to the invariant mass distribution is used in order to statistically disentangled the signal events (i.e. B0 s→J/ψK∗0decays) using the sPlot technique [113], the toy MC studies must be performed in two steps. First, a study using toy MC to check the presence of potential biases on the parameters entering the mass fit model is performed. The signal yield should not exhibit a large bias 85 in order to obtain an unbiased set of sWeights. The presence of significant biases on the other parameters should not affect the sWeights corresponding to the signal. The results of this study are presented in Appendix F.1. In a second step, as described in Chapter 4.4, an angular analysis is performed using the sFit technique [132] in order to extract the parameters of interest. Therefore biases originating from two sources may occur here: intrinsic biases due to the fit model, and biases from the sWeights applied to the data sample. These two potential sources of biases are studied using toy studies, as described in Appendix F.2. Note that the mass and the angular distributions are generated together to ensure that the sWeights extracted from the fit to the mass are applied to the correct events when performing the toy studies of the angular fit model. Results from these studies are taken into account as systematic uncertainties for each corresponding parameter obtained from the final fit (see Chapter 4.6.5). 86 4.4 Angular analysis and CP asymmetries This analysis uses the decay angles defined in the helicity basis. The helicity angles are denoted by (θK, θµ, ϕh) and their definition is shown in Fig. 4.13. The polar angle θK (θµ) is the angle between the kaon (µ+) momentum and the direction opposite to the B0 s momentum in the Kπ (µ+µ−) centre-of-mass system. The azimuthal angle between the Kπ and µ+µ−decay planes is ϕh. This angle is defined by a rotation from the pion side of the Kπ plane to the µ+side of the µ+µ−plane. The rotation is positive in the µ+µ− direction in the B0 srest frame. The definitions are the same whether a B0 sor a B0 sdecays. They are also the same for the B0→J/ψK∗0decays. θµ µ+µ− K−π+ θK y ϕh x z π+ µ− µ+ B0 s K− Figure 4.13: Definition of helicity angles. 4.4.1 Angular formalism The angular distribution of B0 s→J/ψK∗0decays is obtained as [127] PDF(θK, θµ, ϕh) = X αµ=±1 |λ|<J X λ,J r2J+ 1 4πHJ λe−iλϕhd1 λ,αµ(θµ)d1 −λ,0(θK) 2 ,(4.12) where λ= 0,±1 is the J/ψ meson helicity, αµ=±1 is the helicity difference between the muons, Jthe spin of the Kπ system, Hare the helicity amplitudes, and d, the Wigner matrices. In order to determine the CP components, the helicity amplitudes are transformed into “transversity amplitudes”, AS=H0 0,(4.13) AJ0=HJ 0,(4.14) AJ|| =1 √2(HJ ++HJ −),(4.15) AJ⊥=1 √2(HJ +−HJ −).(4.16) For simplicity, the transversity amplitudes associated with the P-wave (Kπ system with spin J= 1) are simply written A0,A|| and A⊥, while those associated with a Dwave (Kπ system with spin J= 2) are written as A20, A2|| and A2⊥. The modulus of 87 the transversity amplitude Axis noted as |Ax|while its CP-conserving phase is noted as δx. The convention |A0|2+|A|||2+|A⊥|2+|AS|2= 1 is adopted, and a S-wave fraction is defined as FS=|AS|2/(|A0|2+|A|||2+|A⊥|2+|AS|2). The polarisation fractions are defined in the same way. The distribution of the CP conjugate decay is obtained by flipping the sign of the interference terms which contain |A⊥|or |A2⊥|. The K+π−and K−π+samples are separated and fitted through a simultaneous fit. The full decay rate is shown in Appendix C.1. A check of this description by fitting MC-truth (required over kaons and pions) samples generated with several values for the amplitudes and phases, as well as by fitting the data used in a previous LHCb B0→J/ψK∗0analysis [133], is also performed. In all cases, values in very good agreement with the expectations are obtained. For details, see Appendix C.2. The mKπ window around the K∗0peak has been increased to ±70 MeV/c2with respect to the ±40 MeV/c2window used in the previous publication [134]. In order to account for the variation of the amplitudes with mKπ while keeping the framework of an angularonly fit, the mass range is subdivided into 4 bins of 35 MeV/c2in size, which are fitted simultaneously. 4.4.2 Partial wave correction factors The parameters |AS|2and δSare defined independently for each bin, in order to not include any mKπ dependency in the fit. If the D-wave is included (for a systematics study, or for studies on B0 s→J/ψK∗ 2(1430)0), one more fraction, FD= (|A20|2+|A2⊥|2+ |A2|||2)/(|A0|2+|A⊥|2+|A|||2+|A20|2+|A2⊥|2+|A2|||2), and one more phase, δ20, are needed in order to absorb the variations along the mKπ bins. After this re-definition, the PDF defined in (4.12) still contains some mass dependent terms, associated to the interference between waves [135]. For the case of the S-wave and P-wave alone, being sand ptheir respective propagators, such interference terms correspond to the complex integrals RmH Kπ mL Kπ p×s∗PHSP εm(mKπ)dmKπ rRmH Kπ mL Kπ |p|2PHSP εm(mKπ)dmKπ RmH Kπ mL Kπ |s|2PHSP εm(mKπ)dmKπ =CSP e−iθSP , (4.17) where εmis the mKπ acceptance, and PHSP stands for the phase-space. The phase θSP can be absorbed in the definition of δSbut the CSP factors, corresponding to real numbers in the range [0,1], have to be computed and inserted in the angular fit as an input. If the D-wave is present, analogous CSD and CPD factors need to be included to account for the extra interference terms. The Cij are calculated numerically from the integrals above, given a certain assumption for the mass lineshapes and mhh resolution, and included as fixed parameters in the fit. A systematic (see Chapter 4.6.7) is further added to cover difference choices of the mass propagator models. In order to calculate the factors defined in (4.17), a model for the S, P and D wave propagators is needed. Instead of choosing a given a priori model, a choice is made based 88 on a test on data. To check which model has a better description of data, a three-step procedure is followed: 1. The mKπ range, from 826 MeV/c2to 1631 MeV/c2, is subdivided into 23 bins of 35 MeV/c2each one. For each bin, an angular fit is performed and the S-wave, P-wave, and D-wave amplitudes are extracted. 2. The obtained amplitudes in the previous step per bin are translated into three separated distributions on mKπ, representing the fitted contribution of each wave. In order to account for the errors associated to the normalisation weights due to the limited statistics of the simulated samples, a systematic uncertainty is addressed to the wave yields per bin by comparing their measured values with those obtained by using a real data sample of B0→J/ψK∗0(with high statistics) to compute the normalisation weights. 3. The three distributions are fitted with different possible models, in order to choose the best propagator set. This procedure is first performed using the B0→J/ψ(Kπ) data sample, in order to select one propagator per wave, given the high statistics of this channel in the sample and its similarity to B0 s→J/ψ(Kπ). In a second round, the study is repeated using the B0 s→J/ψ(Kπ) data sample, now only with the selected propagators, so as to account for the differences in physics between the two channels. In this sense, the free parameters of each propagator (if any) are floated during the mKπ fits, and then used as the default values in the analysis. As the sWeights presented some problems for the B0 sin the low statistic bins of the high mKπ region, an alternative method is used to remove the background in this study. A ±20 MeV/c2mass window cut around the B0 snominal mass is applied. Part of the offline selection requirements, namely the MVA cut, are re-optimised for the whole mKπ range, both for 2011 and 2012 samples. The negative weights from Monte Carlo are kept in order to remove all peaking backgrounds but those coming from Λbdecays, that are neglected here. As candidate propagators for the S-wave component, the following models are used: an isobaric combination of K∗ 0(800)0,K∗ 0(1430)0and a non-resonant (NR) term (M1), the LASS parametrisation [136] with K∗ 0(1430)0and a NR term (M2), and a K-Matrix model with K∗ 0(800)0,K∗ 0(1430)0and a NR term (M3). For the P-wave distribution, a model with the K∗(892)0alone (M1), one with an isobaric combination of K∗(892)0and K∗ 1(1410)0(M2), and another one with an isobaric combination of K∗(892)0,K∗ 1(1410)0 and K∗ 1(1680)0, are used. Finally, for the D-wave, only the K∗ 2(1430)0is considered. For the resonances and the LASS propagator, the parametrisation explained in [137] is used. The nominal masses and widths of the resonances are taken from PDG [117]. The rest of the parameters are allowed to vary during the fit. The three distributions obtained for B0→J/ψ(Kπ), accompanied by the fits performed using the different candidate propagators, can be found in the left plots of Figure 4.14. The corresponding χ2and p-values for each fit are written in Table 4.16. For the S-wave, the LASS parametrisation results to be the best model, having the highest 89 Table 4.26: Binning scheme for each of the re-weighted variables. Bins have equal width. variables range #bins pK±[0,140] GeV/c210 pπ±[0,60] GeV/c210 In the nominal fit to B0 s→J/ψK∗0data, the normalisation weights calculated with B0→J/ψK∗0simulated events are used. To validate this choice, fits performed using weights extracted from B0 s→J/ψK∗0and B0→J/ψK∗0simulated samples before the iterative procedure are compared. The fits are performed simultaneously in 4 bins of mKπ around the K∗0nominal mass, i.e mKπ ∈[826,966] MeV/c2. The results of both fits are compatible, as reported in Table 4.27. Table 4.27: Parameters resulting from the angular fit performed simultaneously in 4 mKπ bins around the K∗(892)0nominal mass, using simulated samples. The values of the polarisation-dependent CP asymmetries are blinded. The last column is the difference between the fitted value of each parameter in both fits. Parameter B0→J/ψK∗0B0 s→J/ψK∗0Abs. diff. ACP 0blind ±0.061 blind+0.061 −0.060 0.015 ACP Sblind+0.114 −0.112 blind+0.115 −0.112 0.023 ACP kblind ±0.164 blind ±0.164 0.035 ACP ⊥blind+0.101 −0.100 blind+0.101 −0.100 0.023 f00.502 ±0.026 0.507 ±0.026 0.005 fk0.177+0.029 −0.027 0.173+0.028 −0.027 0.003 δk−2.570+0.169 −0.174 −2.524+0.168 −0.173 0.046 δ⊥0.033+0.121 −0.122 0.056+0.119 −0.120 0.023 FS826 861 0.445+0.117 −0.119 0.433+0.117 −0.116 0.012 δS826 861 0.482+0.170 −0.173 0.513+0.170 −0.175 0.032 FS861 896 0.075+0.030 −0.024 0.077+0.030 −0.024 0.002 δS861 896 −0.497+0.265 −0.224 −0.522+0.250 −0.212 0.025 FS896 931 0.065+0.054 −0.039 0.060+0.052 −0.037 0.005 δS896 931 −1.744+0.175 −0.224 −1.763+0.182 −0.240 0.019 FS931 966 0.589+0.105 −0.114 0.584+0.105 −0.113 0.005 δS931 966 −1.841+0.146 −0.161 −1.826+0.144 −0.158 0.015 96 4.4.4 CP asymmetries In this analysis, the following CP asymmetry can be built ACP (B0 (s)→f(s)) = Z∞ 0hΓ(B0 (s)→¯ f(s)) + Γ(B0 s→¯ f(s))idt−Z∞ 0hΓ(B0 (s)→f(s)) + Γ(B0 s→f(s))idt Z∞ 0hΓ(B0 (s)→¯ f(s)) + Γ(B0 s→¯ f(s))idt+Z∞ 0hΓ(B0 (s)→f(s)) + Γ(B0 s→f(s))idt ,(4.18) being f(s)=J/ψK∗0(K∗0) and ¯ f(s)=J/ψK∗0(K∗0), where B0 sdecays into a K∗0meson (→K−π+) and B0decays into a K∗0meson (→K+π−). The angular distribution as a function of the amplitudes for B0 sand B0 sis given in Appendix C.1. If |p/q|= 1 is assumed, it is clear from (4.18) that the time-dependence factorizes and can be cancelled out to get, in a simplified notation (here and throughout this section), ACP =Γ(B0 s→¯ f(s))−Γ(B0 (s)→f(s)) Γ(B0 s→¯ f(s)) + Γ(B0 (s)→f(s)).(4.19) For the three polarisation states (0,k,⊥), it is measured Araw CP (B0 (s)→f(s)) = Nobs(¯ f(s))−Nobs(f(s)) Nobs(¯ f(s)) + Nobs(f(s)),(4.20) then, calling N+(N−) the number of events with a positive (negative) final state kaon, one can write |Ai|2=N+|A+ i|2+N−|A− i|2 N++N−,(4.21) where idenotes a given polarisation state (i=S, 0,k,⊥) and A± ithe corresponding amplitude measured in the sample with a positive (negative) kaon. Explicitly imposing the normalisation Pi|Ai|2= 1 and introducing untagged polarisation fractions for the P-wave, f0,fkand f⊥, it can be written |Ak|2= (1 −|As|2)fk(k= 0,k,⊥),(4.22) with the normalisation condition Pkfk= 1. The CP asymmetry for the given polarisation is ACP i=N+|A+ i|2−N−|A− i|2 N+|A+ i|2+N−|A− i|2,(4.23) so given the CP asymmetries, the untagged polarisation fractions and the overall signal yields, one can easily compute the polarisation fractions to be used in each sample, where 97 ξ=N++N−/2N+, as |A+ S|2=ξ(1 + ACP S)|AS|2,(4.24) |A+ k|2=ξ(1 + ACP k)(1 −|AS|2)fk,(4.25) |A− S|2=ξ 2ξ−1(1 −ACP S)|AS|2,(4.26) |A− k|2=ξ 2ξ−1(1 −ACP k)(1 −|AS|2)fk.(4.27) (4.28) However, the raw asymmetry is corrected as follows ACP (B0 (s)→f(s)) = Araw CP (B0 (s)→f(s))−ζ(s)AD(f)−κ(s)AP(B0 (s)),(4.29) where AD(f) is the detection asymmetry, AP(B0 (s)) the production asymmetry, ζ(s)= +1(−1) and κ(s)account for the dilution due to B0 (s)−B0 soscillations [141]. κ(s)can be written as κ(s)=R∞ 0e−Γ(s)tcos∆M(s)tε(B0 (s)→Kπ;t)dt R∞ 0e−Γ(s)tcosh∆Γ(s) 2tε(B0 (s)→Kπ;t)dt ,(4.30) where ε(t) is the time-dependent acceptance function. Now, the extended PDFs used in the fit cannot be normalised to N±because the overall yields are affected by previously defined asymmetries. Therefore, the chosen definition for the normalisation factors of the PDFs is ˜ N±= (1 ±ACP I)N±,(4.31) where ACP Icontains the induced CP asymmetries. The presence of a B0 (s)−B0 sproduction asymmetry must be considered. The effective Bproduction asymmetries for this analysis are obtained from reweighting the results reported in Tables 3 and 4 of ref. [142] for the different bins in Btransverse momentum and pseudorapidity. The production asymmetry is defined as Aprod(B)≡σ(B)−σ(B) σ(B) + σ(B),(4.32) where σrepresents the production cross-section. The production asymmetries AP(B) reported in Tables 3 and 4 are reweighted as Aeff prod(B)≡X Bins i fiAP,i(B), fi≡#B∈Bin i NB ,(4.33) where fiis the fraction of B0 (s)events in bin i, obtained by summing over the sWeights obtained from a fit to the mass distribution of the nominal data sample. Using the weights 98 Table 4.28: B0production asymmetries in bins of Btransverse momentum pTand pseudorapidity η, and the event weights obtained from sWeighted B0→J/ψK∗0candidates. For AP,i(B0) the first uncertainty is statistical, whereas the second is systematic. Bin pT( GeV/c)ηWeight fiAP,i(B) 1 ( 1.0, 4.0) (4.5,5.2) 0.0350 ±0.0004 0.0016 ±0.0253 ±0.0016 2 ( 1.0, 4.0) (3.7,4.5) 0.1037 ±0.0007 −0.0158 ±0.0162 ±0.0015 3 ( 2.0, 4.0) (3.0,3.7) 0.0552 ±0.0005 0.0055 ±0.0254 ±0.0016 4 ( 4.0,12.0) (4.5,4.7) 0.0031 ±0.0001 0.0160 ±0.0736 ±0.0067 5 ( 4.0, 7.0) (3.7,4.5) 0.0957 ±0.0007 −0.0189 ±0.0158 ±0.0032 6 ( 4.0, 7.0) (3.0,3.7) 0.1671 ±0.0010 −0.0311 ±0.0132 ±0.0014 7 ( 4.0, 7.0) (2.5,3.0) 0.0513 ±0.0005 0.0556 ±0.0254 ±0.0020 8 ( 7.0,12.0) (3.7,4.5) 0.0432 ±0.0005 −0.0145 ±0.0205 ±0.0027 9 ( 7.0,12.0) (3.0,3.7) 0.1558 ±0.0009 −0.0142 ±0.0111 ±0.0015 10 ( 7.0,12.0) (2.5,3.0) 0.1035 ±0.0007 −0.0236 ±0.0138 ±0.0014 11 ( 7.0,12.0) (2.2,2.5) 0.0172 ±0.0003 −0.0190 ±0.0348 ±0.0034 12 (12.0,30.0) (3.7,4.5) 0.0080 ±0.0002 −0.0550 ±0.0473 ±0.0020 13 (12.0,30.0) (3.0,3.7) 0.0508 ±0.0005 0.0067 ±0.0180 ±0.0021 14 (12.0,30.0) (2.5,3.0) 0.0557 ±0.0005 0.0177 ±0.0162 ±0.0023 15 (12.0,30.0) (2.0,2.5) 0.0276 ±0.0004 −0.0018 ±0.0236 ±0.0020 A ( 0.2, 1.0) (4.5,6.0) 0.0098 ±0.0002 −0.0391 ±0.0501 ±0.0016 B ( 1.0, 2.2) (5.2,6.0) 0.0034 ±0.0001 0.0523 ±0.0684 ±0.0025 and production asymmetries listed in Table 4.28 and Table 4.29 for the B0and B0 ssystem, respectively, the obtained effective production asymmetries are Aeff prod(B0) = ( −1.04 ±0.48 (stat) ±0.14 (syst))% ,(4.34) Aeff prod(B0 s) = ( −1.64 ±2.28 (stat) ±0.55 (syst))%.(4.35) In order to calculate the κ(s)factor (4.30), the decay time acceptance is determined on the nominal data sample after applying the B0sWeights (see Figure 4.15). As in [143], ε(t) = [1 + β(t−t0)][a(t−t0)]n 1+[a(t−t0)]n,(4.36) where a= 1.814, n = 1.552, t0= 0.219 and β= 0.020. The dilution factor in (4.30) is equal to 0.06% for B0 sdecays, and 41% for B0decays. This reduces the effect of the production asymmetry to the level of 10−5for B0 s→J/ψK∗0and 10−3for B0→J/ψK∗0 decays. At the level of 0.4%, the production asymmetry can still significantly contribute to the overall direct CP violation in the B0→J/ψK∗0decay channel. Another asymmetry arises from the detector acceptance, event reconstruction and the difference in the interaction cross-section between particles and antiparticles in the final 99 Table 4.29: B0 sproduction asymmetries in bins of Btransverse momentum pTand pseudorapidity η, and the event weights obtained from sWeighted B0 s→J/ψK∗0candidates. For AP,i(B0 s) the first uncertainty is statistical, whereas the second is systematic. Bin pT( GeV/c)ηWeight fiAP,i(B) 1 ( 2, 4) (3.0,5.0) 0.1670 ±0.0104 −0.1475 ±0.0895 ±0.0192 2 ( 4, 8) (3.5,4.5) 0.1811 ±0.0109 −0.0471 ±0.0513 ±0.0112 3 ( 4, 9) (2.5,3.5) 0.2819 ±0.0142 0.0376 ±0.0467 ±0.0083 4 ( 8,12) (3.5,4.5) 0.0523 ±0.0055 0.0582 ±0.0537 ±0.0053 5 ( 8,12) (2.5,3.5) 0.1820 ±0.0110 0.0370 ±0.0332 ±0.0051 6 (12,30) (3.5,4.5) 0.0123 ±0.0026 −0.0339 ±0.0750 ±0.0095 7 (12,30) (2.5,3.5) 0.0786 ±0.0069 −0.0333 ±0.0309 ±0.0040 8 ( 8,30) (2.2,2.5) 0.0281 ±0.0040 −0.0351 ±0.0485 ±0.0059 B0_LOKI_DTF_CTAU 0.5 1 1.5 2 2.5 Events / ( 0.05 ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time acceptance Figure 4.15: Decay time acceptance fit on data. state and the detector. AD(f) is the detection asymmetry of the final state f, defined in terms of the detection efficiencies as AD(f)≡(¯ f)−(f) (¯ f) + (f),(4.37) where AD,i(Kπ) is measured in bins of the K+momentum is used, assuming a negligible contribution from the pion to this asymmetry [144], and then weighting this with the 100 Table 4.30: (K−π+) detection asymmetries in bins of kaon momentum, and the event weights obtained from sWeighted B0→J/ψK∗0candidates. The uncertainty is statistical [144]. Bin p( GeV/c) Weight fiAD,i(K−) 1 (02.0,10.0) 0.1838 ±0.0010 −1.37 ±0.11 2 (10.0,17.5) 0.2957 ±0.0013 −1.21 ±0.10 3 (17.5,22.5) 0.1458 ±0.0009 −1.15 ±0.11 4 (22.5,30.0) 0.1445 ±0.0009 −1.10 ±0.12 5 (30.0,50.0) 0.1580 ±0.0009 −0.89 ±0.16 6 (50.0,70.0) 0.0471 ±0.0005 −0.72 ±0.29 7 (70.0,100) 0.0191 ±0.0003 −0.33 ±0.30 8 (100 ,150) 0.0054 ±0.0002 0.18 ±0.45 Table 4.31: (K−π+) detection asymmetries in bins of kaon momentum, and the event weights obtained from sWeighted B0 s→J/ψK∗0candidates. The uncertainty is statistical [144]. Bin p( GeV/c) Weight fiAD,i(K−) 1 (02.0,10.0) 0.1655 ±0.0104 −1.37 ±0.11 2 (10.0,17.5) 0.2782 ±0.0141 −1.21 ±0.10 3 (17.5,22.5) 0.1349 ±0.0092 −1.15 ±0.11 4 (22.5,30.0) 0.1424 ±0.0095 −1.10 ±0.12 5 (30.0,50.0) 0.1842 ±0.0110 −0.89 ±0.16 6 (50.0,70.0) 0.0664 ±0.0063 −0.72 ±0.29 7 (70.0,100) 0.0210 ±0.0034 −0.33 ±0.30 8 (100 ,150) 0.0066 ±0.0019 0.18 ±0.45 momentum distribution of the kaon resulting from B0 (s)→J/ψK∗0(K∗0) decay. Aeff D(B)≡X Bins i fiAD,i(B), fi≡#B∈Bin i NB (4.38) For simplicity, a correlation of 100% between the bins is assumed. Using the kaon detection asymmetries reported in Table 4.30, the following detection asymmetries for B0and B0 s are obtained, respectively Aeff D(B0) = (1.115 ±0.547 (stat))%,(4.39) Aeff D(B0 s) = (−1.086 ±0.531 (stat))%.(4.40) As a reminder, B0 sdecays to a K∗0, while the B0gives K∗0, hence the above opposite signs are expected, following the definition in (4.29). 101 4.5 Measurement of B(B0 s→J/ψK∗0) Two normalised branching fractions are obtained: one with respect to the B0 s→J/ψφ decay channel (ideal for the study of penguin pollution), and the other one with respect to the B0→J/ψK∗0mode (ideal for the cancellation of systematic uncertainties in the efficiency evaluation). Then, a weighted average taking into account both results is calculated, leading to a final value of the B0 s→J/ψK∗0branching fraction. For the first step, the following expression to calculate the normalised B0 s→J/ψK∗0 branching fraction to a given decay Bq→J/ψX is used, B(B0 s→J/ψK∗0)×B(J/ψ →µ+µ−)×B(K∗0→K+π−) B(Bq→J/ψX)= NB0 s→J/ψK∗0 NBq→J/ψX ×εBq→J/ψX εB0 s→J/ψK∗0×P(b→Bq) P(b→B0 s),(4.41) where Nrefers to the number of events of that given decay, εcorresponds to the total (reconstruction, trigger and selection) efficiency (see 4.5.1), and Pare the hadronisation probabilities of the bquark to a given Bmeson. For the second step, the procedure to obtain the weighted average is described in detail in Appendix D.1. 4.5.1 Efficiency ratios obtained from simulation The ratios of efficiencies are taken from simulation, separately for 2011 and 2012 conditions. Simulated samples used are described in Chapter 4.1.2, where an MC-truth condition is imposed for daughter hadrons. A total efficiency using simulated samples (reconstruction, trigger and selection), εTOT, is computed separately for each data-taking year conditions. The requirements of the offline selection used for the B0 s→J/ψφ normalisation mode are listed in Table 4.32, where the same BDTG constructed and optimised for B0 s→J/ψK∗0signal decays (see Chapter 4.1.4) is used. For the B0→J/ψK∗0channel, the same final selection requirements as for B0 s→J/ψK∗0decays are used, described in Chapter 4.1. The values of these total efficiencies are shown in Table 4.33, where their ratios are, for 2011 (2012) conditions, εMC B0→J/ψK∗0 εMC B0 s→J/ψK∗0 = 0.929 ±0.012 (0.927 ±0.012),(4.42) εMC B0 s→J/ψφ εMC B0 s→J/ψK∗0 = 1.991 ±0.025 (1.986 ±0.027).(4.43) A detailed discussion can be found in Appendix D.2. Due to the similarity of the final state between signal and normalisation channel in the case of the normalisation to the B0→J/ψK∗0decay mode, the systematics associated to discrepancies between data and simulation are assumed to cancel out. However, as the efficiency depends on the 102 angular distribution of the decay products, a correction due to the difference between the angular amplitudes used in simulation and those measured on data has to be done. This is discussed in Chapter 4.5.2, for both normalisations to B0→J/ψK∗0and B0 s→J/ψφ decay channels. Table 4.32: Final selection criteria for B0 s→J/ψφ candidates. Cut variable Cut value J/ψ →µµ |M(µ+µ−)−M(J/ψ)|<150 MeV/c2 χ2 vtx/ndof(J/ψ)<16 χ2 DOCA/ndof(J/ψ)<20 ∆LLµπ(µ)>0 χ2 IP(µ)>16 pT(µ)>0.5 GeV/c IsMuon(µ) true φ→K−K+|M(K−K+)−1019.46|<20 MeV/c2 pT(φ)>1.0 GeV/c χ2 vtx/ndof(φ)<25 χ2 DOCA/ndof(φ)<30 pT(K)>0.5 GeV/c χ2 IP(K)>2 ∆LLKπ(K)>0 χ2 track/ndof(K)<5 ProbNNK(K)>0.21 ProbNNK(K)/ProbNNp(K)>0.99 B0 s→J/ψφ M(B0 s)∈[5150,5650] MeV/c2 χ2 vtx/ndof(B0 s)<10 DIRA(B0 s)>0.999 VS >1.5 mm BDTG (2011/2012) >0.2/>0.12 B+→J/ψK+veto |M(J/ψ, K)−5279|>60 MeV/c2 Table 4.33: Total efficiencies obtained from simulation. εMC (2011) (%) εMC (2012) (%) B0→J/ψK∗00.5482 ±0.0046 0.5052 ±0.0040 B0 s→J/ψφ 1.1742 ±0.0099 1.0823 ±0.0098 B0 s→J/ψK∗00.5898 ±0.0054 0.5451 ±0.0054 103 4.5.2 Physical corrections due to angular distributions The number of events (NB0 s→J/ψK∗0,NB0→J/ψK∗0,NB0 s→J/ψφ) can be approximately obtained from a fit to the mass distribution of Bcandidates selected around the pole of the corresponding hh resonance. The number of events NB0 s→J/ψφ is obtained from a fit to the M(J/ψ, KK) distribution of events selected with the final selection cuts described in Chapter 4.1 (see Figure 4.16). However, some correction is needed, since the peak is polluted with S-wave as well as S-wave/P-wave interference. Thus, Nfit =NP−wave +NS−wave +Ninterference,(4.44) where the last term, Ninterference vanishes in the case of a flat angular acceptance, but not otherwise. Thus, the relative contribution that is not pure P-wave needs to be calculated. This can be done by means of an angular analysis, NP−wave Nfit =R4πR+∞ 0Rmhhbin |A(Ω, t, mhh|AS= 0)|2ε(Ω, t, mhh)dΩdt dmhh R4πR+∞ 0Rmhhbin |A(Ω, t, mhh)|2ε(Ω, t, mhh)dΩdt dmhh ,(4.45) where the integral is folded over mhh in the CSP factors, and the integral over the angles in the normalisation weights. The decay time acceptance is irrelevant for B0 (s)→ J/ψK∗0(K∗0), but not for B0 s→J/ψφ since the angular distribution is time dependent. Hence, the fraction of the P-wave resonance in a given decay is FRes decay := NP−wave NmassFit =R+∞ 0Pi,j!=S ij ξij ×A∗ iAj(t)ε(t)dt R+∞ 0Pij ξij ×Cij ×A∗ iAj(t)ε(t)dt,(4.46) where ξij are the normalisation weights, shown in Table 4.34. In the case of the B0 s→ J/ψK∗0one can ignore the lifetime dependence of the PDF, since it factorizes out from the angular PDF and hence cancels out in the ratio. In addition to the correction of the observed yield in which the subtraction of the contribution from sub-dominant waves is done, it would be also needed to correct the efficiencies obtained in the simulation because the generator values of the decay parameters differ slightly from the measured ones. For this purpose, it is defined cdecay := εdata decay εMC decay =R+∞ 0Pi,j!=S ij ξij ×a∗ iaj(t)ε(t)dtkdata R+∞ 0Pi,j!=S ij ξij ×a∗ iaj(t)ε(t)dtkMC ,(4.47) where in this case the P-wave amplitudes aare re-normalised so that |a|||2+|a0|2+|a⊥|2= 1. For B0 s→J/ψφ decays, it can be assumed cB0 s→J/ψφ = 1 to a very good precision, since the simulated samples were generated with latest measurements from data [145]. Defining κdecay =cdecay FRes decay ,(4.48) 104 Table 4.34: Uncorrected angular acceptance weights computed on B0 s→J/ψφ simulated samples. The normalisation weights are normalised with respect to the ξ00 weight. k ξk/ξ1 1 (00) +1.00000 2 (kk) +1.19377 3 (⊥⊥) +1.05515 4 (k⊥)−0.03926 5 (0k) +0.24583 6 (0⊥)−0.02961 7 (SS) +1.10256 8 (Sk)−0.06505 9 (S⊥) +0.09569 10 (S0) −0.12612 ] 2 KK) [MeV/cψM(J/ 5150 5200 5250 5300 5350 5400 5450 5500 5550 5600 5650 Events / ( 5 ) 0 2000 4000 6000 8000 10000 12000 14000 16000 Figure 4.16: Simultaneous fit (2011 + 2012 conditions) to M(J/ψ, KK) using Hypatia distribution to model B0 s→J/ψK+K−and an exponential distribution to model the combinatorial background (resulting in 58091 ±243 (stat) ±319 (syst) candidate events). which is convenient since Fand cshare common parameters, one can rewrite the normalisation expression as B(B0 s→J/ψK∗0) B(Bq→J/ψX)=NmassFit B0 s→J/ψKπ NmassFit Bq→J/ψX ×εMC Bq→J/ψX εMC B0 s→J/ψK∗0×κBq→J/ψX κB0 s→J/ψK∗0 .(4.49) To calculate κB0 s→J/ψφ, the time-dependent efficiency ε2(t) of the B0 s→J/ψφ events is needed. It is obtained from simulation and parametrised as (see Figure 4.17) ε2(t)∝p2 1 + p1×tp0.(4.50) The parameter values are shown in Table 4.36. 105 Table 4.38: Summary of the measured B0 s→J/ψK∗0P-wave properties and their statistical and systematic uncertainties. When no value is given, it means an uncertainty below 5×10−4, except for the two phases, δkand δ⊥, where the uncertainty is below 5 ×10−3. f0fkδkδ⊥ACP 0ACP kACP ⊥ Nominal value 0.497 0.179 −2.70 0.01 −0.048 0.171 −0.049 Statistical uncertainties +0.024 −0.025 +0.027 −0.026 +0.15 −0.16 0.11 0.057 0.152 +0.095 −0.096 Angular acceptance 0.018 0.008 0.02 0.01 0.009 0.017 0.008 (sim. stat) Angular acceptance 0.015 0.007 0.17 0.10 0.007 — 0.015 (data-sim. corrections) CSP factors — 0.001 — — 0.001 0.002 0.002 D-wave contribution 0.004 0.003 — — 0.002 0.015 0.002 Background +0.004 −0.003 0.002 0.02 0.01 +0.003 −0.004 +0.012 −0.004 0.002 angular model Mass parameters and — — — — 0.001 0.001 — B0contamination Mass–cos(θµ)0.007 0.006 0.07 +0.02 −0.04 0.014 +0.009 −0.012 0.016 correlations Fit bias — 0.001 0.01 0.07 0.003 0.002 0.005 Detection — — — — 0.005 0.005 +0.005 −0.006 asymmetry Production — — — — — — — asymmetry Quadratic sum of 0.025 0.013 0.19 +0.012 −0.013 +0.019 −0.020 +0.028 −0.027 0.025 systematics Total uncertainties 0.035 +0.030 −0.029 +0.24 −0.25 +0.016 −0.017 0.060 0.154 +0.098 −0.099 112 Table 4.39: Summary of the measured B0 s→J/ψK∗0S-wave properties and their statistical and systematic uncertainties. When no value is given, it means an uncertainty below 5 ×10−4, except for the four strong phases related to the S-wave component, δS, where the uncertainty is below 5 ×10−3. ACP S mbin1 Kπ mbin2 Kπ mbin3 Kπ mbin4 Kπ FSδSFSδSFSδSFSδS Nominal value 0.167 0.475 0.54 0.080 −0.53 0.044 −1.46 0.523 −1.76 Statistical uncertainties +0.113 −0.114 +0.108 −0.112 0.16 +0.031 −0.025 +0.25 −0.21 +0.042 −0.029 +0.22 −0.19 +0.109 −0.112 +0.13 −0.14 Angular acceptance 0.028 0.039 0.03 0.012 0.065 0.015 0.10 0.065 0.06 (sim. stat) Angular acceptance 0.015 0.058 0.08 0.019 0.18 0.027 0.27 0.006 0.04 (data–sim. corrections) CSP factors — 0.002 0.01 0.001 — 0.002 — 0.001 0.01 D-wave contribution 0.008 0.010 0.02 0.005 0.03 0.008 0.08 0.002 0.04 Background 0.001 0.002 0.01 +0.000 −0.001 0.01 — +0.03 −0.02 +0.002 −0.000 +0.07 −0.04 angular model Mass parameters and 0.001 0.001 +0.00 −0.01 — — — — — — B0contamination Mass–cos(θµ)+0.023 −0.029 +0.040 −0.028 0.05 0.003 0.04 +0.006 −0.016 0.02 +0.009 −0.011 +0.02 −0.03 correlations Fit bias 0.004 0.005 0.01 0.003 0.02 0.007 0.032 0.015 0.01 Detection 0.005 — — — — — — — — asymmetry Production — — — — — — — — — asymmetry Quadratic sum of +0.041 −0.044 +0.081 −0.076 0.10 0.023 0.20 +0.033 −0.036 0.30 0.068 +0.11 −0.09 systematics Total uncertainties +0.120 −0.122 0.135 0.19 +0.039 −0.034 +0.32 −0.29 +0.054 −0.047 +0.37 −0.35 +0.128 −0.131 0.17 113 4.7 Results The main results from this analysis are summarized in this section. A further discussion on penguin pollution in the φsphase, using these results, is presented in next Chapter 5. 4.7.1 Angular analysis and mass fit Using 3 fb−1of real data, a simultaneous fit is carried out in 4 bins of mKπ around the K∗0 nominal mass, i.e mKπ ∈[826,966] MeV/c2. All the steps of the fit model construction are described in Chapter 4.4.1. The parameters of interest are the polarisation fractions and polarisation-dependent CP asymmetries. The angular parameters obtained from the fit are summarized in Table 4.40 with their statistical uncertainties. The P-wave amplitudes and strong phases are common among the 4 bins of mKπ, while the S-wave parameters are split in the different bins. The previous analysis of B0 s→J/ψK∗0polarisation amplitudes and phases was based on fits with a single bin in mKπ and did not account for possible CP asymmetries. Using 0.37 fb−1, LHCb has measured [134] f0= 0.50 ±0.08 ±0.02,(4.65) fk= 0.19+0.10 −0.08 ±0.02,(4.66) δk=−2.78 ±0.54,(4.67) where f0and fkare the longitudinal and parallel polarisation fractions, respectively, defined as fi=|Ai|2/Pi|Ai|2,i= 0,k,⊥. The first uncertainty is statistical, the second is systematic. The results with 3 fb−1are compatible with (4.65), (4.66) and (4.67), and more accurate by a factor of 3. The signal angular distribution and the projections of the fitted PDF are shown in Figure 4.18. Slices of the same plots in bins of mKπ are shown in Appendix E. Additionally, the correlations between the fitted parameters are presented in Table 4.41. An additional compatibility check of the polarisation amplitudes between B0 s→J/ψK∗0and B0→J/ψK∗0decay modes is performed in view of the fitted parameters of Table 4.40. Namely the P-wave, S-wave fractions and the S-wave phases in bins of mKπ which are shown in Figure ??. The plots emphasize on the compatibility of P-wave and S-wave fractions trends between B0 s→J/ψK∗0and B0→J/ψK∗0. This is why the absolute scale is ignored and both curves are normalised to one. The fraction central values in each mKπ bin are estimated using (4.45) of Chapter 4.5.2, whereas the errors using σ(NS-wave B0 s,B0) = σ(NB0 s,B0·FS), σ(NP-wave B0 s,B0) = σ(NB0 s,B0·(1 −FS)).(4.68) The plots include only statistical uncertainties coming from NB0 s,B0and FS. As a reminder, NB0 s,B0is the B0 s,B0fitted signal yield that comes from the fit B0 smass of Chapter 4.3.2. An additional systematic is added due to the assumption of ACP = 0. The dominant source of uncertainty is statistical. 114 Table 4.40: Parameters resulting from the angular fit performed simultaneously in four mKπ bins around the K∗(892)0nominal mass. Measured value ACP 0−0.048 ±0.057 ACP k0.171 ±0.152 ACP ⊥−0.049+0.095 −0.096 ACP S0.167+0.113 −0.114 f00.497+0.024 −0.025 fk0.179+0.027 −0.026 δk−2.70+0.15 −0.16 δ⊥−0.01 ±0.11 FS826 861 0.475+0.108 −0.112 δS826 861 0.54 ±0.16 FS861 896 0.080+0.031 −0.025 δS861 896 −0.53+0.25 −0.21 FS896 931 0.044+0.042 −0.029 δS896 931 −1.46+0.22 −0.19 FS931 966 0.523+0.109 −0.112 δS931 966 −1.76+0.13 −0.14 4.7.2 Comparison with results from B0→J/ψρ0analysis The polarisation fractions and CP asymmetries obtained here for B0 s→J/ψK∗0are also compared with those from a previous LHCb B0→J/ψρ0analysis [112] in Table 4.42. In the SU(3)-limit and ignoring contributions from additional decay topologies, these results should agree. However, because the B0→J/ψρ0mode also has contributions from exchange and penguin-annihilation diagrams which do not have a counterpart in B0 s→J/ψK∗0decays, differences can arise. The direct CP asymmetries are in good agreement with one another. The difference is not significant enough to deduce any information on SU(3)-breaking. 4.7.3 Branching fraction measurement A correlated weighted average for B(B0 s→J/ψK∗0) is also obtained (see Chapter 4.5.5), B(B0 s→J/ψK∗0) = (4.14 ±0.18(stat) ±0.26(syst) ±0.24(fd fs )) ×10−5,(4.69) which is in good agreement with previous LHCb publication [115] as well as with SM expectations [22]. 115 Table 4.41: Statistical correlation matrix for the parameters from the angular fit. ACP 0ACP SACP kACP ⊥F0 SF1 SF2 SF3 Sδkδ⊥δ0 Sδ1 Sδ2 Sδ3 Sf0fk ACP 0+1.00 −0.12 −0.11 −0.17 −0.13 −0.02 −0.06 −0.01 +0.03 +0.02 +0.10 −0.00 +0.07 +0.01 +0.06 −0.05 ACP S+1.00 −0.14 −0.12 +0.16 −0.12 +0.03 −0.10 +0.00 −0.06 +0.02 +0.07 +0.05 +0.07 +0.01 +0.03 ACP k+1.00 −0.49 +0.02 +0.09 −0.02 +0.08 +0.09 +0.06 −0.06 −0.04 −0.05 −0.12 −0.04 −0.07 ACP ⊥+1.00 −0.00 −0.01 −0.06 −0.07 −0.09 −0.03 −0.03 +0.01 −0.02 +0.07 +0.01 −0.06 F0 S+1.00 +0.01 −0.01 −0.03 −0.10 −0.24 −0.77 +0.01 +0.04 −0.00 +0.10 −0.09 F1 S+1.00 −0.01 −0.00 −0.02 −0.05 −0.01 −0.25 +0.03 −0.01 +0.15 −0.10 F2 S+1.00 +0.01 −0.04 +0.07 +0.01 −0.00 −0.22 +0.00 −0.02 +0.04 F3 S+1.00 +0.08 +0.08 +0.00 −0.01 −0.03 −0.29 −0.09 +0.04 δk+1.00 +0.62 +0.10 +0.14 +0.03 +0.11 +0.04 −0.03 δ⊥+1.00 +0.17 +0.13 −0.02 +0.13 +0.05 −0.04 δ0 S+1.00 +0.04 +0.03 +0.04 +0.08 +0.04 δ1 S+1.00 +0.04 +0.04 +0.13 −0.05 δ2 S+1.00 +0.04 +0.27 −0.08 δ3 S+1.00 +0.11 +0.00 f0+1.00 −0.34 fk+1.00 116 Figure 4.18: Angular PDF plots on top of the fitted sWeighted data for B0 s→J/ψK∗0. Blue solid: total. Blue dashed: P-wave + P-P interference. Green dotted: S-wave. Red dotteddashed: S-P interference. ) K θcos( 1−0.5−0 0.5 1 Candidates / 0.1 20− 0 20 40 60 80 100 ) K θcos( 1−0.5−0 0.5 1 4−2−0 2 4 ) µ θcos( 1−0.5−0 0.5 1 Candidates / 0.1 0 20 40 60 80 100 ) µ θcos( 1−0.5−0 0.5 1 4−2−0 2 4 (rad) h φ 2−0 2 ] -1 Candidates / 0.31 [rad 0 20 40 60 80 100 (rad) h φ 2−0 2 4−2−0 2 4 Table 4.42: Comparison between the results from B0 s→J/ψK∗0decays presented in this work and those from B0→J/ψρ0analysis [112]. The systematic uncertainties are included. B0→J/ψρ0B0 s→J/ψK∗0Difference Sig. ACP 00.094 ±0.071 −0.048 ±0.060 −0.142 ±0.093 −1.5σ ACP k0.122 ±0.120 0.171 ±0.155 0.049 ±0.196 0.3σ ACP ⊥−0.034 ±0.222 −0.049 ±0.099 −0.015 ±0.243 −0.1σ f00.574 ±0.037 0.497 ±0.035 0.077 ±0.051 1.5σ fk0.234 ±0.021 0.179 ±0.030 0.055 ±0.037 1.5σ f⊥0.192 ±0.042 0.324 ±0.033 −0.132 ±0.053 −2.5σ 117 Chapter 5 Penguin pollution in the φsphase The penguin pollution as given by (2.33) in Chapter 2.3, ∆φs,i, is parameterised [110,150] by the relative size aiof the penguin to tree amplitudes, which has an associated strong phase difference θiand weak phase difference is given by the UT angle γ. Alternatively, the penguin effects can also be parametrised in cartesian coordinates as <[ai] = aicos θi and =[ai] = aisin θi. The penguin parameters aiand θican be extracted from two times three parameters (two for each polarisation i) [108,110,150]: •Hi, related to the branching fraction ratios and polarisation fractions, Hi≡1 A0 i Ai 2PHSP (B0 s→J/ψφ) PHSP(B0 s→J/ψK∗0)B(B0 s→J/ψK∗0)theo B(B0 s→J/ψφ)theo fi f0 i ,(5.1) =1−2aicos θicos γ+a2 i 1+2a0 icos θ0 icos γ+2a02 i , •ACP i, the direct CP violation asymmetries, 1 ACP i=−2aisin θisin γ 1−2aicos θicos γ+a2 i .(5.2) In the above equations, the prime (0) refers to the B0 s→J/ψφ channel while the nonprimed quantities refers to the B0 s→J/ψK∗0channel. A0 i/Aiare hadronic quantities discussed in the Chapter 5.1. Here, PHSP(B→V1V2)≡1 16πmB ΦmV1 mB ,mV2 mB,(5.3) is a phase-space factor, where mBis the mass of the Bmeson, and Φ is the standard two-body phase-space factor. Contrary to B→V P and B→PP decays and due to the complexity of the expressions for the hadronic amplitudes of B→V V decays, all 1Conventions: ACP i=−ACP dir used in ref. [110]. 118 other mass-dependent terms are absorbed into the ratio A0 i/Ai. Note that the conversion factors [151] B(Bs→f)theo B(Bs→f)exp =1−y2 s 1 + A∆Γ ys, ys≡∆Γs 2Γs ,(5.4) between the “theoretical” branching ratio concept and the experimentally measured timeintegrated branching fraction depend on the CP observable A∆Γ2and are therefore polarisation dependent. As B0 s→J/ψK∗0is a flavour specific decay, A∆Γ(B0 s→J/ψK∗0) = 0, thus the conversion factor is equal to 0.9963 ±0.0006. For B0 s→J/ψφ,A∆Γ depends on the penguin parameters again. For simplicity, a=θ= 0 is assumed when calculating the correction factor in (5.4), obtaining 1.0608 ±0.0045 (0.9392 ±0.0045) for the CP even (odd) states. Assuming ai=a0 i, θi=θ0 i,(5.5) each pair of observables (5.1) and (5.2) can be used to determine the penguin parameters aiand θi. In turn, the penguin parameters quantify the penguin shift tan(∆ φs,i) = 2a0 icos θ0 isin γ+2a02 isin 2γ 1+2a0 icos θ0 icos γ+2a02 icos 2γ.(5.6) affecting the determination of φsfrom B0 s→J/ψφ decays. 5.1 External inputs The hadronic amplitudes |A0 i/Ai|are calculated following the method described in ref. [153], using the latest results on form factors from Light Cone QCD Sum Rules (LCSR) [154]. Further details on the calculation can be found in Section 5.5.1 of ref. [152]. The results are A0 0(B0 s→J/ψφ) A0(B0 s→J/ψK∗0)= 1.23 ±0.16 ,(5.7) A0 k(B0 s→J/ψφ) Ak(B0 s→J/ψK∗0)= 1.28 ±0.15 ,(5.8) A0 ⊥(B0 s→J/ψφ) A⊥(B0 s→J/ψK∗0)= 1.20 ±0.12 ,(5.9) and lead to H0= 0.98 ±0.07 (stat) ±0.06 (syst) ±0.26 (|A0 i/Ai|) = 0.98 ±0.28 ,(5.10) Hk= 0.90 ±0.14 (stat) ±0.08 (syst) ±0.21 (|A0 i/Ai|) = 0.90 ±0.26 ,(5.11) H⊥= 1.46 ±0.14 (stat) ±0.11 (syst) ±0.28 (|A0 i/Ai|) = 1.46 ±0.33 .(5.12) 2Defined e.g. in Eq. 4.47 of [152]. 119 5.2 Fit results For each of the three polarisation states individually, a modified least squares fit is performed. This means that correlations between the experimental inputs are ignored. It has three degrees of freedom: <[a], =[a] and γ, with the latter parameter being Gaussian constrained to [155] γ=73.2+6.3 −7.0◦.(5.13) The χ2functions reach their minimum value at <[a0] = 0.03+0.97 −0.32 ,=[a0] = 0.025+0.034 −0.031 , χ2 min = 1.3×10−7,(5.14) <[ak] = 0.31+0.57 −0.50 ,=[ak] = −0.082+0.074 −0.085 , χ2 min = 4.5×10−3,(5.15) <[a⊥] = −0.43+0.27 −0.21 ,=[a⊥] = 0.037+0.078 −0.075 , χ2 min = 1.2×10−6,(5.16) which translates to a0= 0.04+0.95 −0.04 , θ0=40+140 −220◦,(5.17) ak= 0.32+0.57 −0.32 , θk=−15+148 −14 ◦,(5.18) a⊥= 0.44+0.21 −0.27 , θ⊥=175+11 −10◦.(5.19) For the longitudinal polarisation state, the strong phase θis unconstrained. The constraints on the penguin parameters derived from the individual observables entering the χ2fit are illustrated as different light-coloured bands in Figure 5.1 and Figure 5.2 for the parametrisations in terms of (<[a],=[a]) and (θ, a), respectively. Assuming perfect SU(3) symmetry, the penguin parameters from (5.14) to (5.16) result in a penguin phase shift on φs(B0 s→J/ψφ), ∆φJ/ψφ s,0= 0.003+0.084 −0.011 (stat)+0.014 −0.009 (syst)+0.047 −0.030 (|A0 i/Ai|) = 0.003+0.097 −0.033 ,(5.20) ∆φJ/ψφ s,k= 0.031+0.047 −0.037 (stat)+0.010 −0.013 (syst)+0.032 −0.032 (|A0 i/Ai|) = 0.031+0.058 −0.051 ,(5.21) ∆φJ/ψφ s,⊥=−0.045+0.012 −0.012 (stat)+0.007 −0.008 (syst)+0.017 −0.024 (|A0 i/Ai|) = −0.045+0.022 −0.028 ,(5.22) or in degrees ∆φJ/ψφ s,0=0.2+4.8 −0.6(stat)+0.8 −0.5(syst)+2.7 −1.7(|A0 i/Ai|)◦=0.2+5.6 −1.9◦,(5.23) ∆φJ/ψφ s,k=1.8+2.7 −2.1(stat)+0.6 −0.8(syst)+1.8 −1.9(|A0 i/Ai|)◦=1.8+3.3 −2.9◦,(5.24) ∆φJ/ψφ s,⊥=−2.6+0.7 −0.7(stat)+0.5 −0.4(syst)+1.4 −1.0(|A0 i/Ai|)◦=−2.6+1.6 −1.3◦.(5.25) 5.3 SU(3)-breaking SU(3)-breaking effects are parametrised by including the SU(3)-breaking parameters ξ and δin the relation (5.5) a0 i=ξ×ai, θ0 i=θi+δ . (5.26) 120 Figure 5.4: Determination of the penguin parameters <[ai] and =[ai] through intersecting contours derived from the CP observables and branching ratio information in B0 s→ J/ψK∗0and B0→J/ψρ0. The inner dark-coloured line represents the contour associated with the central value of the input quantity.Superimposed are the confidence level contours obtained from a χ2fit to the data. Shown are the longitudinal (left), parallel (right) and perpendicular (bottom) polarisation. −1.0−0.8−0.6−0.4−0.2 0.0 0.2 0.4 0.6 0.8 1.0 Re[a0] −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 Im[a0] LHCb C0(B0→J/ψρ0) S0(B0→J/ψρ0) ACP 0(B0 s→J/ψK∗0) H0(B0→J/ψρ0) H0(B0 s→J/ψK∗0) Re[a0] = 0.00+0.10 −0.13 Im[a0] = −0.006 ±0.024 39 % C.L. 68 % C.L. 90 % C.L. −1.0−0.8−0.6−0.4−0.2 0.0 0.2 0.4 0.6 0.8 1.0 Re[ak] −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 Im[ak] LHCb Ck(B0→J/ψρ0) Sk(B0→J/ψρ0) ACP k(B0 s→J/ψK∗0) Hk(B0→J/ψρ0) Hk(B0 s→J/ψK∗0) Re[ak] = 0.01+0.11 −0.16 Im[ak] = −0.073+0.050 −0.052 39 % C.L. 68 % C.L. 90 % C.L. −1.0−0.8−0.6−0.4−0.2 0.0 0.2 0.4 0.6 0.8 1.0 Re[a⊥] −1.0 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 Im[a⊥] LHCb C⊥(B0→J/ψρ0) S⊥(B0→J/ψρ0) ACP ⊥(B0 s→J/ψK∗0) H⊥(B0→J/ψρ0) H⊥(B0 s→J/ψK∗0) Re[a⊥] = 0.03+0.12 −0.16 Im[a⊥] = 0.024 ±0.047 39 % C.L. 68 % C.L. 90 % C.L. 127 Figure 5.5: Determination of the penguin parameters aiand θithrough intersecting contours derived from the CP asymmetries and branching ratio information in B0 s→J/ψK∗0 and B0→J/ψρ0. The inner dark-coloured line represents the contour associated with the central value of the input quantity. Superimposed are the confidence level contours obtained from a χ2fit to the data. Shown are the longitudinal (top), parallel (middle) and perpendicular (bottom) polarisation. −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ0[deg] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a0 LHCb C0(B0→J/ψρ0) S0(B0→J/ψρ0) ACP 0(B0 s→J/ψK∗0) H0(B0→J/ψρ0) H0(B0 s→J/ψK∗0) a0= 0.01+0.10 −0.01 θ0=−(83+97 −263)◦ 39 % C.L. 68 % C.L. 90 % C.L. −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θk[deg] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 ak LHCb Ck(B0→J/ψρ0) Sk(B0→J/ψρ0) ACP k(B0 s→J/ψK∗0) Hk(B0→J/ψρ0) Hk(B0 s→J/ψK∗0) ak= 0.07+0.11 −0.05 θk=−(85+72 −63)◦ 39 % C.L. 68 % C.L. 90 % C.L. −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ⊥[deg] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a⊥ LHCb C⊥(B0→J/ψρ0) S⊥(B0→J/ψρ0) ACP ⊥(B0 s→J/ψK∗0) H⊥(B0→J/ψρ0) H⊥(B0 s→J/ψK∗0) a⊥= 0.04+0.12 −0.04 θ⊥= (38+142 −218)◦ 39 % C.L. 68 % C.L. 90 % C.L. 128 Chapter 6 Analysis of A0 1→µ+µ−decays First steps of a model-independent search for A0 1→µ+µ−decays, where A0 1corresponds to the light CP-odd Higgs boson in an extension of the Standard Model, the Next-To-Minimal Supersymmetric Standard Model (NMSSM) [31,32], are performed, using 2.97 fb−1of data from pp collisions recorded by the LHCb experiment at a centre-of-mass energy of √s= 7 (8) GeV during 2011 (2012). Upper limits in B(A0 1→µ+µ−) are prospected to be calculated using the CLs technique [156]. A possible model-dependent search, considering certain NMSSM production modes, may be taken into account. However, at the moment of writing this document, only selection and mass model studies were performed. In Chapter 6.1, the selection of A0 1→µ+µ−candidates, consisting in a simple “cutbased” selection together with more complex multivariate requirements using Uniform Boosted Decision Trees (UBDT), is presented. In Chapter 6.2, studies of the mass model used to fit the two-muon mass spectrum are explained. A summary of these early studies and future prospects for this analysis are presented in Chapter 6.3. 6.1 Event selection and data samples Real data (Chapter 6.1.1) and simulated data (Chapter 6.1.2) samples used for this analysis are presented in this section, with the requirements from the offline selection (Chapter 6.1.3) as well. The offline selection consists of two parts: a “cut-based” set of requirements to reduce the size of the real data sample to a manageable level, followed by the use of Uniform Boosted Decision Trees [116,157] to reject background as much as possible, keeping a high signal efficiency. 6.1.1 Real data samples Real data events for this analysis are selected from two LHCb datasets with a total integrated luminosity of 2.97 fb−1of pp collision data: •Reco14-Stripping21r1: corresponding to 0.98 fb−1of integrated luminosity, collected during 2011 at a centre-of-mass energy of √s= 7 TeV. 129 •Reco14-Stripping21: corresponding to 1.99 fb−1of integrated luminosity, collected during 2012 at a centre-of-mass energy of √s= 8 TeV. Both datasets have been analysed with DaVinci v36r1 and Bender v28r2p1 (Erasmus v11r2), and reconstructed using Brunel v43r2p6, CondDB tag cond-20141107. For 2011 (2012) conditions, the DDDB tag was dddb-20130929 (dddb-20130929-1). 6.1.2 Simulated samples Simulated samples used in this analysis can be classified in three different groups: •A first group of three sets of samples containing each one simulated decays of different spectroscopic excited states of the Υ meson, Υ(1S) →µ+µ−decays, Υ(2S) →µ+µ−decays and Υ(3S) →µ+µ−decays, respectively. •A second group of two sets of samples, containing each one simulated decays of the A0 1→µ+µ−mode, but under different mass hypotheses for the A0 1boson, M(A0 1) = 10 GeV/c2and M(A0 1) = 12 GeV/c2, respectively. •A third group of a single set of samples, containing simulated Drell-Yan (DY) processes with a mass threshold of 5 GeV/c2and where the virtual neutral boson decays to a pair of muons, namely Z/γ∗→µ+µ−decays. Two pair of samples per set, containing each pair approximately the same number of simulated events, are used: one pair is representative of the data taken during 2011 (Reco14a/Reco14c-Stripping20r1, flagging mode, TCK 0x40760037), whilst the other pair is representative of the data taken during 2012 (Reco14a/Reco14c-Stripping20, flagging mode, TCK 0x409f0045). The only difference between members of a same pair is the polarity of the LHCb dipole magnet in the simulation. In summary, four samples (one per year and magnet polarity) per decay mode (three Υ meson decays, two A0 1boson modes and one Drell-Yan channel) are used: 2 (polarity) ×2 (year) ×6 (decay mode). The total number of simulated events per simulated mode are approximately 6 M per each Υ decay mode, 0.2 M per each A0 1decay channel, and 2 M of Drell-Yan events. This information is summarized in Table 6.1. Information about the software packages used to simulate these samples can be found in Chapter 3.2.5, where Table 3.2 summarizes their corresponding versions. 6.1.3 “Cut-based” requirements The “cut-based” set of requirements consists of two subsets: a first subset of cuts, applied once by the LHCb computing team to the triggered LHCb data immediately before the data sample is constructed, called “stripping line” (see Chapter 3.2.5); followed by a second subset of offline cuts tuned for the present analysis. To select A0 1→µ+µ−signal decays in real (simulated) data samples, the stripping line used is named Stripping(A1MuMu)A1MuMuLine. Table 6.2 lists the final “cut-based” selection 130 Table 6.1: Simulated samples used in the analysis of A0 1→µ+µ−decays. Approximately half of the events are simulated with the LHCb magnet polarity up, while the other half with polarity down. Decay mode Simulated events Sim pass TCK (year) Stripping version Υ(1S) →µ+µ−2 024 999 Sim08c 0x40760037 (2011) Stripping20r1 4 019 988 Sim08c 0x409f0045 (2012) Stripping20 Υ(2S) →µ+µ−2 019 995 Sim08c 0x40760037 (2011) Stripping20r1 4 036 985 Sim08c 0x409f0045 (2012) Stripping20 Υ(3S) →µ+µ−2 019 995 Sim08c 0x40760037 (2011) Stripping20r1 4 033 488 Sim08c 0x409f0045 (2012) Stripping20 A0 1→µ+µ−124 069 Sim08h 0x40760037 (2011) Stripping20r1 M(A0 1) = 10 GeV/c2115 416 Sim08h 0x409f0045 (2012) Stripping20 A0 1→µ+µ−112 945 Sim08h 0x40760037 (2011) Stripping20r1 M(A0 1) = 12 GeV/c2115 464 Sim08h 0x409f0045 (2012) Stripping20 Drell-Yan 1 089 769 Sim08h 0x40760037 (2011) Stripping20r1 M(µ+µ−)>5 GeV/c21 200 892 Sim08h 0x409f0045 (2012) Stripping20 criteria (already taking into account both subsets of cuts). However, the background sample used to construct the UBDT (see Chapter 6.1.4) consists of µ±µ±events, where both muons have the same sign (SS) in terms of electrical charge. To select these events in real data, a different stripping line, StrippingA1MuMuA1MuMuSameSignLine, is used. Since the only difference between both stripping lines is how the candidate muons are chosen, and both consists of the same kinematic and hadronic PID cuts, no distinction is made in Table 6.2. The analysis is not restricted to any particular trigger line, i.e. an event should just pass at least one of the LHCb trigger lines. Table 6.2: Selection criteria for A0 1→µ+µ−decays. Cut variable Cut value µcandidates pT(µ)>2.5 GeV/c χ2 track/ndof(µ)<10 χ2 vtx(µ)<25 χ2 DOCA(µ)<30 ∆LLµπ(µ)>0 ∆LLKπ(µ)<10 χ2 IP(µ)>4 A0 1candidates M(µµ)∈[5.5,15] GeV/c2 pT(µµ)>7.5 GeV/c χ2 vtx/ndof(µµ)<12 τ(µµ)<0.1 ps 131 For daughter µcandidates, a threshold cut in the pTof 2.5 GeV/c is imposed, along with good track, vertex and DOCA reconstruction criteria (χ2 track/ndof <10, χ2 vtx <25, χ2 DOCA <30). Also, good muon identification by the muon system, a cut in the RICH particle identification variables to avoid mis-identification of muons as kaons, and a cut in the χ2of the reconstructed impact parameter (∆LLµπ > 0, ∆LLKπ < 10, χ2 IP >4), are imposed. Alternative possible particle identification cuts would be studied in further steps on the analysis (see Chapter 6.3). For parent di-muon resonances (A0 1candidates), a mass constraint in the two-body mass is required (M∈[5.5,15] GeV/c2), where the lower limit of the mass range is set above the mass of the B0 smeson, in order to avoid possible contamination from B0 s→µ+µ−decays. A threshold cut in the pTof 7.5 GeV/c and good vertex reconstruction criterion, χ2 vtx/ndof <12, are imposed. Finally, since a possible A0 1boson is assumed to decay promptly, a very restrictive cut in the lifetime of A0 1candidates (τ < 0.1 ps) is imposed. A first estimation of the signal efficiency (background rejection) of this selection is computed using a simulated sample of A0 1→µ+µ−decays where the mass hypothesis of the A0 1boson is set to 10 GeV/c2(real data sample of SS muon candidates), leading to an efficiency (rejection) above than 95% (75%). An example of the discriminant behaviour of two of the selected variables, namely τ(µµ) and ∆LLµπ(µ), is presented in Figure 6.1, where the distribution of those variables is compared among different simulated samples and the SS muon real data sample. ))µµ(τ( 10 log -4 -3 -2 -1 0 1 2 0 0.01 0.02 0.03 0.04 0.05 0.06 (10 GeV) MC 2011 0 1 A Drell-Yan MC 2011 -SS 2011µµReal data (1S) MC 2011Υ )µ(µDLL -4 -2 0 2 4 6 8 10 12 14 0 0.01 0.02 0.03 0.04 0.05 (10 GeV) MC 2011 0 1 A Drell-Yan MC 2011 -SS 2011µµReal data (1S) MC 2011Υ Figure 6.1: Comparison between the distributions for τ(µµ) in log10 scale (top) and ∆LLµπ(µ) (bottom) variables for different simulated and SS muon real data samples, normalised to the same area. 132 6.1.4 UBDT requirements In order to leave the data samples with prompt di-muon signal and reject any other component to the background (heavy flavour, combinatorial...) as much as possible, a MVA method consisting of boosted decision trees is used. However, since this analysis aims for a model independent search in a certain di-muon mass range from 5.5 GeV/c2 to 15 GeV/c2, it is necessary to avoid possible induced bias (false peaks) because of the mass structure of the chosen training sample. For this reason, the uBoost method [157] is used, where the boosted decision trees are trained such the response efficiency is kept flat in mass. These kind of boosted decision trees are known as Uniform Boosted Decision Trees. This MVA method has been successfully used in previous LHCb analyses [158]. This UBDT is trained and tested separately for both 2011 and 2012 samples, but following a common procedure. Henceforth, the procedure described in the following paragraphs is assumed to be performed in parallel for 2011 and 2012 samples. For this purpose, a signal sample from Drell-Yan simulated decays and a background sample extracted from real data SS muon are constructed. Extensive studies in order to decide which is the optimal simulated sample to be used as signal sample were performed: despite of the fact that there is no resonant di-muon structure, the Drell-Yan sample shows similar behaviour of the most relevant kinematic and particle identification discriminating variables, along with the fact that there is signal available in the whole mass range considered. On the other hand, a simple decision was taken for the background sample: due to its own structure, real data SS muon sample is the only one where it is 100% assured that there is no trace of A0 1→µ+µ−signal. For both samples, a common selection, which consists of the same requirements as in Table 6.2, is applied. For the signal sample, true MC-truth for both muons is imposed. For the background sample, validation studies show that no same sign replica is present for some of the trigger lines, thus a requirement on a certain set of HLT (see Chapter 3.2.3) lines was imposed. The only consequence of this cut is a minor reduction of the size of the background sample. TMVA toolkit [116] was used for this MVA procedure. After their preparation, each sample is split in two halves: 50% of the sample is used for training while the other 50% used for testing. An UBDT method consisting of 100 efficiency steps is trained and tested over those samples using the following discriminating variables for the MVA procedure: •mu12iso5: sum of the two track isolation [159] variables, “iso5”, each one computed per candidate muon. •logmu1(2)ip: decimal logarithm of the impact parameter of one of the candidate muons (labelled as 1 or 2) of the pair. •logmu1(2)pt: decimal logarithm of the tranverse momentum of one of the candidate muons (labelled as 1 or 2) of the pair. •logmu1(2)ptot: decimal logarithm of the total momentum of one of the candidate muons (labelled as 1 or 2) of the pair. 133 •logBip: decimal logarithm of the impact parameter of the dimuon (A0 1candidate) pair. •mu1(2) track Chi2Dof: track reconstruction significance of one of the candidate muons (labelled as 1 or 2) of the pair. •lessIPSmu: minimum of all significances on the impact parameter of muon candidates. •C angle: angle between the two candidate muons in the centre-of-mass reference frame. A better agreement in track isolation variables is achieved using information from real data of the number of hits in the VELO and in the SPD, for this purpose simulated samples are re-weighted using Yandex software.1Signal and background distributions for discriminating variables are presented in Figure 6.3 and Figure 6.4, together with the UBDT method response in Figure 6.2, for both 2011 and 2012 conditions separately. No overtraining is observed in Figure 4.1, showing a smooth background response and thus no false peaks. For 2011 (2012) conditions, approximately 22 600 (24 300) signal and 51 100 (44 700) background events were used to train the UBDT discriminant. As shown in the signal and background correlation matrices of the discriminating variables, Figure 6.5 and Figure 6.6 respectively, some of those variables are correlated. In a further step of these MVA studies, a clean-up of the discriminating variables may be considered. UBDT response 0 0.2 0.4 0.6 0.8 1 dx / (1/N) dN 0 5 10 15 20 25 30 Signal (test sample) Background (test sample) Signal (training sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = 0.348 (0.0798) U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% TMVA overtraining check for classifier: UBDT UBDT response 0 0.2 0.4 0.6 0.8 1 dx / (1/N) dN 0 5 10 15 20 25 30 Signal (test sample) Background (test sample) Signal (training sample) Background (training sample) Kolmogorov-Smirnov test: signal (background) probability = 0.000334 ( 0.13) U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% TMVA overtraining check for classifier: UBDT Figure 6.2: UBDT response to signal and background distributions for 2011 (left) and 2012 (right) conditions. Validation studies of the flatness of the previously constructed UBDT response efficiency are performed as well: for different random UBDT threshold cuts, its efficiency is calculated in bins of the di-muon invariant mass. These studies are performed separately on SS muon real data and DY simulated events, for both 2011 and 2012 conditions. On 1For more information, see (a). 134 logmu2ip [units] -3 -2 -1 0 1 0.13 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 1.2 Signal Background U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: logmu2ip mu12iso5 [units] 0 2 4 6 8 10 12 14 16 18 20 0.515 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 1.2 1.4 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: mu12iso5 logmu2pt [units] 3.5 4 4.5 5 5.5 6 0.0724 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: logmu2pt logmu1ptot [units] 4 4.5 5 5.5 6 6.5 7 0.0894 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: logmu1ptot logmu2ptot [units] 4 4.5 5 5.5 6 6.5 7 0.0893 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: logmu2ptot logBip [units] -4 -3 -2 -1 0 1 0.157 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: logBip logmu1pt [units] 3.5 4 4.5 5 5.5 6 0.0724 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: logmu1pt mu1_track_Chi2DoF [units] 0.5 1 1.5 2 2.5 3 0.0727 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: mu1_track_Chi2DoF C_angle [units] 0.5 1 1.5 2 2.5 3 0.0765 units / (1/N) dN 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: C_angle lessIPSmu [units] 2 4 6 8 10 12 14 0.397 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.3)% Input variable: lessIPSmu mu2_track_Chi2DoF [units] 0.5 1 1.5 2 2.5 3 0.0707 units / (1/N) dN 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)% Input variable: mu2_track_Chi2DoF Figure 6.3: Distributions for MVA discriminating variables under 2011 conditions. simulated signal (DY) events, one can expect a flat efficiency, not necessarily the same on background (SS muon real data) events. 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