Search for violation of leptonic universality in semileptonic decays of strange particles in LHCb

INTERNATIONAL DOCTORAL SCHOOL OF THE USC Alexandre Brea Rodríguez PhD Thesis Search for violation of leptonic universality in semileptonic decays of strange particles in LHCb Santiago de Compostela, 2023 Doctoral Programme in Nuclear and Particles Physics DOCTORAL THESIS SEARCH FOR VIOLATION OF LEPTONIC UNIVERSALITY IN SEMILEPTONIC DECAYS OF STRANGE PARTICLES IN LHCb Author Alexandre Brea Rodríguez Supervisor/s: Diego Martínez Santos Xabier Cid Vidal Tutor: Xabier Cid Vidal PHD PROGRAMME IN NUCLEAR AND PARTICLE PHYSICS SANTIAGO DE COMPOSTELA To Rocío ABSTRACT Theoretical studies have demonstrated that Semileptonic Hyperon Decays (SHD) can be sensitive to Beyond the Standard Model (BSM) dynamics that break leptonic flavour universality (LFU). The LFU test observable defined as the ratio between muon and electron modes 𝑅𝜇𝑒 = Γ(𝐵1→𝐵2𝜇−¯ 𝜈𝜇) Γ(𝐵1→𝐵2𝑒−¯ 𝜈𝑒) is sensitive to non standard scalar and tensor contributions. Moreover, in the Standard Model, the dependency on the form factors is anticipated to simplify when considering the ratio, leading to a precise theoretical prediction. Λ→𝑝𝜇−¯ 𝜈𝜇 was proposed as one of the most promising SHD to be studied at LHCb, due to its high acceptance efficiency and abundance in LHCb events. In addition, the electron mode has already been measured precisely and an improvement in the measurement of the B(Λ→𝑝𝜇−¯ 𝜈𝜇) directly translates into tighter bounds in LFU in 𝑠→𝑢quark transitions. In this thesis is presented the blinded measurement of the branching fraction B(Λ→𝑝𝜇−¯ 𝜈𝜇)=(3.485 ±0.059 (𝑠𝑡𝑎𝑡) ±0.23 (𝑠𝑦𝑠𝑡)) ×10−4 and the consequences of the precision achieved is discussed. It should be noted that this value is multiplied by a blinding constant and that the calculation of the systematic uncertainty is not completely finalized, so the final result of this uncertainty may vary slightly. The measurement is performed using Run 2 LHCb data, produced colliding protons at 13 TeV of energy in the center of mass during the years 2016-2018, reaching an integrated luminosity of 5.4 𝑓 𝑏−1. In addition some prospects fore future SHD measurements are included. iii contents A.8.4 Lppi Stripping Filtered 2018 . . . . . . . . . . . . . . . . . . . 121 A.8.5 Lppi Stripping Filtered 2017 . . . . . . . . . . . . . . . . . . . 122 A.8.6 Lppi Stripping Filtered 2016 . . . . . . . . . . . . . . . . . . . 122 A.8.7 Lpmunu Stripping Filtered 2018 . . . . . . . . . . . . . . . . . 122 A.8.8 Lpmunu Stripping Filtered 2017 . . . . . . . . . . . . . . . . . 123 A.8.9 Lpmunu Stripping Filtered 2016 . . . . . . . . . . . . . . . . . 123 A.8.10 MinBiasMC2018.........................123 A.8.11 Signal Private Production to correct Stripping eff: . . . . . . . 124 A.9 DecFiles ..................................128 A.9.1 Lppi: TightCut (33102103) . . . . . . . . . . . . . . . . . . . . 128 A.9.2 Lpmunu: TightCut SHD (33512008) . . . . . . . . . . . . . . . 129 A.10PIDCalib2 .................................131 A.10.1 SignalLine ............................131 A.10.2 NormLine.............................132 A.11PIDCalib2Schemes ............................134 A.11.1 Signal Stripping Line . . . . . . . . . . . . . . . . . . . . . . . 134 A.11.2 Norm Stripping Line . . . . . . . . . . . . . . . . . . . . . . . 139 Bibliography 145 Glossary 151 x FOREWORD One of the fundamental questions that has consistently intrigued us throughout time is: ’What exactly is our world made of?’. Despite remaining quite uncertain about other fundamental questions, we have made significant progress in addressing this one. Nowadays, we know that all the matter around us is composed of atoms, with protons and neutrons in their nucleus, and electrons in quantum orbitals around them. For the first time, we gained a systematic understanding of the constituents of our world. Yet, our journey did not culminate here; it extended deeper into the subatomic realm, revealing that protons and neutrons, once thought to be elementary particles, are themselves intricate structures composed of particles known as quarks. In our current paradigm, electrons and quarks serve as the fundamental building blocks of matter, forming the very essence of the world around us. In our quest to delve deeper into our understanding of particles, numerous experiments have been conducted, resulting in the discovery of a vast array of particles that initially left us even more perplexed than before. Furthermore, these particles exhibited sensitivity to new fundamental interactions, the strong and weak nuclear interactions, not typically encountered in our daily experiences. However, following significant collective theoretical efforts in the 20th century, a model describing all the known particles and their interactions, excluding gravity, was constructed. It is called Standard Model (SM), and it achieved impressive predictive power and resisted all of our attempts to uncover phenomena beyond it. In the SM, matter is composed of particles with half-odd-integer quantum spin numbers, known as fermions, while interactions are mediated by particles with integer spin quantum numbers, referred to as bosons. It describes three fundamental interactions: electromagnetism, the strong interaction, and the weak interaction. Gravity is the only interaction that falls outside of the model. There are two types of fermions: leptons and quarks, and we observe a similar pattern in both categories, with two types of particles (up and down quarks, and electron and electron neutrino leptons), as well as two additional, heavier-generation counterparts, known as the second and third generations. Only quarks are affected by the strong interaction, which is mediated by gluons and confines them within mesons (typically pairs of quarks) or baryons (typically consisting of 3 quarks). In contrast, leptons do not interact with the strong interaction and can exist independently. xi contents The photon, the particle associated with light, serves as the mediator of the electromagnetic interaction, and only charged particles can interact with it. Additionally, all fermions can interact with the 𝑊± and 𝑍0 bosons, which act as mediators of the weak interaction. The electromagnetic and weak interactions are, in fact, two distinct manifestations of a singular unified interaction known as the electroweak interaction. The coupling of the gauge bosons to leptons within the electroweak interaction is invariant with respect to the flavor of the lepton, a phenomenon referred to as lepton flavor universality. In the SM, particles are initially massless and acquire mass through interactions with the Higgs field. This mechanism was proposed in 1964, and with the discovery of the Higgs boson in 2012 by the ATLAS and CMS collaborations in the Large Hadron Collider (LHC), the Standard Model was completed. Despite the great success of the Standard Model, several well-known issues remain unexplained. Ordinary matter can only account for approximately 5 % of the observed energy in the universe, with around 25 % attributed to dark matter and approximately 70 % to dark energy. The nature of both energy sources is completely unknown as of now. Moreover, the observation of neutrino oscillations implies that they have mass, but it is not yet established how they acquire it. In addition, the observed matter-antimatter imbalance in the universe cannot be explained with the known sources of CP violation and we don’t know how to fit gravity in the model. Figure 1: Approximate contribution from ordinary matter, dark matter and dark energy to the observed energy in the universe. This is the context in which this thesis is framed. Semileptonic Hyperon Decays were proposed to test lepton flavor universality, one of the main features of the SM. The Λ (uds) particle is the lightest hyperon and the branching ratio of the Λ→𝑝𝜇−¯ 𝜈𝜇 decay is sensitive to BSM physics since the ratio between the electronic and muonic branching fractions is precisely predicted by the SM, and the electronic mode branching ratio is accurately measured. Additionally, it can also contribute to xii contents testing the unitarity of the CKM matrix, which will be explained in detail in the main text. The LHC is currently our most powerful tool for testing the Standard Model in order to identify any deviations from its predictions that can give us a hint of what is going . An extensive campaign of direct and indirect searches for physics Beyond the Standard Model (BSM) is being conducted in the four major experiments at the LHC: A ToroidaL AparatuS (ATLAS), Compact Muon Solenoid (CMS), Large Hadron Collider beauty (LHCb), and A Large Ion Collider Experiment (ALICE). Among the experiments at the LHC, LHCb is the only one capable of attempting to improve the current measurements of the B(Λ→𝑝𝜇−¯ 𝜈𝜇) , and that it is precisely the main goal of this thesis. The measurement is done using pp collision data collected by the LHCb experiment at a centre-of-mass energy of 13 TeV in the period 2016-2018, corresponding to an integrated luminosity of 5.4 fb−1. xiii chapter 1 INTRODUCTION The Standard Model (SM) is the theoretical framework that describes the known fundamental particles and their interactions through three of the four fundamental interactions: electromagnetic, weak and strong interactions. In the SM, matter is composed of particles with half-odd-integer quantum spin numbers, known as fermions, while interactions are mediated by particles with integer spin quantum numbers, referred to as bosons. It describes three fundamental interactions: electromagnetism, the strong interactions, and the weak interactions. Gravity is the only force that falls outside of the model. A schematic summary of the SM particles can be found in Figure 1.1. There are two types of fermions: leptons and quarks, and we observe a similar pattern in both categories, with two types of particles (up and down quarks, and electron and electron neutrino leptons), as well as two additional, heavier-generation counterparts, known as the second and third generations. From a mathematical point of view, the electroweak gauge symmetry 𝑆𝑈 (2)𝑊× 𝑈(1)𝑌 is chiral and, as a consequence, quarks are organized in three left-handed doublets 𝑄𝑖 𝐿 with i=1,2,3, where 𝑄1 𝐿 = 𝑢𝐿 𝑑𝐿 , 𝑄2 𝐿 = 𝑐𝐿 𝑠𝐿 , 𝑄3 𝐿 = 𝑡𝐿 𝑏𝐿 with the correspondents right-handed quark singlets 𝑢𝑅,𝑑𝑅,𝑐𝑅,𝑠𝑅,𝑡𝑅and 𝑏𝑅. Something similar happens with the leptons, being organized in three left-handed doublets 𝐿𝑖 𝐿 with i=1,2,3, where 𝐿1 𝐿 = 𝜈𝑒𝐿 𝑒𝐿 , 𝐿2 𝐿 = 𝜈𝜇𝐿 𝜇𝐿 , 𝐿3 𝐿 = 𝜈𝜏𝐿 𝜏𝐿 with the right-handed lepton singlets 𝑒𝑅 , 𝜇𝑅 , 𝜏𝑅 . Notice that, from our current understanding, there are not right-handed neutrinos. Only quarks are affected by the strong interaction, which is mediated by gluons and confines them within mesons (typically pairs of quarks) or baryons (typically consisting of 3 quarks). In contrast, leptons do not interact with gluons and can exist deconfined. The photon, the particle associated with light, serves as the mediator of the 1 chapter 1. introduction electromagnetic force, and only charged particles can interact with it. Additionally, all fermions can interact with the 𝑊± and 𝑍0 bosons, which act as mediators of the weak interaction. In the SM, particles are initially massless and acquire mass through interactions with the Higgs field. This mechanism was proposed in 1964, and with the discovery of the Higgs boson in 2012 by the ATLAS and CMS collaborations in the Large Hadron Collider (LHC), the Standard Model was completed. μ− e− τ− νe νμ ντ u d c s t b Leptons Quarks 2 3 1 2 2 3 1 2 2 3 1 2 −1 3 1 2 −1 3 1 2 −1 3 1 2 charge spin 1 2 1 2 1 2 1 2 1 2 1 2 −1 −1 −1 0 0 0 I II III Fermions :3 Generations Bosons :Force carriers g 0 1 Z0 0 1 W± ±1 1 H 0 0 Higgs Gauge Bosons Strong Weak up down strange bottom charm top electron muon tau (electron) neutrino (muon) neutrino (tau) neutrino γ 0 1 EM Electro Magnetic Fermions photon gluon Scalar Boson Figure 1.1: Standard Model particles and interactions. In the SM, every particle has a corresponding antiparticle. However, there are specific instances where a particle is its own antiparticle, such as the 𝛾, 𝑍0and Higgs bosons. Despite the great success of the Standard Model, several well-known issues remain unexplained. Ordinary matter can only account for approximately 5 % of the observed energy in the universe, with around 25 % attributed to dark matter and approximately 70 % to dark energy. The nature of both energy sources is completely unknown as of now. Moreover, the observation of neutrino oscillations implies that they have mass, but it is not yet established how they acquire it. In addition, the observed matter-antimatter imbalance in the universe cannot be explained with the known sources of CP violation and we do not know how to fit gravity in the model. 2 1.1. an almost symmetric world 1.1 an almost symmetric world In 1918, the mathematician Emmy Noether’s proof, which showed that every differentiable symmetry of the action of a physical system subjected to conservative forces corresponds to a conservation law, was published. She had originally proved this three years earlier [62]. After Emmy Noether’s groundbreaking work on symmetries and conservation laws, physicists began to delve deeper into understanding the fundamental symmetries inherent in particle interactions. These symmetries are crucial for understanding the laws that govern the subatomic world. They originate the conservation principles we observe, such as conservation of energy, momentum, and angular momentum. However, particle physics also introduces other symmetries, both exact and broken, that are not obvious at macroscopic scales. Some of these symmetries are termed "Discrete Space-Time Symmetries", such as charge conjugation (C), parity (P), time (T), CP, and CPT. Others fall under "Number Conservation Laws", including lepton, baryon, flavor, and charge conservation. In quantum field theories of particle physics, a charge conjugation transformation (C) is a fundamental operation that transforms a particle into its antiparticle. Meanwhile, a parity transformation (P) represents the inversion of spatial coordinates, equivalent to a point reflection. The discovery that weak interactions do not conserve parity symmetry was shocking. This observation was first made by Chien-Shiung Wu in 1956 during her experiment on the beta decay of cobalt-60 [79]. Additionally, weak interactions also maximally violate C symmetry. This is because the charge conjugation does not change the chirality of particles. For instance, a left-handed neutrino, when subjected to charge conjugation, becomes a left-handed antineutrino, which does not participate in charged weak interactions according to the Standard Model. To reconcile these observations, it was proposed that weak interactions would conserve the combined CP symmetry, just as the strong and electromagnetic interactions do. In other words, it was believed that if all particles in a process were swapped with their antiparticles, it would mirror the initial process, thereby conserving the combined CP-symmetry in weak interactions. Nonetheless, subsequent experiments revealed that this symmetry is slightly violated in specific weak decay processes. CP-violation is responsible for the matter-antimatter imbalance in our universe. However, the degree of CP violation observed within the SM so far is not large enough to explain the observed matter-antimatter asymmetry [74]. Invariance under the combined transformation CPT is required by general principles of relativistic field theory and implies that masses and lifetimes of a particle and its anti-particle must be equal. As as consequence, CP and T violation are equivalent. 1.2 flavor structure of the standard model As it can be seen in Fig. 1.1, there are six types of quarks and six types of leptons. Each type is considered a different "flavor". Flavor is conserved in strong and electromagnetic interactions. But, through charged current weak interactions, quarks and 3 chapter 1. introduction leptons can change from one flavor to another. A very well known example is the beta decay in atomic nuclei, where a neutron decays into a proton, an electron and an electron neutrino. In fact, the fundamental process that is going on is 𝑑→𝑢 𝑒−𝜈𝑒(1.1) where the d quark decays to an up type quark via the exchange of a 𝑊− boson. A common way to visualize it is using a Feynman diagram: uu u d dd W−e− νe Figure 1.2: Feynman diagram of a neutron beta decay. Notice that this decay is completely analogous to the semileptonic hyperon decay that we aim to study, denoted as Λ→𝑝𝜇−¯ 𝜈𝜇 . The only differences are that in our case we study an 𝑠→𝑢 transition and that the leptons in the final state belong to the second generation. To clarify, "semileptonic" means that in the final state we have a lepton, its associated neutrino, and a hadron. A hyperon is any baryon containing one or more strange quarks, but no charm, bottom, or top quark, being the Λ the lightest of them. The SM lagrangian can be splitted in two terms: LSM =LGauge(𝐴𝑎,Ψ𝑖) +LHiggs(𝐻, 𝐴𝑎,Ψ𝑖)(1.2) In the gauge part, we identify 3 identical replica of the basic fermion family [Ψ=𝑄𝐿,𝑢𝑅,𝑑𝑅, 𝐿𝐿, 𝑒𝑅] and we observe a huge flavor degeneracy. LGauge =∑︁ 𝑎−1 4𝑔2 𝑎(𝐹𝑎 𝜇𝜈 )2+∑︁ Ψ∑︁ 𝑖=1,2,3 Ψ𝑖𝑖/ 𝐷Ψ𝑖(1.3) The Gauge lagrangian is invariant under 5 independent U(3) global rotations for each of the independent fermion fields: 𝑄𝑖 𝐿→𝑈𝑖 𝑗𝑄𝑗 𝐿(1.4) Within the SM, the flavor-degeneracy is broken only by the Yukawa interaction. In the quark sector L𝑌=−𝑌𝑑 𝑖 𝑗𝑄𝐼 𝐿𝑖 𝜙 𝑑𝐼 𝑅𝑗 −𝑌𝑢 𝑖 𝑗𝑄𝐼 𝐿𝑖𝜖 𝜙∗𝑢𝐼 𝑅𝑗 +ℎ.𝑐. (1.5) 4 1.2. flavor structure of the standard model where 𝑌𝑢,𝑑 are 3 × 3 complex matrices, 𝜙 is the Higgs field, 𝑖, 𝑗 are the generation labels, 𝜖 is the 2 × 2 anti-symmetric tensor and "h.c." stands for the Hermitian conjugate, which gives the corresponding term for the𝑊−boson [73]. The residual flavor symmetry allows us to choose a gauge-invariant flavor basis where only one of the two Yukawa couplings is diagonal. We can choose 𝑌𝑑= 𝑑𝑖𝑎𝑔(𝑦𝑑,𝑦𝑠,𝑦𝑏) and 𝑌𝑢=𝑉+×𝑑𝑖𝑎𝑔(𝑦𝑢,𝑦𝑐,𝑦𝑡) or 𝑌𝑑=𝑉×𝑑𝑖𝑎𝑔(𝑦𝑑,𝑦𝑠,𝑦𝑏) and 𝑌𝑢= 𝑑𝑖𝑎𝑔(𝑦𝑢,𝑦𝑐,𝑦𝑡), where V is a unitary matrix. To diagonalize also the second matrix we need to rotate separately 𝑢𝐿 and 𝑑𝐿 , so we do not have a gauge-invariant basis. This V matrix appears in charged-current gauge interactions. This charged-current interactions, mediated by a 𝑊±boson can be written as 𝐽𝜇 𝑊=−𝑔 √2𝑢𝐿𝛾𝜇𝑊+ 𝜇𝑉𝐶𝐾𝑀 𝑑𝐿+ℎ.𝑐. (1.6) which basically means that the weak interactions couples to pairs 𝑢 𝑑′ , 𝑐 𝑠′ and 𝑡 𝑏′, where d’, s’ and b’ are linear combinations of the physical d, s, b: ©« 𝑑′ 𝑠′ 𝑏′ª®¬=©« 𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏 𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏 𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏 ª®¬©« 𝑑 𝑠 𝑏ª®¬(1.7) This non-trivial mixing arises solely from the Higgs sector. Only interactions mediated by 𝑊± and h interactions are flavor physics. Note that the rotation of the right-handed sector is not observable and neutral currents remain flavor diagonal. The 3 × 3 quark-mixing unitary matrix in question is termed the CKM matrix, named after Cabibbo, Kobayashi, and Maskawa. Originally, Cabibbo proposed this matrix structure for two generations in 1963. A decade later, Kobayashi and Maskawa extended this formulation to accommodate three generations. Essentially, the CKM matrix encapsulates information regarding the strength of flavor-changing weak interactions. Each element of the matrix signifies the probability amplitude for a transition from one quark flavor 𝑗 to another quark flavor 𝑖 . The probabilities of these transitions are proportional to |𝑉𝑖 𝑗 |2. Up to this point, we have consistently observed that the leptonic generation number (often simply referred to as the lepton number) is conserved in particle decays. For instance, in our Λ→𝑝𝜇−¯ 𝜈𝜇 decay, we do not need to identify the specific flavor of the anti-neutrino in the final state to ascertain that it’s an anti-muon neutrino, since the muonic lepton number in the initial state is 0 . In a hypothetical scenario where cross-generational quark transitions do not occur, quantities such as ’upness’ plus ’downness’ would be conserved, similar to how the electron number is conserved. Likewise, ’strangeness’ plus ’charm’ and ’topness’ plus ’bottomness’ would also be conserved. Such a world would be described by a CKM matrix that is simply the identity matrix. In fact, the CKM matrix is very close to the identity matrix, being the numbers in the diagonal extremely close to 1. The world average of the CKM elements is [78]: 5 chapter 1. introduction to this relative theoretical precision ( O((𝑀1−𝑀2)2 𝑀2 1) ) the ratio does not depend on form factors. A precise measurement of 𝑅𝜇𝑒 implies a constraint on the Wilson coefficients, since the mentioned new physics scalar and tensor operators will contribute to the ratio in the following way [26]: 𝑅𝜇𝑒 NP =𝜖𝑆𝑓𝑆(0) 𝑓1(0)+12𝜖𝑇𝑔1(0) 𝑓1(0) 𝑓𝑇(0) 𝑓1(0) (1−3 2𝛿)1+3𝑔1(02) 𝑓1(0)2Π(Δ,𝑚𝜇)(1.27) where the phase-space integral Π(Δ,𝑚𝜇)is Π(Δ,𝑚𝜇)=5 2 𝑚𝜇 Δh(2+13𝑚2 𝜇 Δ2)√︄1−𝑚2 𝜇 Δ2−34𝑚2 𝜇 Δ2+𝑚4 𝜇 Δ4arctanh(√︄1−𝑚2 𝜇 Δ2))i(1.28) It is useful to express the ratio of 𝑅𝜇𝑒 NP and 𝑅𝜇𝑒 SM encapsulating the scalar and tensor related dimensionless contributions in 𝑟𝑆 and 𝑟𝑇 in order to express the sensitivity to the Wilson coefficients [26]: 𝑅𝜇𝑒 NP 𝑅𝜇𝑒 SM =1+𝑟𝑆𝜖𝑆+𝑟𝑇𝜖𝑇(1.29) being the SHD sensitivity to the Wilson coefficients very channel-dependent [26]. Given that the SM-NLO predictions, 𝑅𝜇𝑒 SM , for the various SHD modes are precise, these decays are excellent candidates for performing tests of LFU. Combining Eq. 1.26 and Eq. 1.20 we arrive to the SM prediction for the muon mode branching ratio. ΓSM(𝐵1→𝐵2𝜇−¯ 𝜈𝜇) ≃ 𝐺2 𝐹|𝑉𝑢𝑠 𝑓1(0)|2Δ5 60𝜋3h1−3 2𝛿+31−3 2𝛿𝑔1(0)2 𝑓1(0)2−4𝛿𝑔2(0) 𝑓1(0) 𝑔1(0) 𝑓1(0)i √︄1−𝑚2 𝜇 Δ21−9 2 𝑚2 𝜇 Δ2−4𝑚4 𝜇 Δ4+15 2 𝑚4 𝜇 Δ4arctanh√︄1−𝑚2 𝜇 Δ2! (1.30) 1.4.2 𝑉𝑢𝑠 from B(Λ→𝑝𝜇−¯ 𝜈𝜇) Condensing the 𝑅𝜇𝑒 term in Eq. 1.30 and considering no BSM contributions, we can write 𝑉𝑢𝑠 in terms of the form factors predicted by theory and the decay rates ratio. |𝑉𝑢𝑠 |2≃ ΓSM(𝐵1→𝐵2𝜇−¯ 𝜈𝜇)60𝜋3 𝑅𝜇𝑒𝐺2 𝐹𝑓1(0)2Δ5h1−3 2𝛿+31−3 2𝛿𝑔1(0)2 𝑓1(0)2i(1.31) where the - 4𝛿𝑔2(0) 𝑓1(0) 𝑔1(0) 𝑓1(0)term is not being considered, since it is O(𝛿). 12 1.5. motivation of this measurement For the Λ→𝑝𝜇−¯ 𝜈𝜇 case, using the current PDG measurements and theoretical computation, the values for the parameters involved in this expressions are Δexp = 177.4110 ±0.0060 , 𝛿exp =0.1590160 ±0.0000050 , 𝑓1(0)=−√︃3 2 , 𝑔1(0) 𝑓1(0)=0.718 ±0.015 , 𝑅𝜇𝑒 =0.153 ±0.008 [26] and 𝐺𝐹 (ℏ𝑐)3=1.1663787(6) ×10−5𝐺𝑒𝑉 −2[78]. Considering that we aim to measure B(Λ→𝑝𝜇−¯ 𝜈𝜇) , we should rewrite the decay rate Γ(Λ→𝑝𝜇−¯ 𝜈𝜇)=Γ(Λ) B(Λ→𝑝𝜇−¯ 𝜈𝜇)(1.32) where the Γ(Λ) can be obtained from the particle life-time ( 𝜏(Λ)=(2.632 ± 0.020) ×10−10 [78]) using Γ(Λ)=ℏ 𝜏(Λ)=(2.501 ±0.019) ×10−15 [𝐺𝑒𝑉 ](1.33) Including the values in GeV units in Eq. 1.31, we obtain: |𝑉𝑢𝑠 |2≃BSM(𝐵1→𝐵2𝜇−¯ 𝜈𝜇) (4.652 ±0.035) ×10−12 (1.06 ×0.06) ×10−14 =BSM(𝐵1→𝐵2𝜇−¯ 𝜈𝜇)·(437±26) (1.34) Using the current B(Λ→𝑝𝜇−¯ 𝜈𝜇) PDG value [78] we obtain 𝑉𝑢𝑠 ≃0.257 ±0.018 , with a large uncertainty compared to our current knowledge on this CKM matrix element, 𝑉𝑢𝑠 =0.22500 ±0.00067 . On top of this, this 𝑉𝑢𝑠 prediction was done within a theoretical precision of O(𝛿2), estimated to be between 1 to 5 %. Even having a large uncertainty using the current available values for the B(Λ→ 𝑝𝜇−¯ 𝜈𝜇) and the theoretical prediction, this uncertainty can be reduced performing a precise measurement of the B(Λ→𝑝𝜇−¯ 𝜈𝜇) in LHCb, as we plan to do in this thesis. Moreover, as it is explained in detail in the next section, the two most precise 𝑉𝑢𝑠 measurements exhibit a 3 𝜎 discrepancy. In this context, precise SHD 𝑉𝑢𝑠 measurements are required to put light in this puzzle. Despite the considerable uncertainty in the current values of the branching ratio ( B(Λ→𝑝𝜇−¯ 𝜈𝜇) ) and the theoretical prediction, this uncertainty can be mitigated with theoretical efforts and by conducting a precise measurement of the B(Λ→𝑝𝜇−¯ 𝜈𝜇) at LHCb, which is a key objective of this thesis. Furthermore, as detailed in the following section, the two most precise measurements of 𝑉𝑢𝑠 currently show a 3 𝜎 discrepancy. In this context, accurate measurements of 𝑉𝑢𝑠 from SHD are essential to shed light on this puzzle 1.5 motivation of this measurement In the last decades the focus was in the higher mass sector of the CKM matrix. However it is the low mass sector, 𝑉𝑢𝑑 and 𝑉𝑢𝑠 , where is it possible to obtain the highest precision and the most sensitive test of the unitary of the CKM matrix. One of the strongest tests of the unitarity of the CKM matrix can be achieved by accurately measuring |𝑉𝑢𝑠 |. This is because eq. 1.14, implies that: 13 chapter 1. introduction |𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2≡1(1.35) Given that the contribution from |𝑉𝑢𝑏 |2 element is almost entirely negligible (approximately 1.3×10−5 [78]), this relation is reduced to the Cabibbo universality (|𝑉𝑢𝑑 | ≈𝑐𝑜𝑠 𝜃12,|𝑉𝑢𝑠 | ≈𝑠𝑖𝑛 𝜃12). Since |𝑉𝑢𝑑 | has already been measured with great precision, with a value of |𝑉𝑢𝑑 |=0.97436 ±0.00016 [78], the focus shifts to 𝑉𝑢𝑠 . In fact, using our current best measurements of 𝑉𝑢𝑑 ,𝑉𝑢𝑠 and 𝑉𝑢𝑏 we obtain |𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2=0.9985 ±0.0007 (1.36) showing a 2.2 𝜎 tension with the expected unitarity in the first CKM row. Currently, enhanced precision in theoretical uncertainties when estimating |𝑉𝑢𝑑 | and |𝑉𝑢𝑠 | is uncovering potential anomalies. These anomalies might indicate the presence of NP phenomena at the TeV scale [47]. Moreover, the measurements of 𝑉𝑢𝑠 in leptonic ( 𝐾𝜇2 ) and semileptonic ( 𝐾𝑙3 ) kaon decays exhibit a 3 𝜎 discrepancy. Such a disagreement can hint towards two potential scenarios: the existence of physics beyond the Standard Model or a significant, yet unidentified, systematic effect within the Standard Model itself [72]. Given this context, it becomes paramount to explore other avenues to measure 𝑉𝑢𝑠 with high precision. In this regard, semileptonic hyperon decays emerge as a promising alternative. If these decays yield values of 𝑉𝑢𝑠 consistent with one set of kaon decays and not the other, it could potentially pinpoint the origin of the aforementioned discrepancy. On the other hand, if the value from hyperon decays stands in contrast to both kaon measurements, it would further complicate our understanding and suggest deeper underlying issues. Thus, intensifying the focus on measuring 𝑉𝑢𝑠 from semileptonic hyperon decays could be instrumental in shedding light on this puzzle. Whether it ends up reinforcing the Standard Model, identifying systematic flaws, or pointing towards new physics, the endeavor will undoubtedly provide valuable insights into the realm of particle physics. It is also natural to investigate if contributions in charged-current quark decays breaking LFU can be found in s → u since this can open a door to physics BSM. Especially taking into account the results coming from b → c transitions that point in this direction [30]. From a theoretical perspective, hyperon semileptonic decays have been identified as potentially sensible to BSM mechanisms that break lepton universality. These decays are governed by a minor SU(3) flavor symmetry breaking parameter, enabling systematic expansions and precise forecasts with minimal reliance on hadronic form factors. The muonic decay channels are particularly receptive to non-standard scalar and tensor contributions, potentially offering a significant complementary approach to direct new physics searches at the LHC [26]. In the Λ→𝑝𝑙−¯ 𝜈𝑙 case, the LFU test observable defined in 1.15 is predicted by theory to be 𝑅𝜇𝑒 =0.153 ±0.008 working at next-to-leading order [26]. Current best measurent of this observable was performed by BESIII in 2021, obtaining 𝑅𝜇𝑒 = 0.178 ±0.028, consistent within uncertainties with the predicted value [6]. 14 1.5. motivation of this measurement However, since the decay mode involving the electron is measured with greater precision, B(Λ→𝑝𝑒−¯ 𝜈𝑒)=(8.34 ±0.14) ×10−4 [78], most of the uncertainty arises from the BESIII measurement of the muonic mode, given by B(Λ→𝑝𝜇−¯ 𝜈𝜇) = [1.48 ±0.21,(stat) ±0.08,(syst)] ×10−4. Increasing the precision in the B(Λ→𝑝𝜇−¯ 𝜈𝜇) is essential to test lepton universality in 𝑠→𝑢transitions. 15 chapter 2 EXPERIMENTAL CONDITIONS 2.1 the lhc The Large Hadron Collider (LHC) is the most powerful and the largest particle accelerator of the world. It began operations on September 10, 2008. It is the most recent expansion to CERN’s complex of accelerators. This accelerator features a 27-kilometre ring equipped with superconducting magnets, along with several accelerating structures designed to incrementally increase the energy of the particles as they travel through the ring [45]. Within the accelerator, two beams of high-energy particles are accelerated to nearly the speed of light and are then directed to collide with each other. These beams move in opposite directions, each contained within its own beam pipe – a pair of tubes maintained under ultra-high vacuum conditions. A powerful magnetic field, generated by superconducting electromagnets, maintain the beams around the ring of the accelerator. The particle beams within the LHC are made to collide at four specific points along the accelerator’s ring. These collision points align with the locations of four major particle detectors: A ToroidaL AparatuS (ATLAS), Compact Muon Solenoid (CMS), A Large Ion Collider Experiment (ALICE), and LHCb. 2.2 the lhcbdetector LHCb is one of the four big detectors collecting data in the LHC, at CERN. The name comes from its purpose of detecting the decay of particles that contain b quarks. These particles, formed in pp collisions, and the particles in which they decay, do not move away too much from the direction of incidence of the beam. This is reflected in the forward design of the detector [58] which, unlike other LHC detectors which 17 chapter 2. experimental conditions CMS ATLAS LHCb ALICE LHC SPS PS Leir 27 km 628 m 78 m Linac 2 Booster 157 m Linac 3 Lead ions, … Protons 7 km Figure 2.1: Display of the CERN accelerator complex, including the LHC and its four experiments. cover the entire solid angle around the collision of the protons, presents its multiple subdetectors arranged in the forward direction The LHCb, one of the four major detectors at the LHC located at CERN, is specifically designed for the detection of decays involving b quarks. Originating from pp collisions, these particles and their decay products tend to travel close to the incident beam’s direction. This characteristic is the basis for the forward design of the LHCb detector, as detailed in [58]. Unlike other detectors at the LHC, which cover the entire solid angle around the proton collisions, the LHCb has its subdetectors on the forward direction [37] with an acceptance of 1.6≤𝜂≤4.9, where 𝜂is the pseudorapidity 𝜂=1 2ln 𝑝+𝑝𝑧 𝑝−𝑝𝑧 =−ln tan 𝜃 2(2.1) In this expression p is the magnitude of the particle momentum, 𝑝𝑧 the magnitude in the direction of the colliding protons and 𝜃 is the angle between the particle’s path and the trajectory of the colliding protons. This acceptance is equivalent to an angular acceptance of 10 mrad ≤𝜃≤300 mrad. The LHCb detector was specifically designed for the accurate measurement of CP symmetry violation and the rare decay of mesons, particularly those comprising b quarks or their antiparticles ( 𝑏 ). Its unique design is tailored to efficiently study these specific processes. This optimization has facilitated significant discoveries, including the determination of the branching ratio for the rare decay of the 𝐵𝑠 meson into a muon-antimuon pair, as well as the measurement of the CP violation phase in the 18 2.2. the lhcbdetector VELO RICH1 TT Imán T1 T2 T3 RICH2 M5M4M3M2M1 HCALECAL Vertex Locator Rich1 TT Magnet T1 T2 T3 Rich2 M1 ECAL HCAL M2 M3 M4 M5 Figure 2.2: The LHCb detector according to the plane of curvature of the trajectory of the charged particles. decay of 𝐵𝑠→ J/ Ψ𝜙 . Examples of the key physics measurements by LHCb can be found in [7]. The LHCb experiment is designed to operate at a reduced instantaneous luminosity of 2 - 5 ·1032 𝑐𝑚−2·𝑠−1 , which is lower than the nominal LHC luminosity of 1034 𝑐𝑚−2· 𝑠−1 . This is achieved by employing larger 𝛽∗ (which denote the amplitude modulation of the beam at the interaction point and are directly related to the beam size) compared to other LHC detectors, resulting in less focused beams. The idea behind this approach is to simplify the task of accurately pinpointing the location of the initial proton-proton collision Primary Vertex (PV) and the subsequent decay points of other short-lived particles Secondary Vertex (SV). Accurately identifying these vertices is crucial for the physics objectives of the LHCb experiment. The LHCb experiment adopts a coordinate system consistently utilized throughout this thesis. The origin is designated at the pp interaction point, extending the 𝑧axis along the beam direction towards the remainder of the detector apparatus. Oriented vertically upwards, influenced by gravity, the 𝑦 axis is established, while the 𝑥 axis maintains the system’s “right-handedness” ( ˆ 𝑥׈ 𝑦=ˆ 𝑧 ), positioned horizontally, facing the detector’s left when observed from the negative 𝑧 side. A prevalent metric, “transverse momentum” ( 𝑝𝑇 ), referencing a particle, is defined within this particular coordinate framework as 𝑝𝑇=√︃𝑝2 𝑥+𝑝2 𝑦(2.2) The first period of data taking, Run I, took place from 2009 to 2012. Run II refers to the second data-taking run of the LHCb experiment, that took place from 2015 to 2018. In Run II, the LHC operated at a higher energy, with proton-proton collision energies reaching 13 TeV and a luminosity of almost 6 𝑓 𝑏−1was recorded. 19 chapter 2. experimental conditions Table 2.1: Energy in the center of mass (s) and integrated luminosity recorded for each year of data taking during Run1 and Run2. Year Energy (TeV) Integrated Luminosity (𝑓 𝑏−1) 2010 7 0.04 2011 7 1.11 2012 8 2.08 2015 13 0.33 2016 13 1.67 2017 13 1.71 2018 13 2.19 This analysis uses Run II LHCb data. As a consequence, the detector described is the one that took data from 2015 to 2018 and not the upgraded one that is taking data currently [48]. 2.2.1 technical specifications. LHCb features a single-arm spectrometer design, providing forward angular coverage ranging from roughly 10 mrad to 300 mrad in the bending plane and up to 250 mrad in the non-bending plane. This specific geometry is chosen because, at high energies, both b and ¯ 𝑏 hadrons are predominantly produced within the same forward or backward directional cone. The basic characteristics of LHCb are: Dimensions: 21 meters long, 13 meters wide and 10 meters high. Weight: 5 600 tons. 2.3 subdetectors We essentially have a Vertex Locator ( VELO ) (to determine the trajectory of the particles near the point of interaction, with the main objective of separating the primary vertices where, for example, the B-mesons are produced and the secondary ones, where they decay), RICH (to identify the particles producing each track by obtaining their mass and charge), T-stations (give the trajectories and momentum of charged particles), ECAL (detect electrons and photons), HCAL (detect hadrons), Muon Chambers (detect muons). 2.3.1 magnet: The LHCb dipole magnet [59] provides a magnetic field of 4 T.m that curve the charged particles in the horizontal plane of the detector with the idea of allowing the 20 2.3. subdetectors measurement of their momenta. The measurement covers the forward acceptance of ±250 mrad vertically and of ±300 mrad horizontally. To account for potential systematic effects, the orientation of the magnetic field is alternated periodically between upward and downward directions. The magnetic field provided by the dipole must be known with excellent precision, in order to yield a momentum resolution as good as possible. The precision of the measurement obtained for the field mapping in the tracking volume is about 4·10−4 . The trajectory of beams circulating within the LHC is influenced by the existence of the LHCb dipole magnet. To mitigate this impact, three compensatory magnets are strategically positioned around the detector [45]. 2.3.2 vertex locator: The Vertex Locator (VELO) [[37],[36],[35]] is the subdetector placed closer to the proton interaction point (primary vertex). It is designed to locate the primary and secondary vertices, focusing in b and c-hadrons decays. The VELO also provides an excellent time resolution to measure the lifetimes of this particles, something crucial to investigate CP violation effects. The Run 2 VELO contains two halves with 21 stations each, positioned along and perpendicular to the beam axis. Two types of silicon sensors are used: one measures the r coordinate with circular strips centered around the beam axis, the other measures the 𝜙 coordinate with straight, almost radial strips (including a stereo-angle built in). The VELO is retractable, which allows to increase the separation between the two halves during injection and to adjust it (±5mm) to the position of the beam. The sensors are housed in a vacuum, isolated from the LHC vacuum by a slender, corrugated aluminum sheet. The design geometry enables the two halves of the VELO to overlap when completely closed, reducing the material a charged particle traverses from the interaction point to the sensors. The uncertainty in the primary vertex’s position primarily depends on the number of tracks generated during a proton-proton collision. On average, the resolution is 42 𝜇𝑚 in the 𝑧 -direction and 10 𝜇𝑚 in the direction perpendicular to the beam. The resolution of the impact parameter is 20 𝜇𝑚 , excluding the influence of the primary vertex, for tracks exhibiting the maximum transverse momentum. The accuracy of the decay length measurement varies between 220 𝜇𝑚 and 370 𝜇𝑚 , contingent on the specific decay channel. For the 𝐵0 𝑠→𝐷− 𝑠𝜋+ decay channel, a lifetime resolution of 40 𝑓 𝑠 has been attained, enabling a 5𝜎 measuring of Δ𝑚𝑠 up to 54𝑝𝑠−1 after a year of data collection [36]. 2.3.3 tracking system: In LHCb tracks are reconstructed forming particle trajectories from the hits that the tracking system collects. Appart from the VELO, the LHCb tracking system is composed by the Tracker Turicensis (TT) [35], a single station right upstream the magnet, and by three tracking stations downstream the magnet and before RICH2. The tracking stations have two different substructures: the inner tracker (IT) [14] 21 chapter 2. experimental conditions 2.4.4 tis / tos definition The LHCbIDs 1 associated with the final state particles of an offline candidate can be cross-referenced with those archived by the High-Level Trigger (HLT) to ascertain if the offline candidate received approval by the trigger. This comparative analysis yields a classification termed TISTOS (Trigger independent of Signal / Trigger on Signal). An offline candidate is categorized as TOS relative to a trigger selection if it gains acceptance by the respective trigger selection. To articulate this more formally, an offline candidate is Tos if the LHCbIDs of each of its final state particles coincide by over 70% with the LHCbIDs of the final state particles of a trigger-accepted candidate. Conversely, an offline candidate achieves a TIS classification relative to a trigger selection if its removal from the event doesn’t impede the trigger selection’s acceptance of the event. This implies the presence of an alternative particle within the event that also secures acceptance by the trigger selection. Formally, this is validated when the LHCbIDs of all final state particles of any accepted candidates exhibit less than a 1% overlap with the LHCbIDs of the final state particles of the offline candidate. For example, an event is identified as TISTISIS if it is TIS for the three trigger levels: L 0 , HLT1 and HLT2. The strategy for the B(Λ→𝑝𝜇−¯ 𝜈𝜇) measurement involves using TISTISTIS Data both for measuring the Λ→𝑝𝜇−¯ 𝜈𝜇 and Λ→𝑝𝜋− yields to reduce uncertainties as much as possible, since any trigger requirement will imply an extra systematic uncertainty. This is possible due to the large Λ production ratio at LHCb. 2.5 lhcbupgrade After the Run 2 data taking, LHC stopped for 4 years (Long Shutdown 2). During this period, the detector underwent a comprehensive upgrade, with many significant enhancements being made. These improvements enable LHCb to operate at an instantaneous luminosity five times greater than during Run 1 and Run 2 and to reconstruct data at 40 MHz LHC crossing rate, with the goal of accumulating a total integrated luminosity of approximately 50 fb−1 by the end of LHC Run 4 [34]. A side view of the upgraded detector can be seen in 2.5. The VELO underwent a total renovation, with the main technology now centered around hybrid silicon pixel detectors. The integration of pixel-based geometry, coupled with a reduced proximity to the initial measured point and minimized material usage, has markedly enhanced the VELO’s performance [32]. The Upstream Tracker (UT) is situated between RICH1 and the Magnet and enables a significant enhancement in acceptance compared to its predecessor, the TT. As charged particles traverse this tracking system, they produce hits; these UT hits are crucial for the initial stages of the software trigger. When combined with VELO hits, VELO-UT tracks are formed. The presence of a magnetic field in the 1 The LHCbID class serves as a universal channel identifier across the LHCb framework. Its primary function is within the updated track model, ensuring each measurement contributing to a track’s construction is distinctly marked. By having access to a set of LHCbIDs and their associated measurements, one should be able to replicate the track fitting outcomes. 28 2.6. lhcbdata flow VELO RICH1 TT Imán T1 T2 T3 RICH2 M5M4M3M2M1 HCALECAL Vertex Locator RICH1 UT Magnet SciFi Tracker RICH2 ECAL HCAL M2 M3 M4 M5 Figure 2.5: The LHCb upgraded detector according to the plane of curvature of the trajectory of the charged particles. UT region enables an initial estimation of particle momentum with approximately 15% uncertainty. Additionally, UT hits substantially reduce the rate of fake tracks and can markedly boost the statistics for long-lived particles such as 𝐾0 𝑆 or Λ , by providing measurements of the secondary vertex for particles that decay after passing the VELO [34]. The three tracking stations downstream the magnet and before RICH2 (T1, T2 and T3) were replaced by the Scintillating Fibre tracker (SciFi), tasked with tracking charged particles and determining their momentum. The system must attain a momentum resolution and track efficiency for band c-hadrons that is on par with the performance from Run 1 and Run 2, despite operating under conditions of increased particle density [34]. The RICH detectors and calorimeters were also upgraded, while maintaining the fundamental design principles of their predecessors. Concerning the muon system, the 𝑀1 station was removed as it was previously utilized for the Level-0 hardware trigger, which is no longer necessary. A detailed account of the trigger system implemented in the upgrade is provided in Section 3.4. 2.6 lhcbdata flow The first step in the data flow involves data collection using the LHCb subdetectors for actual data and the simulation and digitisation processes for the Monte Carlo simulation (MC). The simulation of events unfolds in three distinct phases: the generation of particles, facilitated by Pythia [19]; the decay of particles, managed by EvtGen [56]; and the propagation of particles through the detector, orchestrated by Geant4 [8]. 29 chapter 2. experimental conditions The Gauss software package oversees the entire simulation process. Subsequently, the digitisation process is simulated using Boole. The remaining stages of the data flow are consistent for both Monte Carlo (MC) and actual data. Initially, there are three trigger steps (refer to Section 2.4), supervised by the Moore software package. This is followed by the reconstruction process, conducted by Brunel, and ultimately, the stripping process, managed by DaVinci. The stripped data is stored and made accessible to analysts, who can utilize DaVinci to generate data and MC NTuples for their analyses. A comprehensive depiction of the LHCb data flow is available in Figure 2.6. Trigger Moore Reconstruction Brunel Stripping DaVinci Digitisation Boole Simulation Gauss Storage NTuple Making Analysis Leptonic.dst, … DaVinci ROOT, Numpy,.. Generation Decay Propagation Pythia EvtGen Geant4 LHCb Data Taking MC MC Storage Storage FULLSTREAM FULLSTREAM ReStripping Re-reconstruction VELO RICH1 TT Imán T1 T2 T3 RICH2 M5M4M3M2M1 HCALECAL Vertex Locator Rich1 TT Magnet T1 T2 T3 Rich2 M1 ECAL HCAL M2 M3 M4 M5 Figure 2.6: LHCb Data flow. 2.7 stripping The stripping process follows the trigger system and reconstruction in the data selection hierarchy. It is an software offline selection that filters specific decay channels or events of interest. In the stripping process, predefined selection criteria, known as "lines," are applied. Each line corresponds to a specific decay channel or a set of requirements. Multiple lines collectively form a "stripping version" or "stripping configuration". This selection is based on particle identification, kinematics, or other event characteristics. The cuts are optimized to retain as many signal events as possible while reducing the background. Events that pass the stripping criteria are retained for further analysis. These events are stored in a more accessible format, allowing physicists to analyze them in detail. 30 2.8. simulation software and frameworks 2.8 simulation software and frameworks Simulation plays a pivotal role in high-energy physics experiments such as those conducted at LHCb. It involves the use of computational models to mimic the physical processes occurring during particle collisions and their interactions with the detector. Simulations provide a theoretical framework that aids in the interpretation and understanding of the experimental data, helping physicists to unravel the mysteries of fundamental particles and their interactions. In the realm of LHCb experiments, various sophisticated software and frameworks play an indispensable role in the generation of accurate and reliable simulations. A notable mention is Gauss, the official LHCb software for event simulation. Gauss allows for the meticulous modeling of proton-proton collisions, subsequent particle decays, and their interactions with the detector’s material, based on the prevailing theoretical models and Monte Carlo techniques. It is complemented by the Gaudi framework [17], a versatile and robust environment used for data processing and analysis within LHCb. Gaudi facilitates the efficient handling of event data, ensuring that both simulated and real data are processed through identical reconstruction and analysis chains. This congruence ensures a coherent and straightforward comparison between experimental observations and theoretical expectations, ensuring the integrity of the results. 2.8.1 event generation Event generation is a key part of simulating physical processes, like those happening in experiments at LHCb. It helps turn theoretical physics ideas into a virtual form that can be studied and analyzed in detail. In LHCb experiments, event generators help simulate the first proton-proton collisions and the following series of particle decays and interactions. These generators use Monte Carlo methods, creating many possible events that show the random nature of quantum processes. This allows for a detailed study of all possible outcomes. The event generators work based on a given particle physics theory (not only the SM, BSM models can also be considered), helping the simulations closely match what we expect to see in the real world under the correspondent theory. Event generators are especially important for simulating rare particle decays, which are crucial for LHCb’s mission to study the behaviour of particles. The events created by these generators act as a base, allowing us to compare real-life experimental results with theoretical expectations, helping us to understand the physics involved. Pythia is a powerful tool used in the field of particle physics to simulate the generation of events in high-energy interactions, such as proton-proton collisions [19]. It provides detailed models of high-energy reactions, allowing us to understand the production and decay of particles and antiparticles. In the context of the LHCb experiment, Pythia is used by Gauss to accurately simulate the particles produced immediately after proton-proton collisions. EvtGen is another essential tool used in particle physics simulations, specializing in the simulation of the decay of heavy particles, like those produced in proton-proton collisions [56]. After Pythia simulates the initial collision and production of particles, 31 chapter 2. experimental conditions EvtGen takes over to handle the detailed simulation of how these generated particles decay into lighter particles. Gauss, the overarching simulation software used in the LHCb experiment, orchestrates this process. 2.8.2 detector simulation Detector simulation is a crucial part of analyzing results in high-energy physics, helping to connect theory with actual experiment results. In the LHCb experiment, detector simulation carefully mimics the paths of particles as they move through the detector, interact with its parts, and leave behind electronic traces that we can measure. Specialized software helps to recreate the physical happenings inside the detector, capturing details like particle interactions and energy left behind. This helps us understand how the detector responds to various particles and events, making it easier to pull out useful information from the raw data. Detector simulation creates a virtual model of the detector’s actions, improving the reliability and precision of the experiment’s analysis. This ensures that the conclusions drawn are based on a detailed understanding of how the detector works and performs. Geant4 is a powerful software tool used to simulate how particles move through and interact with detectors in experiments [8] like those conducted at LHCb. Gauss is a program that uses various tools, including Geant4, to simulate the entire journey of particles produced in high-energy collisions. After the initial collision is simulated, and the particles are produced and decayed using tools like Pythia and EvtGen, Gauss uses Geant4 to simulate the next part of the particles’ journey. Geant4 helps Gauss to create a virtual replica of the LHCb detector. It carefully simulates how the particles travel through the detector, how they interact with the materials in the detector, and how these interactions leave behind signals that can be measured. Geant4 is very detailed and can mimic the real physical processes happening inside the detector, like how particles lose energy and how they scatter. This makes the simulation very realistic, helping researchers to better understand and interpret the actual experimental data collected by the LHCb detector. By using Geant4, Gauss ensures that the simulations are as accurate and useful as possible, helping scientists to make sense of their experiments and explore the mysteries of particle physics. 2.8.3 reconstruction and analysis Reconstruction and analysis are key steps in turning raw data from experiments or computer simulations into useful scientific findings. In the LHCb experiment, reconstruction means taking the basic electronic signals from the detector and turning them into a clear picture of each event. This includes figuring out which particles are present and determining their paths, speeds, and energy. Both real experiment data and simulated data go through the same reconstruction process, making sure the results are consistent and trustworthy. During the analysis part, the refined data is closely studied to find important information about physical properties and behaviors. Different statistical methods and 32 2.8. simulation software and frameworks data selection criteria are used to focus on specific particles or decay types. Insights from both real and simulated data work together to improve our understanding of the physics involved. This collaboration helps to make sure that the experiment results are accurate and can be confidently compared with theoretical expectations. Overall, this process helps to carefully assess the experiment’s methods and results, supporting detailed and reliable discoveries about particle behaviors. 2.8.4 validation and calibration Validation and calibration are important steps that make simulations in the LHCb experiment more accurate and trustworthy. Validation means carefully checking that the simulated data matches up with the real experiment results. This makes sure that the simulations are a reliable tool for testing ideas and understanding data. Any differences found during validation are studied closely to improve the simulations, making them better at predicting what will happen. Calibration is about adjusting the simulations to make sure they match the actual responses of the detector and the real experimental conditions. Since experiments can be complicated and changeable, calibration helps keep the simulations up-to-date and accurate in reflecting what is actually happening in the experiments. Together, validation and calibration help make sure that the simulations are strong and dependable, accurately showing what happens in high-energy physics experiments. This helps increase trust in the results from the simulations, making them useful for planning experiments, understanding results, and discovering new things about the basic particles and how they interact. 2.8.5 use of simulation in this research In this thesis, simulation has been instrumental in refining the analysis strategy and enhancing the robustness of the results. Using the Gauss and Gaudi software frameworks, a detailed simulation of the signal and background processes was conducted. This allowed for a meticulous evaluation of the detector’s response, enabling a comprehensive comparison between the simulated and real data, thereby facilitating a more accurate extraction of the physical parameters under study. For the B(Λ→𝑝𝜇−¯ 𝜈𝜇) measurement, we generated specific Λ→𝑝𝜇−¯ 𝜈𝜇 and Λ→𝑝𝜋− simulation samples (using a specific EvtGen model for the Λ→𝑝𝜇−¯ 𝜈𝜇 ) passing the Λ→𝑝𝜇−¯ 𝜈𝜇 stripping line. For the normalization, we used MinBias MC (see next section) samples to compute the efficiencies needed to compute the total amount of Λparticles in the data sample. 2.8.6 minimum bias simulation A minimum bias (MinBias) simulation aims to resemble as close as possible typical LHCb events without introducing any bias. A complete list of the Pythia processes that are included in the MinBias MC can be found in [33]. This kind of simulation will be used in the normalization process in our case. 33 chapter 2. experimental conditions When normalizing against modes that exhibit high yields in Minimum Bias events (such as Λ→𝑝𝜋− , 𝐾0 𝑆→𝜋+𝜋− ), utilizing specific Decay Files with imposed generator-level cuts for these modes offers no particular advantage. Note that such two-body decays do not require a dedicated EvtGen model. In practice, one is likely to encounter a greater number of these decays in the underlying event. Implementing generator-level cuts complicates matters, as it becomes challenging to ascertain which decay the cuts have impacted, making efficiency calculations increasingly complex. Opting for Minimum Bias allows for a straightforward calculation of the combined generation-level and reconstruction efficiencies in a single step. With an adequately sized Minimum Bias sample, statistical concerns should not arise. 34 chapter 3 STRANGE PHYSICS AT LHCb Precise measurements of the 𝑏→𝑐 transition provide hints of Lepton Flavor Universality (LFU) breaking [30], which could point to physics Beyond the Standard Model (BSM). It is natural to investigate whether similar behavior occurs in other charged-current decays of d-type quarks, namely 𝑠→𝑢. The LHCb experiment has shown its capability to obtain leading strange physics measurements, particularly searching for their rare decays. In fact, the LHCb collaboration has published the world’s most precise measurement in 𝐾0 𝑆→𝜇+𝜇− , 𝐾0 𝑆→𝜇+𝜇−𝜇+𝜇−, and Σ+→𝑝𝜇+𝜇−[2] [4], [3]. In the last decades the focus was in the higher mass sector of the CKM matrix. However it is the low mass sector, 𝑉𝑢𝑑 and 𝑉𝑢𝑠 , where is it possible to obtain the highest precision and the most sensitive test of the unitary of the CKM matrix [23]. For the CKM matrix to be unitary, |𝑉𝑢𝑑 |2 + |𝑉𝑢𝑠 |2 + |𝑉𝑢𝑏 |2≡1 . Since |𝑉𝑢𝑏 | has been measured to be 0.00369 ±0.00011 [78], |𝑉𝑢𝑏 |2 is almost negligible and the unitary test reduces to |𝑉𝑢𝑑 |2 + |𝑉𝑢𝑠 |2 = 1, which can be expressed in terms of the Cabibbo angle ( 𝜃𝑐 ) as cos2𝜃𝑐+sin2𝜃𝑐=1 . Experimentally, |𝑉𝑢𝑑 | can be determined from nuclear beta decay [53], and |𝑉𝑢𝑠 | can be measured in strangeness-changing semileptonic decays [20]. Precise determination of the 𝑠→𝑢 transition is therefore an important component of validating the unitarity of the CKM matrix. As it was explained in the Introduction, a 2.2 𝜎 tension with the expected unitarity was observed in the first CKM row unitarity test. The measurements of 𝑉𝑢𝑠 in leptonic (𝐾𝜇2) and semileptonic (𝐾𝑙3) kaon decays exhibit also a 3𝜎discrepancy [72]. Taking this into account, it is necessary to measure 𝑉𝑢𝑠 with high precision and Semileptonic Hyperon Decays (SHD) are the natural alternative. From a theoretical standpoint, studies have demonstrated that the SHD (refer to Fig. 3.1 for a list of hyperons) can potentially detect specific BSM dynamics that break leptonic universality. These decays are governed by a minor SU(3) flavor breaking parameter, enabling systematic expansions and precise predictions in terms of a reduced dependence on hadronic form factors. Muonic decays are particularly 35 chapter 3. strange physics at lhcb Figure 3.1: A hyperon is any baryon containing one or more strange quarks, but no charm bottom, or top quark, being the Λ the lightest of them. The expected yields for semileptonic hyperon decays in LHCb are large. sensitive to scalar and tensor deviation contributions. Such patterns could complement direct searches for new physical phenomena at the LHC [26]. The LFU test observable defined as the ratio between muon and electron modes 𝑅𝜇𝑒 = Γ(𝐵1→𝐵2𝜇−¯ 𝜈𝜇) Γ(𝐵1→𝐵2𝑒−¯ 𝜈𝑒)(3.1) is sensitive to non standard scalar and tensor contributions [26] . Moreover, in the SM, the dependency on the form factors is anticipated to simplify when considering the ratio. Indeed, by operating at Next-to-Leading Order (NLO), we achieve: 𝑅𝜇𝑒 SM =√︄1−𝑚2 𝜇 Δ2 1−9 2 𝑚2 𝜇 Δ2−4𝑚4 𝜇 Δ4!+15 2 𝑚4 𝜇 Δ4arctanh √︄1−𝑚2 𝜇 Δ2! where Δ=𝑀2−𝑀1. This prediction is remarkable, since up to this relative theoretical precision (O((𝑀1−𝑀2)2 𝑀2 1)) the ratio does not depend on form factors [26]. In 2019 we published a paper, Ref. [10] describing some prospects for measurements with strange hadrons at LHCb. A table with the acceptance efficiencies and invariant mass resolutions for the studied strange hadron decays can be found in Tab. 3.1. The production rate in LHCb, compared to the 𝐾0 𝑆 one, was also computed (see Fig. 3.2). 36 3.1. Λ→𝑝𝜇−¯ 𝜈𝜇 Table 3.1: In this study, the acceptances and invariant mass resolutions for key strange channels were evaluated using a simulation based on the upgraded tracking of the LHCb. The calculated acceptances were then normalized with respect to the fully reconstructed 𝐾0 𝑆→𝜇+𝜇− , which has been determined to be 1% . The efficiency has been presented for both long and downstream tracks, and the invariant mass resolution has been shown for each reconstruction method, as detailed in [10]. Here, R represents the production ratio relative to the 𝐾0 𝑆one. Channel R𝝐𝑳𝝐𝑫𝝈𝑳𝝈𝑫 (𝑀𝑒𝑉 𝑐2) (𝑀𝑒𝑉 𝑐2) 𝐾0 𝑆→𝜇+𝜇−1 1.0 (1.0) 1.8 (1.8) ∼3.0 ∼8.0 𝐾0 𝑆→𝜋+𝜋−1 1.0 (0.30) 1.9 (0.91) ∼2.5 ∼7.0 𝐾0 𝑆→𝜋0𝜇+𝜇−1 0.93 (0.93) 1.5 (1.5) ∼35 ∼45 𝐾0 𝑆→𝛾𝜇+𝜇−1 0.85 (0.85) 1.4 (1.4) ∼60 ∼60 𝐾0 𝑆→𝜇+𝜇−𝜇+𝜇−1 0.37 (0.37) 1.1 (1.1) ∼1.0 ∼6.0 𝐾0 𝐿→𝜇+𝜇−∼1 2.7 (2.7) ×10−30.014 (0.014) ∼3.0 ∼7.0 𝐾+→𝜋+𝜋+𝜋−∼2 9.0 (0.75) ×10−341 (8.6) ×10−3∼1.0 ∼4.0 𝐾+→𝜋+𝜇+𝜇−∼2 6.4 (2.3) ×10−30.030 (0.014) ∼1.5 ∼4.5 Σ+→𝑝𝜇+𝜇−∼0.13 0.28 (0.28) 0.64 (0.64) ∼1.0 ∼3.0 Λ→𝑝𝜋−∼0.45 0.41 (0.075) 1.3 (0.39) ∼1.5 ∼5.0 Λ→𝑝𝜇−¯ 𝜈𝜇∼0.45 0.32 (0.31) 0.88 (0.86) - - Ξ−→Λ𝜇−¯ 𝜈𝜇∼0.04 39 (5.7) ×10−30.27 (0.09) - - Ξ−→Σ0𝜇−¯ 𝜈𝜇∼0.04 24 (4.9) ×10−30.21 (0.068) - - Ξ−→𝑝𝜋+𝜋−∼0.04 0.41 (0.05) 0.94 (0.20) ∼3.0 ∼9.0 Ξ0→𝑝𝜋−∼0.03 1.0 (0.48) 2.0 (1.3) ∼5.0 ∼10 Ω−→Λ𝜋−∼10−395 (6.7) ×10−30.32 (0.10) ∼7.0 ∼20 3.1 Λ→𝑝𝜇−¯ 𝜈𝜇 Among the studied channels, Λ→𝑝𝜇−¯ 𝜈𝜇1 is one of the more interesting SHD due to its high reconstruction efficiency and because, being the lightest hyperon, it is the most abundant in LHCb. The purpose of the main analysis in this thesis is to measure its branching ratio using the LHCb Run2 data sample. In [10] we proposed a strategy to separate Λ→𝑝𝜇−¯ 𝜈𝜇 from the main background, Λ→𝑝𝜋− , using the missing perpendicular momentum in the Λ direction of flight vs 𝑀(𝑝𝜇)plane. 1 From now on, when discussing the decay modes such as Λ→𝑝𝜇−¯ 𝜈𝜇 , Λ→𝑝𝜋 − , among others, we will always implicitly include the charge-conjugate modes as well. 37 chapter 3. strange physics at lhcb VELO UT SciFi Magnet RICH1 RICH2, ECAL, HCAL M2 M3 M4 M5 zfΔtx tx Figure 3.3: Simplified side view of the LHCb detector and a graphic representation of the VELO-UT muon matching algorithm. The implied subdetectors are highlighted in blue. The GPU-based implemented technology of Allen contributed to make possible the removal of the hardware trigger. This hardware trigger, based on selecting only high-energy particles, reduced significantly the strange physics statistics during Run 2. As a consequence, Allen’s flexibility makes possible to develop different strategies to trigger on strange particles. For instance, the HLT now enables triggering based on displacement, which is advantageous for the strange physics program, as particles with lower mass tend to travel further within the detector. The updated reconstruction sequence delivers remarkable results for the decay products of low-momentum signals, particularly for Kaons and other strange particles. The overall efficiency for Forward-tracking tracks originating from strange particle decays stands at 76.5% for energies above 3 GeV and 81.4% for energies above 5 GeV. This represents an improvement of more than double per track compared to the HLT1 Forward-tracking reconstruction utilized in Run 2. Consequently, there is no longer a requirement for distinct reconstruction processes for low-momentum particles at the HLT1 level. This not only streamlines the reconstruction sequence but also ensures uniformity in the HLT1 Forward-tracking reconstruction [60]. 44 chapter 4 OBJECTIVES AND METHODOLOGY This thesis has clear goals that aim to help us learn more about lepton flavour universality. The main goal is to add new knowledge to what we already know and to check if what we think we know is really true by carefully looking at the data and what it shows us. 4.1 objectives The primary goal of this thesis is to measure precisely B(Λ→𝑝𝜇−¯ 𝜈𝜇) , surpassing all existing measurements to set a new world record for precision. Since the Λ→𝑝𝑒−¯ 𝜈𝑒 electron mode has already been measured very precisely ( B(Λ→𝑝𝑒−¯ 𝜈𝑒)=(8.34 ± 0.14) ×10−4 [78]) and the SM gives us a clean prediction for the ratio between the muonic and electron modes, a improved measurement of the B(Λ→𝑝𝜇−¯ 𝜈𝜇) can directly translates into a search for BSM dynamics that can modify the branching fraction. As a result, this measurement will imply new constraints in LFU in 𝑠→𝑢 quark transitions. 4.2 methodology First of all, it is important to mention that this is not a direct B(Λ→𝑝𝜇−¯ 𝜈𝜇) measurement. The branching fraction will be measured using Λ→𝑝𝜋− as normalization channel, and incorporating B(Λ→𝑝𝜋−) as an input. The underlying principle is to fit the amount of Λ→𝑝𝜇−¯ 𝜈𝜇 and Λ→𝑝𝜋− events in the Run 2 LHCb dataset (using TISTISTIS data) and, dividing those extracted yields by the efficiencies computed with our MC, extract the total amount of Λ→𝑝𝜇−¯ 𝜈𝜇 and Λ→𝑝𝜋−generated at LHCb during the 2016-2018 period. 45 chapter 4. objectives and methodology Dividing the number of Λ→𝑝𝜋− by the B ( Λ→𝑝𝜋− ) we can compute the total amount of Λ particles. Afterwards, we can divide this number by the total Λ→𝑝𝜇−¯ 𝜈𝜇 yield to compute B(Λ→𝑝𝜇−¯ 𝜈𝜇). The normalization fit will be performed to a double sided crystal ball + an exponential PDF using the M(p 𝜋 ) variable where Λ→𝑝𝜋− peaks. The crystal ball tail parameters will be extracted by fitting the Λ→𝑝𝜋− MC. Previously some cuts will be introduced to remove the 𝐾0 𝑆→𝜋+𝜋−component. The signal yield will be determined through a binned two-dimensional (2D) fit in a plane that reasonably separates Λ→𝑝𝜋− and Λ→𝑝𝜇−¯ 𝜈𝜇 . This fit will utilize Poisson statistics and employ the MC distributions as templates. The adoption of a 2D fit aids in managing the challenge posed by low background MC statistics. Various systematic uncertainties will be considered and calculated. Most will pertain to discrepancies between data and Monte Carlo behaviors, with the most significant arising from the choice of binning scheme and modes in the 2D fit. The Λ→𝑝𝜇−¯ 𝜈𝜇 MC utilized is generated with a specific EvtGen model to verify its differential decay rate, and both Λ→𝑝𝜇−¯ 𝜈𝜇 and Λ→𝑝𝜋− MC samples are produced using LHCb’s full simulation, passing through all the steps of the LHCb data-flow. Minimum Bias (MinBias) MC is employed to determine the efficiency and behavior of Λ→𝑝𝜋−for the normalization channel. 46 chapter 5 ANALYSIS The main challenge associated to the B(Λ→𝑝𝜇−¯ 𝜈𝜇) measurement at LCHb will be discriminating the signal from peaking background, primarily from Λ→𝑝𝜋− decays, but also from 𝐾0 𝑆→𝜋+𝜋− decays. In addition, removing the combinatorial background can be challenging due to the presence of a neutrino in the Λ→𝑝𝜇−¯ 𝜈𝜇 final state, which results in missing momentum that we have to account for. Only long tracks will be used in this analysis. As we are not dominated by statistical uncertainties, there is no pressing need to include downstream tracks, whose resolution could adversely affect the measurement. This is because our kinematic strategies heavily rely on having a good resolution. To generate simulated events that reproduce the theoretical kinematic distributions, a new EvtGen [56] model will be necessary. The next step will involve studying the signal properties and comparing them with those of the background. Subsequently, we will develop selection criteria to effectively separate the signal from the background and, ultimately, obtain an estimated value for the expected yield of Λ→𝑝𝜇−¯ 𝜈𝜇decays at LHCb. The branching ratio can be expressed as the number of Λ decaying to 𝑝𝜇−¯ 𝜈𝜇 in our dataset over the total amount of Λparticles in our dataset: B(Λ→𝑝𝜇−¯ 𝜈𝜇)=𝑁(Λ→𝑝𝜇−¯ 𝜈𝜇) 𝑁(Λ)(5.1) being 𝑁(Λ→𝑝𝜇−¯ 𝜈𝜇)=𝑁reco 𝑝𝜇𝜈 𝜖𝑝𝜇𝜈 (5.2) where 𝑁reco 𝑝𝜇𝜈 is the number of Λ→𝑝𝜇−¯ 𝜈𝜇 events reconstructed and selected as signal and 𝜖𝑝𝜇𝜈 is the efficiency of this process, extracted from Monte Carlo (MC) studies. Applying Eq. 5.1 and Eq. 5.2 to the Λ→𝑝𝜋−case, is easy to obtain 47 chapter 5. analysis B(Λ→𝑝𝜋−)=𝑁reco 𝑝𝜋 𝜖𝑝𝜋 𝑁(Λ)(5.3) and combining previous equations arrive to: B(Λ→𝑝𝜇−𝜈𝜇)=B(Λ→𝑝𝜋−)𝜖𝑝𝜋 𝜖𝑝𝜇𝜈 𝑁reco 𝑝𝜇𝜈 𝑁reco 𝑝𝜋 (5.4) So, we can define an 𝛼 parameter that relates the Λ→𝑝𝜇−𝜈 branching ratio and the number of reconstructed signal events 𝑁reco 𝑝𝜇𝜈 , B(Λ→𝑝𝜇−𝜈𝜇)=𝛼𝑁reco 𝑝𝜇𝜈 (5.5) being 𝛼=B(Λ→𝑝𝜋−) 𝑁reco 𝑝𝜋 𝜖𝑝𝜋 𝜖𝑝𝜇𝜈 (5.6) Once we calculate the 𝛼 parameter, using the PDG value for the B ( Λ→𝑝𝜋− ), we will be able to obtain the expected yield. Two Stripping Lines with aligned cuts have been created, as will be explained in the next section. The first one is for normalization, where we can fit the yield of Λ→𝑝𝜋−decays, while the other one aims to maximize signal purity. During the Run2, LHCb had 3 trigger levels (L 0 , HLT1 and HLT2). As clarification, an offline candidate is considered to be TIS with respect to a trigger selection if removing it from the event would still cause the trigger selection to accept the event. TISTISTIS means that the event is TIS for the L0, the HLT1 and the HLT2 Trigger. Both fits will be performed to TISTISTIS Data, to reduce systematic uncertainties to the minimum. 5.1 analysis strategy The Λ→𝑝𝜇−¯ 𝜈𝜇 branching ratio will be obtained using as input the B(Λ→𝑝𝜋−) . Two Stripping Lines have been written with this purpose, the normalization one (NormLine) to select Λ→𝑝𝜋− and measure its yield and the signal one (SignalLine) to select Λ→𝑝𝜇−¯ 𝜈𝜇 and measure its yield. Cuts in both lines are aligned to reduce systematic errors, being the particle ID cuts and the mass window the only difference between them. In addition, we have a MinBias MC Sample for 2018 MD and 2018 MU, and a Stripping Filtered Production for both Λ→𝑝𝜋− and Λ→𝑝𝜇−¯ 𝜈𝜇 channels passing SignalLine for 2016, 2017 and 2018 with Magnet Up and Magnet Down configurations. Taking that into account, the analysis strategy can be summarized in the following steps: 1. Add Common Cuts to MC and Data passing NormLine. The idea is to remove the 𝐾0 𝑆→𝜋+𝜋−component. 48 5.1. analysis strategy 2. Fit Λ→𝑝𝜋− from MinBias MC passing NormLine, selected with the TRUE ID 1, to obtain the tail parameters of the Lppi peak. 3. Fit TISTISTIS Data passing NormLine for each year and polarity, setting the tail parameters obtained in the TRUE ID MinBiasMC Fit. By doing this, we obtain the amount of Λ→𝑝𝜋− in Data passing the Normalization StrippingLine (𝑁NormLine Λ→𝑝𝜋 −). 4. Obtain the efficiency for the Λ→𝑝𝜋− passing NormLine ( 𝜖NormLine Λ→𝑝𝜋 − ). This will be obtained by fitting the MinBiasMC passing NormLine setting the tail parameters extracted in point 2 to obtain the amount of Λ→𝑝𝜋− in that sample and dividing this number by the total amount of Λ→𝑝𝜋−in the MinBiasMC sample (before the reconstruction and the stripping). 5. The amount of Λ→𝑝𝜋− in Data before the stripping ( 𝑁Λ→𝑝𝜋 − ) will be obtained dividing the output of step number 3, 𝑁NormLine Λ→𝑝𝜋 − , by the output of step 4, 𝜖NormLine Λ→𝑝𝜋 −. 𝑁Λ→𝑝𝜋 −= 𝑁NormLine Λ→𝑝𝜋 − 𝜖NormLine Λ→𝑝𝜋 − (5.7) 6. Next step will be to perform a fit to measure the amount of Signal in TISTISTIS Data passing the SignalLine, 𝑁SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇. 7. Using the Λ→𝑝𝜇−¯ 𝜈𝜇 stripping filtered MC production we can obtain the selection efficiency for signal, 𝜖𝑆𝑒𝑙 Λ→𝑝𝜇−¯ 𝜈𝜇 . From the production logs we can also obtain the efficiency for the signal passing the SignalLine, 𝜖SignalLine Λ→𝑝𝜇−¯ 𝜈𝜇 . The product of both efficiencies is 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇. 8. The efficiencies 𝜖SignalLine Λ→𝑝𝜇−¯ 𝜈𝜇 and 𝜖NormLine Λ→𝑝𝜋 − are corrected using PidCalib2 and TrackCalib2. 9. The final step, will be to obtain the B(Λ→𝑝𝜇−¯ 𝜈𝜇)appliyng the equation B(Λ→𝑝𝜇−¯ 𝜈𝜇)=𝑁SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇B(Λ→𝑝𝜋−) 𝑁NormLine Λ→𝑝𝜋 − 𝜖NormLine Λ→𝑝𝜋 − 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇 (5.8) Obviously, in the previous analysis description we will be taking into consideration also the charge conjugated modes. Obviously, following the footnote 1 prescription, in the previous analysis description we will be taking into consideration also the charge conjugated modes. A diagram of the Analysis workflow can be found in Fig. 5.1. 1 The TRUE ID variable provides the ID of the particle responsible for producing a track, with the ID numbering following the PDG Monte Carlo numbering scheme [63]. This variable is exclusively defined in MC samples, where the true information of the event is accessible. 49 chapter 5. analysis Figure 5.1: Analysis workflow. Blue color indicates processes related to normalisation and red ones to the signal measurement. Black color is associated to MC and yellow to MC corrections. Dotted lines show the systematic uncertainty sources. 50 5.2. stripping lines 5.2 stripping lines Eventhough in LHCb an event is only recorded if it passes a Trigger Line, we have a huge amount of events in LHCb Data. As a consequence, specific stripping lines (offline selection) are written to reduce the amount of events, selecting only those that verify some cuts. In general, a Stripping Line is designed to select a certain decay channel. In our case we designed two Stripping Lines, one to select the Signal ( Λ→𝑝𝜇−¯ 𝜈𝜇 ) and the other to select the normalization channel (Λ→𝑝𝜋−). From now on we will call the Stripping Line written aiming to select Λ→𝑝𝜇−¯ 𝜈𝜇 SignalLine and the Stripping Line written to select Λ→𝑝𝜋−NormLine. Both Trigger Line Cuts (see Tab. 5.1) are aligned to reduce the systematic errors associated to the Λ→𝑝𝜇−¯ 𝜈𝜇branching fraction measurement as much as possible. Notice the accidentally missing cut in the pion Impact Parameter. This cut will be added in NormLine Data after the stripping process to align both Stripping Lines. Table 5.1: This table compares the cuts applied in the SignalLine and NormLine side-by-side for each category. Note that for the Daughter Cuts (Muon/Pion), the cuts are compared between the muon in the SignalLine and the pion in the NormLine. Category Variable SignalLine Cut NormLine Cut Combination Cuts DOCA 1[mm] <0.3 <0.3 Mother Mass [𝑀𝑒𝑉 /𝑐2]<1141 <1141 Mother Cuts 𝜏[ps] >9>9 Mother Mass [𝑀𝑒𝑉 /𝑐2]<1141 <1141 𝑉𝜒22<9<9 𝜒2distance to PV >50 >50 IP 3[mm] >0.2 >0.2 Proton Cuts Proton ProbNN >0.3 >0.3 Muon ProbNN <0.7 <0.7 Kaon ProbNN <0.7 <0.7 Ghost ProbNN <0.2 <0.2 𝐼𝑃𝜒2>16 >16 Track 𝜒2/d.o.f. <3<3 Muon/Pion Cuts Pion ProbNN <0.7 >0.4 Muon ProbNN >0.3 <0.7 Kaon ProbNN <0.7 <0.7 Ghost ProbNN <0.2 <0.2 ISMUON TRUE FALSE IP >1×Missing 𝐼𝑃𝜒2>60 >60 Track 𝜒2/d.o.f. <3<3 51 chapter 5. analysis 5.2.1 definition of stripping variables 5.2.1.1 probnn This variables, used for particle identification, are derived from Neural Networks (NNs). To obtain these variables, data from various subdetectors are utilized, taking their correlations into account. The objective is to determine a value that correlates with the probability of each track being produced by a specific type of particle. 5.2.2 ismuon The process to spot muons begins by linking the hits in the muon detectors with each track. This involves extending the tracks in a straight line towards the detectors. An area called the Field of Interest (FoI) is then established around the projected spot. The size of this area varies based on the track’s momentum, the specific muon chamber, and its location. Within these FoIs, the search for detections occurs, with the number of detectors involved depending on the track’s momentum. The nearest hits are selected for further consideration, and only tracks with these confirmed hits go on to the subsequent steps in the identification process. The initial outcome of this method is a simple yes-or-no indicator, known in the LHCb community as IsMuon which signifies the most elementary level of identifying a muon. 5.2.2.1 doca The Distance Of Closest Approach (DOCA) of the two daughters. This represents the minimal length that separates two tracks. 5.2.2.2 ip The impact parameter is the perpendicular distance between the trajectory of a particle and the vertex from which it originates or at which it decays. 5.2.2.3 ip𝜒2 The impact parameter significance in units of 𝜒2. 5.2.2.4 𝜒2distance to pv This variable is related to the mother particle distance of flight, since includes the difference between the primary and secondary vertices. 1Distance Of Closest Approach. 2Vertex 𝜒2/d.o.f. 3Impact Parameter. 52 5.2. stripping lines 5.2.2.5 𝜏 Measured lifetime of the mother particle. 5.2.2.6 v𝜒2 The vertex 𝜒2 reflects the quality of fit for the estimated position of the decay vertex. 53 chapter 5. analysis 5.4 background sources Having the MinBias MC passing the SignalLine sample provides us with an overview of what we can expect to observe in the Data. Although the average contribution of each decay in the MC may not be entirely reliable, studying it serves as a helpful exercise and can provide a rough estimate. For instance, it is crucial to note that even having a SignalLine with tight cuts designed to select Λ→𝑝𝜇−¯ 𝜈𝜇, the signal purity in this MinBias MC sample is only 3.48 %. Therefore, it is necessary to analyze the composition of the MinBias MC sample that passes the SignalLine. This analysis was conducted by applying the correspondent truth-matching conditions for each channel, that are detailed in the appendices A.3. Results can be found in Tab 5.9. An additional check was performed to ensure the absence of peaking backgrounds by replacing the mass hypothesis for the combinatorial background events (see Appendix A.6) Table 5.9: Average contribution of each decay channel to the MinBias MC sample after the Stripping process in SignalLine. In the non-obvious cases, reconstructed particles are written in bold symbols. A study of the average contribution after applying tighter PID cuts was performed, and the results can be seen in Appendix A.5. Decay Contribution Λ→𝑝𝜋−(42.7 ±1.5) % Combinatorial Background and Others (35.4 ±1.4) % Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇)(14.7 ±1.1) % Λ→𝑝𝜇−¯ 𝜈𝜇(3.48 ±0.56) % 𝐾0 𝑆→𝜋+𝜋−(2.20 ±0.44) % Ξ−→ (Λ→𝒑𝜋−)𝝅+(1.28 ±0.34) % Ξ−→ (Λ→𝒑𝜋−)(𝜋+→𝝁¯ 𝜈𝜇)(0.275 ±0.16) % Taking this results into account is obvious that Misidentified Λ→𝑝𝜋− and early Decays In Flight (eDIF) are the main backgrounds in this analysis, with a total expected contribution close to 60 %of the SignalLine sample. The early decays in flight (Fig. 5.3), with the pion decaying early to a muon and a neutrino, may be really hard to separate from signal, since we have the same final state in both channels with almost indistinguishable kinematic properties. The good news is that we have a dedicated LHCb production to simulate Λ→𝑝𝜋− passing SignalLine, which will be crucial to understand how to select the signal and how to discriminate these background sources. On the other hand, 𝐾0 𝑆→𝜋+𝜋− is an easier background to kill, since we can design a specific cut in the Armenteros-Podolanski plot to kill most of the 𝐾0 𝑆→𝜋+𝜋− preserving almost all the signal. 60 5.4. background sources Figure 5.3: A representation of an early decay in flight (eDIF). 5.4.1 misidentified Λ→𝑝𝜋− This decay, with a pion misidentified as muon, is the main background contribution to the MinBias MC SignalLine sample. Even though having created the SignalLine stripping line specifically to reduce this contribution, the difference in the branching ratios of Λ→𝑝𝜋− and Λ→𝑝𝜇−¯ 𝜈𝜇 is so large that we still are dominated by Λ→𝑝𝜋− . Despite that, it should be relatevely easy to design some selection cuts to remove most of MisID Λ→𝑝𝜋− . The Armenteros-Podolanski plot [66] should also be a good plane to impose selection requirements [42]. The Armenteros-Podolanski plot has as Y-axis the QPT variable, the transverse momentum of any of the daughters with respect to the mother direction of flight (in a 2-body decay both must be equal) and as X-axis the longitudinal momentum asymmetry, 𝛼=𝑝+ 𝐿−𝑝− 𝐿 𝑝+ 𝐿+𝑝− 𝐿 (5.15) where 𝑝+ 𝐿 and 𝑝− 𝐿 are 𝑝+𝑐𝑜𝑠(𝜃1) and 𝑝−𝑐𝑜𝑠(𝜃2) respectively, supposing that the particle 1 is the positive in Fig. 5.4. The mother direction of flight can be obtained from the primary and second vertex positions. Signal and Λ→𝑝𝜋− MC behaviour in the Armenteros-Podolanski plot can be found in Fig. 5.5. In Prospects for measurements with strange hadrons at LHCb [10] another two dimensional plane was suggested to separate Λ→𝑝𝜋− and Λ→𝑝𝜇−¯ 𝜈𝜇 . This two dimensional plane has as x-axis the missing transverse momentum in the plane that is perpendicular to the the mother particle direction of fly ( / 𝑝𝑇 2 ), and as y-axis the 𝑀(𝑝𝜇) (reconstructed mass with the proton-muon hypothesis). Fig. 5.6 shows the full-simulated behaviour in the plane. 2 This variable represents the missing transverse momentum in the plane that is perpendicular to the the mother particle direction of fly, calculated using reconstructed information. For a more detailed explanation, see subsection 5.5.1.1. 61 chapter 5. analysis Figure 5.4: 2-Body decay scheme in the laboratory frame of reference. Figure 5.5: Armenteros-Podolanski plot for SignalMC and Λ→𝑝𝜋 − MC passing SignalLine. Some conclusions can be extracted from Fig. 5.5 and Fig. 5.6. For example, if we compare the Λ→𝑝𝜋−MC passing the SignalLine behaviour in the ArmenterosPodolanki plot with a typical Λ→𝑝𝜋− dominated Armenteros-Podolanki plot, as the one in Fig. 5.7, we find relevant differences. For example, in Fig. 5.5, even having the usual Λ→𝑝𝜋− ellipse visible, the misidentified Λ→𝑝𝜋− passing NormLine presents a highly populated region under the ellipse. This is because if the pion decays to a muon and a neutrino far enough from the primary vertex it will be reconstructed as pion, but the reconstructed particle will have less momentum than the original pion, since the missing momentum is carried by the neutrino. On another hand, it draws attention an empty space under an ellipse centered in 𝛼≈ 0.82 with its maximum QPT value in QPT ≈ 60 𝑀𝑒𝑉 /𝑐 . An ellipse in the Armenteros-Podolanksi plot is equivalent to a specific mother mass. Taking this into account, the fact of not having misidentified Λ→𝑝𝜋− decays falling below this 62 5.4. background sources Figure 5.6: Missing momentum in the plane transverse to the Λ flight direction ( / 𝑝𝑇 ) vs. reconstructed mass M(𝑝𝜇) for Λ→𝑝𝜇−¯ 𝜈𝜇in blue and misidentified Λ→𝑝𝜋 −in red. Figure 5.7: Armenteros-Podolanski plot of a 10000 entries subsample of the MinBiasMC passing NormLine, where the Λ→𝑝𝜋−ellipse is remarkable. elipse indicates that there is a minimum mass that can be reconstructed with a proton and muon, where the muon comes from an original pion from the Λ→𝑝𝜋− decay. It is also remarkable that this does not happen in the Λ→𝑝𝜇−¯ 𝜈𝜇case. If this explanation is true, we should see the effect in the M(p 𝜇 ) distribution of the Λ→𝑝𝜋− passing SignalLine. The resultant normalised histograms are in Fig. 5.8, verifying our deduction. 63 chapter 5. analysis 1040 1060 1080 1100 1120 1140 M ( p ) MeV / c 2 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Signal MC MisID p MC Figure 5.8: Norm. M(p𝜇) distribution of Λ→𝑝𝜇−¯ 𝜈𝜇in blue and MisID Λ→𝑝𝜋 −in red. As a cross-check, Fig. 5.9 displays those events with low 𝑀(𝑝, 𝜇) , serving as a repetition of Fig. 5.5 and confirming the interpretation. Figure 5.9: Armenteros-Podolanski plot for Λ→𝑝𝜋 − MC passing SignalLine, showing in blue those events with 𝑀(𝑝, 𝜇)<1070 Mev/ 𝑐2 and in black those with 𝑀(𝑝, 𝜇)<1060 Mev/𝑐2. Concerning the / 𝑝𝑇 vs. M( 𝑝𝜇 ) plane (Fig. 5.5), we can also extract some conclusions from the 2-dimensional distributions. For example the higher minimum mass in the Λ→𝑝𝜋− is evident here. But there is also a different correlation between the / 𝑝𝑇 and the M( 𝑝𝜇 ) in both cases. This would allow for a possible selection cut in this plane to select a region with high signal purity. 64 5.4. background sources 5.4.2 early decays in flight (Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇)) If in a Λ→𝑝𝜋− decay the pion decays to a muon and a neutrino close enough to the secondary vertex, more than the 70 % of the track hits will be from the muon, and the track will be correctly matched to a muon. This category present some characteristic features, making it harder to distinguish from the signal. 1080 1090 1100 1110 1120 1130 1140 1150 1160 M ( p ) MeV / c 2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 MisID p MC eDIF p ( ) MC Figure 5.10: Normalised M(p 𝜋 ) distribution of eDIF in green and MisID Λ→𝑝𝜋 − in red. For instance, the eDIF category M(p 𝜋 ) distribution does not peak clearly in the Λ mass, whereas the MisID Λ→𝑝𝜋− presents a narrow peak centered in the Λ mass (see Fig. 5.10). As we can see in Fig. 5.11, the z-component of the muon origin vertex has a maximum value around 650 mm in the MisID Λ→𝑝𝜋− , whereas the eDIF category presents higher z-values for the muon origin vertices. So if the pion decays to a muon after this maximum value, which implies few VELO hits, it will never be reconstructed as a pion. Being the Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇) decays the hardest to separate from signal, having the same final state and similar kinematic properties, we have designed some variables that will help in this task. Those variables are presented in Section 5.5.1. 5.4.3 𝐾0 𝑆→𝜋+𝜋− Another problematic background source is 𝐾0 𝑆→𝜋+𝜋−with one pion misidentified as a proton an the other as muon or decaying in flight to a muon and a neutrino. This is the only peaking background anticipated to contribute to SignalLine events, excluding Λ→𝑝𝜋− . Having multiple peaking modes complicates the fitting of the signal yield. Hence, it’s crucial to eliminate it. Additionally, this decay channel also contaminates the Normalization sample. Even being a channel very different from signal, the 𝐾0 𝑆→𝜋+𝜋− production yield is so high in LHCb that its contribution to the SignalLine is relevant (see Tab. 5.9). 65 chapter 5. analysis 0 2000 4000 6000 8000 10000 True Muon Origin Vertex Z [mm] 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 MisID p MC 0 2000 4000 6000 8000 10000 True Muon Origin Vertex Z [mm] 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 eDIF p ( ) MC Figure 5.11: Normalised distribution of the true origin vertex z-component for the particle reconstructed as a muon for MisID Λ→𝑝𝜋 − (left) and for eDIF (right). Notice that the Origin Vertex Z refers to a different vertex for each channel. In the MisID Λ→𝑝𝜋 −case, where the particle reconstructed as a muon is actually a pion, its true origin vertex is the Λ decay vertex, whereas in the eDIF case, the true muon origin vertex is the pion decay vertex. The good news are that the 𝐾0 𝑆→𝜋+𝜋− falls inside a specific region in the Armenteros-Podolanksi plot. In general, 𝐾0 𝑆→𝜋+𝜋− decays should correspond to a narrow elipse in this plane. See for example Fig. 5.12, where we are selecting 𝐾0 𝑆→𝜋+𝜋− from the MinBias MC sample passing NormLine and the 𝐾0 𝑆→𝜋+𝜋− ellipse is clearly visible. On the other hand, the 𝐾0 𝑆→𝜋+𝜋− MC in the SignalLine is also, as it happens with the Λ→𝑝𝜋− channel, blurred around the usual 𝐾0 𝑆→𝜋+𝜋− ellipse, because of the missing momentum when the pion decays to a muon and a neutrino. The correspondent Armenteros-Podolanksi plot is depicted in Fig. 5.13. 0.5 0.6 0.7 0.8 0.9 0 20 40 60 80 100 120 140 QPT [ MeV / c ] K 0 S + MC NormLine Figure 5.12: Armenteros-Podolanski plot for 𝐾0 𝑆→𝜋+𝜋− from the MinBias MC sample passing NormLine, where the typical 𝐾0 𝑆→𝜋+𝜋−ellipse is remarkable. 66 5.4. background sources Figure 5.13: Armenteros-Podolanski plot for 𝐾0 𝑆→𝜋+𝜋−MC passing SignalLine. Even being less concentrated around the usual 𝐾0 𝑆→𝜋+𝜋− ellipse, it is easy to create a selection cut to remove this background. This will be explained in detail in the Selection section 5.5. 67 chapter 5. analysis 5.5 selection and new variables 5.5.1 variables Having background sources almost identical to our signal, the development of new variables was mandatory to be able to separate both. The idea is to use the kinematic properties of each decay channel to design specific variables that allow us to distinguish that channel. Being the Λ→𝑝𝜇−¯ 𝜈𝜇 case the most problematic for us, we started by separating those decays into two categories. If the pion decays early enough, we will have a muon in the vertex locator. If the pion decays into a muon and a neutrino after passing the VELO, then we will observe a pion at the VELO level. Those two categories and the strategies to recover the missing information are detailed in Fig. 5.14. It is important to note that these new variables are only computed for the SignalLine events, as they are not required for the normalization process. Figure 5.14: In the muon at VELO level case, the neutrino 𝑃𝑇 can be obtained from proton and muon momentum components and the neutrino 𝑃𝐿 by impossing Λ mass. In the pion at VELO level case, if the measured |® 𝑝𝜋| is not the correct one, Λ will not point to the primary vertex. Imposing Λto point to PV allows to solve for |® 𝑝𝜋|. 5.5.1.1 missing perpendicular momentum (/ 𝒑𝑻) In the muon at VELO level, when the pion decays to a muon and a neutrino within the Vertex Locator, the neutrino 𝑃𝑇 can be obtained from proton and muon momentum components. This can be done using the Λ flight direction −−−−−−−−−→ (𝑆𝑉 −𝑃𝑉 ) and using the GramSchmidt idea [70] to find two orthogonal vectors to that flight direction. First we should obtain the flight direction vector ( −→ 𝑓 ) using the Primary Vertex and the Λ Decay Vertex, and then compute the correspondent unit vector, dividing each component by |−→ 𝑓|. If the mother flight direction unit vector is called ˆ 𝑓 , the first perpendicular unit vector will be obtained by constructing a vector 𝑥𝑢=(− ˆ 𝑓𝑦,−ˆ 𝑓𝑥,0) and then obtaining a correspondent unit vector ˆ 𝑥𝑢 . Finally, the second unit perpendicular momentum will be the cross product ˆ 𝑦𝑢=ˆ 𝑓׈ 𝑥𝑢. 68 5.5. selection and new variables Having this orthogonal base allows us for obtain the missing perpendicular momentum in the mother flight direction. For example, we can add the two daughters momentum to obtain the −−→ 𝑝𝑝𝜇 and then project its components to the new base: −−→ 𝑝𝑝𝜇′=(−−→ 𝑝𝑝𝜇 .ˆ 𝑥𝑢,−−→ 𝑝𝑝𝜇 .ˆ 𝑦𝑢,−−→ 𝑝𝑝𝜇 .ˆ 𝑓)=(𝑝′ 𝑝𝜇𝑥, 𝑝′ 𝑝𝜇𝑦, 𝑝′ 𝑝𝜇𝑧)(5.16) Taking this into account, the missing perpendicular momentum in the mother flight direction will be / 𝑝𝑇=√︃𝑝′2 𝑝𝜇𝑥+𝑝′2 𝑝𝜇𝑦(5.17) 5.5.1.2 longitudinal neutrino momentum (/ 𝒑𝑻) In the muon at VELO level case, the neutrino 𝑃𝑇 can be obtained from proton and muon momentum components and the neutrino 𝑃𝐿by impossing Λmass. We can start by obtaining the perpendicular components of the neutrino momentum as it was explained in previous subsection. After that there will be only one piece missing, the longitudinal component of the neutrino momentum, that can be obtained imposing the Λmass. 𝑀2 Λ=(𝐸𝑝𝜇 +𝐸𝜈)2− |−−→ 𝑝𝑝𝜇 +−→ 𝑝𝜈|2=𝑀2 𝑝𝜇 +0+2.(𝐸𝑝𝜇 .𝐸𝜈−−−→ 𝑝𝑝𝜇 .−→ 𝑝𝜈)(5.18) where 𝐸𝑝𝜇 =√︃𝑀2 𝑝𝜇 + |−−→ 𝑝𝑝𝜇′|2(5.19) and 𝐸𝜈=√︃/ 𝑝2 𝑇+𝑝𝐿(𝜈𝜇)2(5.20) Taking into account that −−→ 𝑝𝑝𝜇 .−→ 𝑝𝜈=−/ 𝑝2 𝑇+𝑝′ 𝑝𝜇𝑧.𝑝𝐿(𝜈𝜇)(5.21) we finally obtain the expression to compute the 𝑝𝐿(𝜈𝜇): 𝑝𝐿(𝜈𝜇)= 𝐸𝑝𝜇 .√︃𝐴2−2𝐴./ 𝑝2 𝑇+/ 𝑝2 𝑇.𝑝′2 𝑝𝜇𝑧+/ 𝑝4 𝑇−/ 𝑝2 𝑇.𝐸2 𝑝𝜇 −𝐴.𝑝′ 𝑝𝜇𝑧+𝑝′ 𝑝𝜇𝑧./ 𝑝2 𝑇 (𝑝′ 𝑝𝜇𝑧)2−𝐸2 𝑝𝜇 (5.22) where 𝐴=𝑀2 Λ−𝑀2 𝑝𝜇 2(5.23) 69 chapter 5. analysis Table 5.11: Sel1 efficiencies for Signal, Lppi and eDIF MC. Sel1 Efficiency Signal MC 𝜖Sel1 Λ→𝑝𝜇−¯ 𝜈𝜇0.63656 ±0.00065 Lppi MC 𝜖Sel1 Λ→𝑝𝜋 −0.3175 ±0.0060 eDIF MC 𝜖Sel1 Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇)0.325 ±0.011 5.5.2.3 selection 2 (armenteros-podolanski plot) As mentioned earlier, the Armenteros-Podolanski plot can be useful in enhancing signal purity. In Fig. 5.23, possible selection cuts in this plane are shown. The central ellipse represents the region with higher signal density, while the region below the ellipse on the right corresponds to the area with higher expected signal purity in the data. Both cuts can be applied together or separately. However, selecting only events under the ellipse on the right poses a challenge as we would have insufficient background Monte Carlo (MC) statistics passing this cut. On the other hand, choosing to select only events inside the central ellipse would result in a loss of some signal without a substantial justification. Therefore, it appears more favorable to select events inside the yellow ellipse or below the green curve in Fig. 5.23. This cut will be named Sel2. Figure 5.23: Armenteros-Podolanski plane for Data (left) and MC (right) with positive 𝑃𝐿(𝜈𝜇). Dashed lines represent possible selection cuts. It is also remarkable that the requirement of a positive 𝑃𝐿(𝜈𝜇) is an exceptionally effective cut for removing 𝐾0 𝑆→𝜋+𝜋− background. Initially, our approach involved applying a cut in the Armenteros-Podolanski plot to eliminate this background contribution. However, we found that the removal power of both selections was comparable, with the positive longitudinal neutrino momentum requirement offering the advantage of preserving a larger number of signal, Lppi, and eDIF decays. Both strategies 76 5.5. selection and new variables Table 5.12: Sel2 efficiencies for Signal, Lppi and eDIF MC. Sel2 Efficiency Signal MC 𝜖Sel2 Λ→𝑝𝜇−¯ 𝜈𝜇0.54024 ±0.00065 Lppi MC 𝜖Sel2 Λ→𝑝𝜋 −0.3537 ±0.0061 eDIF MC 𝜖Sel2 Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇)0.3713 ±0.011 are represented in Fig. 5.24. So, in summary, we are applying the Sel1 + Sel2 selection, and there is no need for any additional cut in the Armenteros-Podolanski plot. Figure 5.24: Armenteros-Podolanski plane for Data and 𝐾0 𝑆→𝜋+𝜋− MC previously to any selection (left) and requiring positive 𝑃𝐿(𝜈𝜇) (right). Solid and dashed lines represent possible selection cuts. 5.5.2.4 signal selection summary In summary, our selection strategy focused on removing combinatorial background and 𝐾0 𝑆→𝜋+𝜋− while preserving a substantial number of Λ→𝑝𝜋− decays and early decays in flight for the purpose of performing a fit. The requirement of 𝑃𝐿(𝜈𝜇)>0 , implicit in Sel1, effectively addressed most of our concerns. Both Sel1 and Sel2 cuts proved to be useful in enhancing signal purity and preventing any potentially harmful background from entering the selection. An additional requirement of 𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋)< 1160 and 𝑀(𝑝𝜋)< 1120 was applied. Taking into account that: 77 chapter 5. analysis Sel1 =/ 𝑝𝑇>16&𝑀(𝑝, 𝜇)<(1116.3−1.03/ 𝑝𝑇) &𝑀(𝑝, 𝜇)>(1122.683 −2/ 𝑝𝑇) Sel2A =𝑄𝑃𝑇 <(√︄0.182−𝛼−0.7 0.52 ×128 +60) &𝑄𝑃𝑇 >(−√︄0.182−𝛼−0.7 0.52 ×128 +60) Sel2B = (𝑄𝑃𝑇 <((40 +√︃502−4× (252−372× (1− (𝛼−0.79)2 0.0852)))/2)) Sel2 = (Sel2A |Sel2B) The final selection applied is as follows: Sel = Sel1 &Sel2 &𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋)<1160 &𝑀(𝑝, 𝜋)<1120 The Selection Efficiency for Signal for each year and polarity can be found in Tab. 5.13. Table 5.13: 𝜖Selection Λ→𝑝𝜇−𝜈𝜇for each year and polarity. Magnet Down Magnet Up 𝜖Selection Λ→𝑝𝜇−𝜈𝜇2018 0.3011 ±0.0015 0.3011 ±0.0015 𝜖Selection Λ→𝑝𝜇−𝜈𝜇2017 0.3004 ±0.0015 0.3016 ±0.0015 𝜖Selection Λ→𝑝𝜇−𝜈𝜇2016 0.3033 ±0.0015 0.2989 ±0.0015 With this selection the signal purity in the MinBias MC passing SignalLine increases from 3.48 % to 9.82 %, with the additional advantage of the strong combinatorial background suppression. 78 5.5. selection and new variables 5.5.3 normalisation selection The initial idea was to have two stripping lines with aligned cuts, excluding particle identification ones. But one of the cuts, the muon impact parameter required in the SignalLine, was not included in the NormLine, so the first cut to add was to require an impact parameter for the pion greater than one (𝜋𝐼𝑃 >1 mm). Besides that, another cut was designed to remove the 𝐾0 𝑆→𝜋+𝜋− component that pollutes the NormLine Data sample. This can easily be observed in the ArmenterosPodolanski plot (Fig. 5.25). 0.4 0.5 0.6 0.7 0.8 0.9 0 20 40 60 80 100 120 140 160 QPT [MeV/c] KspipiMC NormLine Figure 5.25: Armenteros-Podolanski plot for 𝐾0 𝑆→𝜋+𝜋− MC passing NormLine (left) and Data passing NormLine (right). The cut is excluding events falling inside the region bounded by the red lines and can be applied imposing (Cut 1 |Cut 2), where these cuts are: Cut 1 :𝑄𝑃𝑇 >©«25.2+√︄(25.2)2−4.252−2002.1−𝛼2 0.8152ª®¬/2(5.25) Cut 2 :𝑄𝑃𝑇 <©«25.2+√︄(25.2)2−4.252−1302.1−𝛼2 0.8152ª®¬/2(5.26) The cut to kill the 𝐾0 𝑆→𝜋+𝜋− component was designed by studying different simulation samples passing the NormLine. This 𝐾0 𝑆→𝜋+𝜋−behaviour can be observed in Fig. 5.25. 79 chapter 5. analysis 5.6 normalisation 5.6.1 fit minbias mc Λ→𝑝𝜋−peak Our first step to fit the NormLine 𝑀(𝑝𝜋) is to obtain the tail parameters of the Λ→𝑝𝜋−peak. To obtain these parameters, we should fit a pure sample of Λ→𝑝𝜋− MC passing the NormLine. The sample is selected by applying to the MinBias MC that passes the NormLine truth-matching conditions, which are equivalent to those used for selecting Λ→𝑝𝜋− MC passing the SignalLine. The explicit requirements can be found in the appendices, A.4. The 𝑀(𝑝𝜋) distribution was fitted to a double sided Crystal Ball pdf, as can be seen in Fig. 5.26. 0 500 1000 1500 2000 2500 3000 3500 4000 CB pdf LppiMC MD M(p, ) [ MeV / c 2] 5 0 5 Pulls 0 500 1000 1500 2000 2500 3000 3500 4000 CB pdf LppiMC MU M(p, ) [ MeV / c 2] 5 0 5 Pulls Figure 5.26: 𝑀(𝑝𝜋 ) fit of the pure Λ→𝑝𝜋 − MC passing NormLine. Magnet Down (MD) is depicted on the left and Magnet Up (MU) on the right. 𝜒2 /ndof is 1.52 for MU and 1.16 for MD. The double sided Crystal Ball tail parameters extracted from the fit are in table 5.14. These two fits were performed using zfit. Table 5.14: Tail parameters of the double sided crystal ball that fits the 𝑀(𝑝𝜋 ) of the pure Λ→𝑝𝜋 − MC passing NormLine. Λ→𝑝𝜋 − decays were selected from a MinBias MC LHCb production for 2018MU and 2018MD. 𝛼𝐿𝛼𝑅𝑛𝐿𝑛𝑅 2018MU 1.046 ±0.027 1.025 ±0.026 3.43 ±0.14 3.30 ±0.13 2018MD 1.085 ±0.026 1.012 ±0.024 3.21 ±0.12 3.39 ±0.13 80 5.6. normalisation 5.6.2 fit data normline Having the tail parameters, we can perform a fit to the Data in NormLine. The combinatorial background can be parameterized with an exponential function and the Λ→𝑝𝜋− component with a double sided crystal ball, where we set the tail parameters obtained by fitting the pure Λ→𝑝𝜋− MC NormLine sample in previous subsection. This process should be repeated for all years and polarities to measure the total amount of Λ→𝑝𝜋−in NormLine ( 𝑁NormLine Λ→𝑝𝜋 −). Fig. 5.27 shows the fit result for 2018MU and 2018MD, applying Common Cuts to NormLine Data. Only 𝛼𝐿 , 𝛼𝑅 , 𝑛𝐿 and 𝑛𝑅 were set, whereas we let the width and the center of the double sided Crystal Ball and the exponential parameter to float. The fit process was repeated for all years and polarities, and the number of Λ→𝑝𝜋−decays measured in each case are shown in Tab. 5.15. 0 5000 10000 15000 20000 25000 30000 total background Lppi Data M(p, ) [MeV/ c 2] 5 0 5 Pulls 0 5000 10000 15000 20000 total background Lppi Data M(p, ) [MeV/ c 2] 5 0 5 Pulls Figure 5.27: 𝑀(𝑝𝜋 ) fit of the Λ→𝑝𝜋 − yield in Data passing NormLine. Magnet Up is depicted on the left and Magnet Down on the right. 𝜒2 /ndof is 2.54 for MU and 2.33 for MD. Table 5.15: Number of Λ→𝑝𝜋 − decays in NormLine Data for each year and polarity. 𝑁NormLine Λ→𝑝𝜋 − was extracted from the fit of NormLine 𝑀(𝑝𝜋 ) with common cuts to an exponential + a double sided Crystal Ball where the tail parameters have been set to match the TRUE ID ones. Magnet Down MagnetUp 2018 16080300 ±4900 17254500 ±5100 2017 14454500 ±4700 13933100 ±4600 2016 16527000 ±4900 14902400 ±4700 81 chapter 5. analysis 5.6.3 Λ→𝑝𝜋−efficiency passing normline Our next goal is to know how many Λ→𝑝𝜋− decays we have before the stripping process. This can be computed once we obtain the average of the Λ→𝑝𝜋− events that are reconstructed and pass the NormLine (𝜖NormLine Λ→𝑝𝜋 −). The efficiency can be computed performing a fit to the MinBias MC sample that passes the NormLine to a double sided Crystal Ball + a exponential, where we also set the tail parameters obtained in the Fig. 5.14. Dividing the number of Λ→𝑝𝜋− events measured with the fit in the MinBias MC NormLine sample by the original amount of Λ→𝑝𝜋−in the sample before any reconstruction or stripping. The original amount of Λ→𝑝𝜋− in the sample before any reconstruction or stripping for each year and polarity can be found in Tab. 5.16. These values are the number of entries in the MCDecayTree, generated in the same tuple processing that created the MinBias MC NormLine samples to ensure that we are always comparing the same original sample. The fit results for the MinBias MC sample passing NormLine can be found in Fig. 5.28 and Tab. 5.17. Table 5.16: Number of Λ→𝑝𝜋 − decays before the reconstruction and stripping process for each year and polarity in the MinBias MC sample. Magnet Down MagnetUp 2018 294,890752 M 295,092897 M 0 1000 2000 3000 4000 total Lppi background Data M(p, ) [MeV/ c 2] 5 0 5 Pulls 0 500 1000 1500 2000 2500 3000 3500 4000 total Lppi background Data M(p, ) [MeV/ c 2] 5 0 5 Pulls Figure 5.28: 𝑀(𝑝𝜋 ) fit of MinBias MC passing NormLine to an exponential + a double sided Crystal Ball, were the tail parameters were set to match the TRUE ID fit ones. Magnet Up is depicted on the left and Magnet Down on the right. 𝜒2 /ndof is 1.20 for MU and 1.17 for MD. Dividing the Tab. 5.17 results by the Tab. 5.16 ones, we obtain the 𝜖NormLine Λ→𝑝𝜋 − (Tab. 5.18 ). 82 5.6. normalisation Table 5.17: Number of Λ→𝑝𝜋 − decays in NormLine MinBias MC for each year and polarity. Numbers were extracted from the zfit of NormLine 𝑀(𝑝𝜋 ) with common cuts to an exponential + a double sided Crystal Ball where tail parameters have been set to match the TRUE ID ones. Magnet Down MagnetUp 2018 46590 ±250 46620 ±250 Table 5.18: Computed NormLine Λ→𝑝𝜋 − efficiencies for Magnet Down and Magnet Up. Magnet Down MagnetUp 𝜖NormLine Λ→𝑝𝜋 −(1.5799 ±0.0085) ×10−4(1.5798 ±0.0085) ×10−4 5.6.4 number of Λ→𝑝𝜋−before stripping Having the amount of Λ→𝑝𝜋− in NormLine and the efficiency 𝜖NormLine Λ→𝑝𝜋 − we can compute the amount of Λ→𝑝𝜋−before Stripping using Eq. 5.7. Table 5.19: Number of Λ→𝑝𝜋−decays before the stripping for each year and polarity. Magnet Down MagnetUp 2018 (101780 ±550) M (109220 ±590) M 2017 (91490 ±490) M (88200 ±480) M 2016 (104610 ±560) M (94330 ±510) M 5.6.5 number of Λparticles before stripping Dividing 𝑁Λ→𝑝𝜋 − by the branching ratio ratio B(Λ→𝑝𝜋−) we will obtain the number of Λs before the stripping, 𝑁Λ. 𝑁Λ=𝑁Λ→𝑝𝜋 − B(Λ→𝑝𝜋−)(5.27) Introducing the PDG B(Λ→𝑝𝜋−) in Eq. 5.27 we obtain the number of Λ particles before Stripping (Tab. 5.20). 83 chapter 5. analysis Table 5.20: Number of Λparticles before the stripping for each year and polarity. Magnet Down MagnetUp 2018 (159300 ±1500) M (170900 ±1600) M 2017 (143200 ±1400) M (138000 ±1300) M 2016 (163700 ±1600) M (147600 ±1400) M 5.6.6 normalisation As usual, we can define an 𝛼parameter, being: B(Λ→𝑝𝜇−¯ 𝜈𝜇)=𝛼𝑁 SignalLine Λ→𝑝𝜇−¯ 𝜈𝜇(5.28) where we have included all the efficiencies in the 𝛼parameter: 𝛼=B(Λ→𝑝𝜋−) 𝑁NormLine Λ→𝑝𝜋 − 𝜖NormLine Λ→𝑝𝜋 − 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇 (5.29) and 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇 =𝜖SignalLine Λ→𝑝𝜇−¯ 𝜈𝜇. 𝜖Selection Λ→𝑝𝜇−¯ 𝜈𝜇(5.30) Where the current PDG value for the branching ratio of the Normalization Channel is B(Λ→𝑝𝜋−)=64.1±0.5% ,the NormLine Sselection + Stripping efficiency 𝜖NormLine Λ→𝑝𝜋 − = (1.5799±0.0085)×10−4 for Magnet Down and 𝜖NormLine Λ→𝑝𝜋 − = (1.5798±0.0085)× 10−4 for Magnet Up polarity, and 𝑁NormLine Λ→𝑝𝜋 − , 𝜖SignalLine Λ→𝑝𝜇−¯ 𝜈𝜇 and 𝜖Selection Λ→𝑝𝜇−¯ 𝜈𝜇 values for each year and polarity can be found in Tab. 5.15, Tab. 5.5 and Tab. 5.13 respectively. Table 5.21: 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇for each year and polarity. Magnet Down Magnet Up 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇2018 (1.0810 ±0.0070) ×10−4(1.0860 ±0.0070) ×10−4 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇2017 (1.0870 ±0.0070) ×10−4(1.1030 ±0.0070) ×10−4 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇2016 (1.1020 ±0.0070) ×10−4(1.0820 ±0.0070) ×10−4 As explained in Subsection 5.6.3, 𝜖NormLine Λ→𝑝𝜋 − was computed by fitting the MinBias MC sample passing the NormLine. This MinBias MC sample is only available for 2018MD and 2018MU, and the results are very similar for both cases. We will use this 𝜖NormLine Λ→𝑝𝜋 −value also for 2017 and 2016. 84 5.6. normalisation As we will fit the Signal in all the Run II Data, without separating by year and polarity, we should weight the 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇. 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇 =Í YearPol(𝑁YearPolNormLine Λ→𝑝𝜋 −. 𝜖YearPolSignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇) Í YearPol(𝑁YearPolNormLine Λ→𝑝𝜋 −)(5.31) The result is 𝜖SignalLineSel Λ→𝑝𝜇−¯ 𝜈𝜇 = (1.0902 ±0.0027) ×10−4 . With all this values we can finally compute 𝛼: 𝛼=(1.073 ±0.011) ×10−8(5.32) 85 chapter 5. analysis 1040 1060 1080 1100 1120 1140 M(p, ) [ MeV / c 2] 0 100 200 300 400 500 600 CombBkg from SignalGen SignalMC 1080 1100 1120 1140 1160 1180 M(p, ) [ MeV / c 2] 0 100 200 300 400 500 600 700 800 CombBkg from SignalGen SignalMC 1040 1060 1080 1100 1120 1140 M(p, ) [ MeV / c 2] 0 20 40 60 80 100 CombBkg from BkgGen BkgMC 1080 1100 1120 1140 1160 1180 M(p, ) [ MeV / c 2] 0 20 40 60 80 100 120 140 CombBkg from BkgGen BkgMC Figure 5.31: 𝑀(𝑝𝜇) and 𝑀(𝑝𝜋 ) distributions of "Comb Bkg MC " from Signal (top) and Lppi (bottom) stripping filtered MC samples where it is easy to see that most of events identified as combinatorial background are in fact misidentified signal or Lppi background events. A sklearn GradientBoostingClassifier [64] was trained using as signal the Λ→ 𝑝𝜇−¯ 𝜈𝜇MC and as background the 𝜌𝑆𝑉 <2data. The training variables were 𝑀(𝑝𝜇), APLA, Armenteros 𝛼, Lambda ETA, Lambda PT and Lambda EndVertex_Z. 0.0 0.2 0.4 0.6 0.8 1.0 BDT response 0 10 20 30 40 50 60 MC Signal Combinatorial Bkg 1040 1060 1080 1100 1120 1140 M ( p , ) [ MeV / c 2] 0 100 200 300 400 500 600 CombBkg SignalGen CombBkg SignalGen BDT<0.4 Figure 5.32: The BDT response can be used to separate Λ→𝑝𝜋 − and Signal from combinatorial background (left). In the plot placed at the right the effect of selecting events with BDT response < 0.8 in the events identified as combinatorial background from the Stripping Filtered MC sample can be found. This process serves two purposes. Firstly, it allows us to enhance the statistics of our combinatorial background MC sample by separating the signal and combinatorial 92 5.8. signal yield fit background components (see Fig. 5.32). Secondly, we can evaluate the BDT response values for combinatorial background events from the MinBias MC sample that satisfy the 𝑃𝐿(𝜈𝜇)>0 cut. This enables us to determine whether these events are genuine combinatorial background or potential misidentifications as Signal or Lppi. Figure 5.33 demonstrates that a significant number of events identified as combinatorial background from the MinBias MC sample exhibit signal and peaking background characteristics. More importantly, the events selected with 𝑃𝐿(𝜈𝜇)>0 are highly unlikely to be combinatorial background. This indicates that our previous estimation of 𝜖𝑃𝐿(𝜈𝜇)>0 CombBkg has greatly overestimated its value. Furthermore, it is not appropriate to utilize the events identified as combinatorial background from the MinBias MC with a positive neutrino longitudinal momentum as the combinatorial background template in the signal yield fit.This is because the resulting template would be completely dominated by Lppi, as can be seen in the bottom plots of Figure 5.33. Since we have now obtained the combinatorial background from the signal stripping filtered MC sample (selected using the BDT), we can compute the efficiency 𝜖𝑃𝐿(𝜈𝜇)>0 CombBkg for those events with a BDT response < 0.4. The result is 𝜖𝑃𝐿(𝜈𝜇)>0 𝐶𝑜𝑚𝑏𝐵𝑘𝑔𝐵𝐷𝑇 <0.4=0 . However, this does not imply that there is no combinatorial background in the data with 𝑃𝐿(𝜈𝜇)>0 , as the BDT does not select every single combinatorial background event and we cannot directly compute the efficiency. But it is evident that the combinatorial background is effectively suppressed when applying 𝑃𝐿(𝜈𝜇)>0. 0.0 0.2 0.4 0.6 0.8 1.0 BDT response 0 20 40 60 80 100 120 CombBkg MinBiasMC 0.0 0.2 0.4 0.6 0.8 1.0 BDT response 0 5 10 15 20 25 30 35 CombBkg MinBiasMC PL ( ) > 0 1080 1090 1100 1110 1120 1130 1140 M ( p , ) [ MeV / c 2] 0.00 0.02 0.04 0.06 0.08 0.10 CombBkg MinBiasMC PL ( ) > 0 Bkg MC PL ( ) > 0 1080 1090 1100 1110 1120 1130 1140 1150 CorrM ( p , ) [ MeV / c 2] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 CombBkg MinBiasMC PL ( ) > 0 Bkg MC PL ( ) > 0 Figure 5.33: Top plots show BDT response for all events identified as combinatorial background in the MinBias MC sample (left) and for those events passing the 𝑃𝐿(𝜈𝜇)>0 cut (right). Bottom plots are 𝑀(𝑝𝜋 ) and 𝐶𝑜𝑟𝑟𝑀 (𝑝𝜋 ) distributions for "combinatorial background" from MinBias MC sample and for Lppi bkg MC, both passing 𝑃𝐿(𝜈𝜇)>0. 93 chapter 5. analysis Taking all that information into account, the best option for selecting a combinatorial background template is to combine the events identified as combinatorial background from both the MinBias MC sample and the background-stripping filtered MC sample. Since we are only interested on the number of signal events, we are not concerned by the fact that most events in our combinatorial background sample are in fact Λ→𝑝𝜋−ghosts. 5.8.2 mc weight To account for the discrepancies between the Monte Carlo (MC) and Data, we performed a reweighting of the MC to align its properties with those observed in the Data. The variables that we are reweighting are Λ𝑃𝑇 and 𝜂 . By fitting the Λ→𝑝𝜋− contribution in the NormLine region of the Data, we can extract the 𝑃𝑇 and 𝜂 distributions of Λ→𝑝𝜋− in the Data and apply corresponding reweighting factors to the MC. The first part of the process is analogous to the one followed when fitting the NormLine to extract the yield of Λ→𝑝𝜋− events.(Subsection 5.6.2). In this case we obtained the sWeights using the hepstats package from the fit results and then we passed those sWeights to a GBreweighter from the hep_ml package. So, the GBReweighter is trained using the whole Λ→𝑝𝜋− data sample passing NormLine, selected with the sWeights method, to correct the differences between MC and Data in Λ𝑃𝑇and 𝜂distributions. Figure 5.34: Reweighting result for Λ→𝑝𝜋 − MC passing NormLine. Λ transverse momentum is depicted in the left plot and its pseudorapidity in the right one. This reweighter, already trained to correct the discrepancies between MC and Data, was used then to predict the corresponding reweighing of Λ→𝑝𝜋− MC passing SignalLine. The reweighted histograms can be found in Fig. 5.34. 94 5.8. signal yield fit 5.8.3 fit The 2D fitter takes as input the number of entries for each channel in each bin, utilizing the MC distributions as templates, and outputs the corresponding number of occurrences for each channel in the Data. It performs a log likelihood calculation using Poisson statistics, addressing the low statistics issue. The maximum likelihood with binned data case procedure [38] is followed to fit the contribution of each channel to the selected data. For each bin, the fitter computes a 𝜒2=2(−OBS ·𝑙𝑜𝑔(EXP) + EXP) , where OBS is the observed amount of selected data in the bin and EXP is the expected sum of all the components in the bin: EXP =𝑓Λ→𝑝𝜇−¯ 𝜈𝜇·B(Λ→𝑝𝜇−¯ 𝜈𝜇) 𝛼+𝑓Λ→𝑝𝜋 −·𝑁Λ→𝑝𝜋 −+𝑓𝑒𝐷𝐼𝐹 ·𝑁𝑒𝐷𝐼𝐹 +𝑓𝐶𝑜𝑚𝑏 ·𝑁𝐶𝑜𝑚𝑏 where the fractions of each channel in each bin are extracted from the MC samples, the 𝛼 parameter was already computed previously in this thesis and the B(Λ→ 𝑝𝜇−¯ 𝜈𝜇) and number of each background channel are being fitted. In the fitting process, a Gaussian constraint for the normalization parameter ( 𝛼 ) is incorporated. This approach effectively integrates prior knowledge about 𝛼into the fit. Different binning schemes were used and the blinded results are presented in Tab. 5.22. Result are blinded by multiplying the 𝛼 normalisation parameter by a random number between 0 and 3 (blinding constant). Three different modes were implemented, the first one (first column) sets the Λ→𝑝𝜋− and Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇) ratio to the one observed in the MinBias MC passing the selection, the second mode (second column) lets this ratio free and the third one (third column) considers also the combinatorial background channel. As it was discussed in the section 5.8.1, the MC template for the combinatorial background is very likely mismatched Λ→𝑝𝜋− , and the expected contribution of combinatorial background to the selected sample is extremely low. Table 5.22: Blinded B(Λ→𝑝𝜇−¯ 𝜈𝜇) fit result for different binning schemes and background templates are included. Scheme Merged Lppi+eDIF Lppi,eDIF Lppi,eDIF,CombBkg Binning 1 (×10−4)B= 3.865 ±0.051 B= 3.913 ±0.068 B= 3.780 ±0.066 Binning 2 (×10−4)B= 3.793 ±0.052 B= 4.041 ±0.074 B= 3.734 ±0.067 Binning 3 (×10−4)B= 3.806 ±0.051 B= 3.965 ±0.072 B= 3.753 ±0.059 Binning 4 (×10−4)B= 3.865 ±0.049 B= 3.899 ±0.073 B= 3.845 ±0.059 Binning 5 (×10−4)B= 3.808 ±0.051 B= 3.964 ±0.070 B= 3.750 ±0.059 95 chapter 5. analysis Binning Scheme 1 coincides with the one shown in Fig. 5.29, while the other binning schemes can be found in Fig. 5.35. The selected central value is B(Λ→ 𝑝𝜇−¯ 𝜈𝜇) = (3.845 ±0.059 (stat)) × 10−4 (blinded) and the systematic uncertainty is determined by considering the largest deviation from the results obtained with other binning schemes and modes, obtaining 5.1 %. Figure 5.35: Proposed binnings of the 𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋 ) vs 𝑀(𝑝𝜋 ) plane to perform a bidimensional fit. Top left is Binning Scheme 2, Top Right Binning Scheme 3, Bottom left is Binning Scheme 4 and Bottom Right Binning Scheme 5. Binning Scheme 4 was selected to be the default, since its diagonal bin is tighter and more sensitive to the Signal behaviour. 96 5.8. signal yield fit 5.8.3.1 1-dimensional fit check Even though the background MC statistics are insufficient to perform a fully valid fit in 1D, we can still conduct a fit in 𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋) as a check. This is possible because the background distribution in that variable exhibits a satisfactory agreement with a double-sided Crystal Ball PDF, allowing us to model the background accurately. The blinded branching ratio result with the signal yield extracted from this fit is B(Λ→𝑝𝜇−¯ 𝜈𝜇) = (4.02 ±0.18) ×10−4 , in good agreement with the 2-dimensional fit result. The 1D fit of the 𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋)distribution can be seen in Fig. 5.36. 1080 1090 1100 1110 1120 1130 1140 1150 1160 0 1000 2000 3000 4000 5000 6000 CorrM(p,pi) [MeV/c^2] total Signal Bkg CB Data Figure 5.36: A 1D fit of the 𝑀𝐶𝑜𝑟𝑟 (𝑝𝜋 ) distribution is performed to extract the signal yield in the Signal Line region after the selection. The background component is fitted using a double-sided Crystal Ball PDF, while the signal component is modeled using a Kernel Density Estimation (KDE). 97 chapter 5. analysis 5.9 systematic uncertainties The entire analysis was structured with the primary goal of minimizing systematic uncertainties. It employs TISTISTIS Data for both the NormLine and SignalLine, ensuring that the cuts used in the Stripping lines are consistent across both lines. The only difference lies in the PID criteria for muons and pions. Furthermore, these PID cuts have been minimized to the extent possible, with the selection completely basaed on kinematic requirements. As a result, this approach should lead to the cancellation of most systematic uncertainties. As we are using Λ→𝑝𝜋− as normalisation, we should include its branching ratio uncertainty as systematic uncertainty. Regarding PidCalib2 and TrackCalib2, the software packages used to correct the MC efficiencies for the Stripping lines PID and tracking cuts, results are affected by the chosen binning. To take into account this systematic source of uncertainty, we can estimate how the obtained efficiency varies by changing the binning scheme. The choosen binning schemes and results can be found in the appendices (A.11). The systematic uncertainty associated with the signal yield fit, which is the predominant factor, was previously detailed in Section 5.8.3. This uncertainty, 5.1 %, could potentially be reduced to 3.64 % if the third mode, accounting for the presence of combinatorial background, were excluded. As discussed earlier, the expected contribution of combinatorial background is minimal. However, we chose to incorporate a "combinatorial background" sample into the fitting process. This sample, despite being dominated by mismatched Λ→𝑝𝜋− , was the unique method to assess the impact of this background. It’s important to note that the presence of Λ→𝑝𝜋− within the combinatorial background sample is not inherently problematic. In principle, there is no issue in fitting the Λ→𝑝𝜋− contribution to the selected data using one sample instead of the other, as the total Λ→𝑝𝜋− count will ultimately be determined by combining both samples. The issue primarily arises from fitting a portion of the Λ→𝑝𝜋− contribution using a sample with significantly fewer statistics. This discrepancy leads to a more pronounced difference in the results and contributes to an increased systematic uncertainty.. The determination of the final systematic uncertainty for TrackCalib2 is currently a Work In Progress (WIP). Additionally, other potential sources of systematic uncertainty are under consideration (refer to Table 5.23). However, their contribution to the overall systematic uncertainty is anticipated to be minimal. The total systematic uncertainty is anticipated to be approximately 6.0 %, without any significant variations expected. 98 5.9. systematic uncertainties Table 5.23: Systematic uncertainties that affect the B(Λ→𝑝𝜇−¯ 𝜈𝜇)measurement. Source Relative Uncertainty (%) B(Λ→𝑝𝜋−)0.78 % NormLine Fit expected to be negligible PidCalib Signal Line 1.61 % PidCalib NormLine 1.04 % Tracking ≈1.0 % (WIP) Λ→𝑝𝜇−¯ 𝜈𝜇yield (fit) 5.1 % Signal fit template expected to be negligible Other sources - 99 chapter 6 RESULTS AND CONCLUSIONS The aim of this thesis is to precisely measure B(Λ→𝑝𝜇−¯ 𝜈𝜇) and test lepton flavour universality in 𝑠→𝑢 transitions. Any deviation from LFU would indicate the presence of new beyond the Standard Model physics. With this purpose, data from the LHCb, produced through proton-proton collisions at the LHC with a centre-of-mass energy of 13 TeV, collected during its second data taking period (2016-2018), is analyzed. 6.1 results In 2021, BESIII published the first measurement of the absolute branching fraction of Λ→𝑝𝜇−¯ 𝜈𝜇 , obtaining the best branching fraction measurement till the date, B(Λ→𝑝𝜇−¯ 𝜈𝜇)) = (1.48 ±0.21) ×10−4[6]. Our measured blinded result, B(Λ→𝑝𝜇−¯ 𝜈𝜇) = (3.485±0.059(stat)±0.23(syst))× 10−4 , shows a significantly reduced uncertainty. We should consider that this blinded result ought to be divided by the blinding constant, which is expected to be approximately equal to the ratio of our value to the measured B(Λ→𝑝𝜇−¯ 𝜈𝜇) result. It should also be noted that the calculation of the systematic uncertainty is not completely finalized, so the final result of this uncertainty may vary slightly. 6.2 conclusions The BESII result has an uncertainty of 14.19% . With this selection and the fit result, we anticipate a statistical uncertainty of 1.5% and a systematic uncertainty of 6.0% . This implies a total uncertainy of 6.2% and aligns with our goal of achieving the most precise measurement of the B(Λ→𝑝𝜇−¯ 𝜈𝜇)using LHCb data. Regarding 𝑉𝑢𝑠 , we have derived its dependence on B(Λ→𝑝𝜇−¯ 𝜈𝜇) 101 chapter 7. resumo |𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2≡1 Dado que a contribución do elemento |𝑉𝑢𝑏 |2 é practicamente desprezábel (approximadamente 1.3×10−5 ), esta relación redúcese á universalidade de Cabibbo (|𝑉𝑢𝑑 | ≈𝑐𝑜𝑠 𝜃12,|𝑉𝑢𝑠 | ≈𝑠𝑖𝑛 𝜃12). Xa que |𝑉𝑢𝑑 | foi medido xa con grande precisión, cun valor de |𝑉𝑢𝑑 |=0.97436 ± 0.00016, o foco móvese a 𝑉𝑢𝑠 . De feito, empregando as mellores medidas de 𝑉𝑢𝑑 ,𝑉𝑢𝑠 e𝑉𝑢𝑏 obtemos |𝑉𝑢𝑑 |2+ |𝑉𝑢𝑠 |2+ |𝑉𝑢𝑏 |2=0.9985 ±0.0007 mostrando unha tensión de 2.2 𝜎 ca unitariedade na primeira ringleira da matriz CKM. Ademais, as medidas de 𝑉𝑢𝑠 en decaementos leptónicos ( 𝐾𝜇2 ) e semileptónicos ( 𝐾𝑙3 ) de kaóns mostran unha discrepancia de 3 𝜎 . Esta diferenza pode ser un indicio de BSM. Tendo isto en conta, tórnase vital atopar outros xeitos de medir 𝑉𝑢𝑠 de forma precisa. Os SHD son unha alternativa prometedora. Pero o maior interese dos SHD é que son un excelente marco de estudo pra investigar a LFU. Desde un punto de vista teórico, demostrouse que os SHD poden ser sensíbeis a dinámicas BSM que rompen a universalidade leptónica. Estes decaementos están controlados por un pequeno parámetro de ruptura de simetría 𝛿 que permite expansións sistemáticas e prediccións precisas. Os modos muónicos son especialmente sensíbeis a contribucións BSM. No caso de Λ→𝑝𝜇−¯ 𝜈𝜇 , o observábel de LFU test está predito pola teoría como 𝑅𝜇𝑒 =0.153 ±0.008 traballando a next-to-leading order. A mellor medida deste observábel foi realizada por BESIII no 2021, obtendo 𝑅𝜇𝑒 =0.178 ±0.028 , consistente dentro das incertezas ca predicción. aínda así, considerando que o modo electrónico foi medido cunha maior precisión B(Λ→𝑝𝑒−¯ 𝜈𝑒)=(8.34 ±0.14) ×10−4 , a maior parte da incerteza ven da medida de BESIII do modo muónico, B(Λ→𝑝𝜇−¯ 𝜈𝜇) = [1.48 ±0.21,(stat) ±0.08,(syst)] ×10−4 . Aumentar a precisión en B(Λ→𝑝𝜇−¯ 𝜈𝜇) é esencial para probar a universalidade leptónica en transicións 𝑠→𝑢. 7.2 condicións experimentais O LHC é o maior e máis potente acelerador de partículas do mundo. Consiste nun anel de 27 km de circunferencia, composto dunha serie de elementos pra acelerar e manter en órbita as partículas. Dentro do acelerador, dous feixes de partículas de alta enerxía viaxan en direccións opostas. Os feixes fanse colidir en catro puntos de interacción correspondentes a catro detectores ATLAS, CMS, ALICE e LHCb. LHCb é un dos catro grandes detectores recollendo datos no LHC. O seu nome provén do principal propósito pra o que foi pensado, detectar os decaementos de partículas contendo quarks b. Estas partículas, formadas nas colisións de protóns do LHC, tenden a xerarse e a decaer sen alonxarse moito da dirección de incidencia do feixe. Isto refléxase na forma do detector que non cubre todo o ángulo sólido ao redor 108 7.3. análise da interacción, senón que se extende na dirección "cara adiante" cunha aceptancia en pseudorapidity de 1.6≤𝜂≤4.9. LHCb está composto de diferentes subdetectores. Basicamente dispomos dun localizador de vértices ( VELO ) (pra determinar a traxectoria das partículas perto do punto de interacción co obxetivo de separar os puntos onde as partículas son xeradas (PV) de onde decaen (SV), un detector chamado RICH (pra identificar que tipo de partícula produce cada traza a partir da súa masa e carga), T-stations (que nos permiten obter a traxectoria e momento das partículas cargadas), ECAL (que detecta electróns e fotóns e mide a súa enerxía), HCAL (que mide a enerxía depositada dos hadrons e Muon Chambers (situadas ao final do detector pra detectar muóns). Esta análise emprega datos recollidos no LHCb durante o Run 2 (2016-2018). 7.3 análise A análise principal desta tese é a medida do B(Λ→𝑝𝜇−¯ 𝜈𝜇) . O maior desafío relacionado con esta medida en LHCb é discriminar o sinal de outras canles que pican en certas masas, principalmente Λ→𝑝𝜋− e 𝐾0 𝑆→𝜋+𝜋− . Ademais destes fondos, o fondo combinatorio tamén nos crea problemas, xa que no sinal temos un neutrino e polo tanto momento perdido no estado final. Isto fai que as distribucións de Λ→𝑝𝜇−¯ 𝜈𝜇 poden resultar parecidas ás do fondo combinatorio. Na análise empréganse só trazas tipo long, xa que non estamos limitados pola estatística e estas presentan unha mellor resolución. O B(Λ→𝑝𝜇−¯ 𝜈𝜇) obterase empregando como input o B(Λ→𝑝𝜋−) . Λ→𝑝𝜋− será a súa vez a canle de normalización. Polo tanto, podemos definir un parámetro 𝛼 que relaciona o B(Λ→𝑝𝜇−¯ 𝜈𝜇) co número de eventos de sinal reconstruídos 𝑁𝑟𝑒𝑐𝑜 𝑝𝜇𝜈 , B(Λ→𝑝𝜇−𝜈𝜇)=𝛼𝑁𝑟𝑒𝑐𝑜 𝑝𝜇𝜈 sendo 𝛼=B(Λ→𝑝𝜋−) 𝑁𝑟𝑒𝑐𝑜 𝑝𝜋 𝜖𝑝𝜋 𝜖𝑝𝜇𝜈 Dúas Stripping lines (selección offline) foron escritas con este propósito, a de normalización (NormLine) pra seleccionar Λ→𝑝𝜋− e medir a súa producción en LHCb e a de sinal (SignalLine) pra facer o mesmo co Λ→𝑝𝜇−¯ 𝜈𝜇 . Ambas seleccións comparten o mesmos cortes pra reducir os sistemáticos, ca única diferenza nos cortes de ID e na xanela de masas. Dispomos de simulación (MC) de MinBias pra 2018 MD and 2018 MU, e produccións de Λ→𝑝𝜋− e Λ→𝑝𝜇−¯ 𝜈𝜇 MC pasando a SignalLine pra 2016, 2017 e 2018 cas configuracións Magnet Up e Magnet Down. A producción de Λ→𝑝𝜇−¯ 𝜈𝜇 foi xerada empregando un modelo de EvtGen desenvolto como parte desta tese e que ten en conta a taxa de decaemento diferencial do sinal. O modelo foi escrito de xeito que poida ser empregado no futuro pra calquera SHD. 109 chapter 7. resumo 7.3.1 fit da canle de normalización O primeiro paso é eliminar a contaminación de 𝐾0 𝑆→𝜋+𝜋− presente na NormLine. Pra isto podemos aplicar o seguinte corte (Cut 1 | Cut 2) no plano de ArmenterosPodolanski, onde os cortes son: Cut 1 :𝑄𝑃𝑇 >©«25.2+√︄(25.2)2−4.252−2002.1−𝛼2 0.8152ª®¬/2 Cut 2 :𝑄𝑃𝑇 <©«25.2+√︄(25.2)2−4.252−1302.1−𝛼2 0.8152ª®¬/2 Unha vez eliminado o 𝐾0 𝑆→𝜋+𝜋− (este corte aplícase a MC e datos pasando a NormLine a partir deste momento), podemos proceder co fit, onde a pdf total está composta dunha double sided crystal ball + exponencial. Comezamos cun fit do Λ→𝑝𝜋− MC puro, pra extraer os catro valores das colas da función double sided crystal ball. A continuación procedemos a facer o fit dos datos da NormLine, onde se aplicou o corte pra eliminar 𝐾0 𝑆→𝜋+𝜋− previamente, fixando os valores das colas obtidos no paso anterior. Isto danos o número de Λ→𝑝𝜋−nos datos que pasaron a NormLine. Por último, repetimos este fit a todo o MinBias MC que pasa a NormLine, pra obter a eficiencia do Λ→𝑝𝜋− de reconstrucción + pasar a NormLine ( 𝜖𝑁𝑜𝑟𝑚𝐿𝑖𝑛𝑒 Λ→𝑝𝜋 − ), dividindo o número de Λ→𝑝𝜋− no fit entre o número total de Λ→𝑝𝜋− no MC sample previo á reconstrucción. Dividindo o número de Λ→𝑝𝜋− nos datos que pasaron a NormLine entre 𝜖𝑁𝑜𝑟𝑚𝐿𝑖𝑛𝑒 Λ→𝑝𝜋 − obtemos o número de sucesos de Λ→𝑝𝜋− en LHCb no Run 2. Podemos dividir este numero entre B ( Λ→𝑝𝜋− ) pra saber o número total de partículas Λ xeradas en LHCb no Run2. 7.3.2 eficiencia de selección do sinal O seguinte paso será obter a eficiencia do sinal, o último valor que precisamos pra calcular o parámetro 𝛼 . Esta eficiencia encapsula os procesos de reconstrucción, stripping e selección. Neste caso a selección está baseada nun corte no plano momento transverso perdido vs masa ca hipótese protón-muón ( / 𝑝𝑇 vs 𝑀(𝑝𝜇) , motivados por unha estratexia quinemática que permite recuperar a información de momento do neutrino: Sel1 =/ 𝑝𝑇>16&𝑀(𝑝, 𝜇)<(1116.3−1.03/ 𝑝𝑇) &𝑀(𝑝, 𝜇)>(1122.683 −2/ 𝑝𝑇) 110 7.3. análise e un corte seleccionando os eventos que caen nas rexións do plano de Armenteros onde a sinal presenta maior pureza. A eficiencia desta selección obtense aplicando os cortes á simulación de Λ→ 𝑝𝜇−¯ 𝜈𝜇 pasando a SignalLine. Esta eficiencia debera ser multiplicada pola eficiencia de xeración, reconstrucción e stripping, que podemos obter directamente dos rexistros da producción oficial de LHCb. Unha vez calculada esta eficiencia, dispomos de todos os elementos precisos pra calcular o parámetro 𝛼. 7.3.3 corrección das eficiencias O cálculo das eficiencias que entran no parámetro 𝛼 parten de supor que a simulación reproduce de forma fiabél os datos. Pero isto pode non ser así, especialmente no relacionado á resposta fronte aos cortes de PID e tracking. Por este motivo, procedemos a correxir estes valores empregando as ferramentas de LHCb PidCalib e TrackCalib. Unha vez aplicadas estas correccións, tanto ás efiencias de normalización como de sinal, obtemos un valor de 𝛼correxido e fiabél. 7.3.4 fit post selección do sinal O último paso é obter o número de eventos de Λ→𝑝𝜇−¯ 𝜈𝜇 nos datos que pasan a SignalLine seleccionados. Dada a dificuldade pra obter MC de Λ→𝑝𝜋− e fondo combinatorio pasando a selección, decidimos facer un fit 2D pra mitigar o problema de baixa estatística de MC. Este fit faise no plano 𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋) vs 𝑀(𝑝, 𝜋) , onde 𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋) é unha variable creada supondo que o pión decae posteriormente a un muón e un antineutrino. Este plano permite separar de xeito satisfactorio Λ→𝑝𝜋− , Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇) e Λ→𝑝𝜇−¯ 𝜈𝜇 . Pra verificar o resultado e obter a incerteza sistemática asociada, empregamos diferentes bineados e modos de fit. Os resultados mostran unha boa compatibilidade entre eles e cun fit 1D na variable 𝑀𝐶𝑜𝑟𝑟 (𝑝, 𝜋) . aínda así, a maior parte da incerteza sistemática da medida provén deste fit bidimensional. 7.3.5 sistemáticos A análise foi pensada dende un comezo pra reducir os sistemáticos todo o posibél, escollendo un modo de normalización cunha quinemática moi similar, empregando datos TISTISTIS e fixando os mesmos cortes en ambas seleccións offline. aínda así, diferentes fontes de erro sistemático son consideradas, especialmente as relacionadas ca corrección do parámetro 𝛼 empregando PIDCalib e TrackCalib. aínda así, o erro sistemático está dominado polo fit do sinal (5.1 %). 7.3.6 conclusións Esta medida do B(Λ→𝑝𝜇−¯ 𝜈𝜇) está aínda multiplicada por un factor de blinding, un procedemento habitual no campo da física de altas enerxías. Ainda así, a incerteza estatística (1.5 %) e sistemática (6.0 %) acadada mellora significativamente a mellor 111 chapter 7. resumo medida de B(Λ→𝑝𝜇−¯ 𝜈𝜇) realizada ata o de agora por BESIII, que presentaba unha incerteza do 14 %. A nosa medida terá importantes consecuencias na comprensión de 𝑅𝜇𝑒 , sendo sensíbel a desviacións significativas do SM. Será, polo tanto, un importante test da LFU en transicións 𝑠→𝑢 Cabe destacar que esta é a primeira vez que se mide a razón de ramificación dun hyperón en LHCb e tamén a primeira vez que se mide un decaemento semileptónico dunha partícula strange en LHCb. 112 appendix a APPENDIX a.1 stripping line efficiencies a.1.1 signal passing signalline This efficiencies can be obtained by running in lxplus lb-dirac dirac-bookkeepingrejection-stats -P sample-number, where sample-number will take the values depicted on Tab. A.1. Table A.1: Production sample codes for each year and polarity. Magnet Down Magnet Up Sample Code 2018 131673 131676 Sample Code 2017 131679 131682 Sample Code 2016 131685 131688 a.1.2 Λ→𝑝𝜋−passing normline The Λ→𝑝𝜋− Stripping Filtered Production Reconstruction Efficiency can be obtained by running in lxplus lb-dirac dirac-bookkeeping-rejection-stats -P sample-number, where sample-number will take the values depicted on Tab. A.2. a.2 trigger lines firing more often in selected events An interesting study is to check wich trigger Lines are firing more often in selected events for NormLine and SignalLine. The result can be seen in Figs. A.1, A.2, A.3. 113 appendix a. appendix Table A.2: Production sample codes for each year and polarity. Magnet Down Magnet Up Sample Code 2018 131695 131698 Sample Code 2017 131701 131704 Sample Code 2016 131707 131710 102103104105106107108109 counts Counter_for_Lambda0_L0Global_TIS Counter_for_Lambda0_L0Global_TOS Counter_for_Lambda0_L0PhotonDecision_TIS Counter_for_Lambda0_L0PhotonDecision_TOS Counter_for_Lambda0_L0ElectronDecision_TIS Counter_for_Lambda0_L0ElectronDecision_TOS Counter_for_Lambda0_L0HadronDecision_TIS Counter_for_Lambda0_L0HadronDecision_TOS Counter_for_Lambda0_L0MuonDecision_TIS Counter_for_Lambda0_L0MuonDecision_TOS Counter_for_Lambda0_L0DiMuonDecision_TIS Counter_for_Lambda0_L0DiMuonDecision_TOS Counter_for_p_L0Global_TIS Counter_for_p_L0Global_TOS Counter_for_mu_L0Global_TIS Counter_for_mu_L0Global_TOS Counter_for_L0DUTCK L0 Tis-Tos SignalLine 103105107109 counts Counter_for_Lambda0_L0Global_TIS Counter_for_Lambda0_L0Global_TOS Counter_for_Lambda0_L0PhotonDecision_TIS Counter_for_Lambda0_L0PhotonDecision_TOS Counter_for_Lambda0_L0ElectronDecision_TIS Counter_for_Lambda0_L0ElectronDecision_TOS Counter_for_Lambda0_L0HadronDecision_TIS Counter_for_Lambda0_L0HadronDecision_TOS Counter_for_Lambda0_L0MuonDecision_TIS Counter_for_Lambda0_L0MuonDecision_TOS Counter_for_Lambda0_L0DiMuonDecision_TIS Counter_for_Lambda0_L0DiMuonDecision_TOS Counter_for_p_L0Global_TIS Counter_for_p_L0Global_TOS Counter_for_pi_L0Global_TIS Counter_for_pi_L0Global_TOS Counter_for_L0DUTCK L0 Tis-Tos NormLine Figure A.1: L0 Trigger Lines firing more often in Selected Events. SignalLine case is depicted in the left plot and NormLine in the right one. Missing lines have counter = 0 a.3 background sources a.3.1 pid and vertex reqirements for each channel (mc, signalline) This appendix contains the truth-matching and vertex requirements for each channel, which are detailed below. As a reminder, 3122 is the numerical code for Λ , 2212 for 𝑝 , 211 for 𝜋+ and 13 for 𝜇− , where the negative numbers are associated to the correspondent antiparticles: Selection requirements for the signal channel (Λ→𝑝𝜇−¯ 𝜈𝜇) The requirements for selecting signal in the MC samples are detailed in Tab. A.3. The TRUE ID of each particle should match the corresponding number code to ensure correct MC association. Both the proton and the muon are required to have a Λ as their mother particle. These two particles should originate from the same vertex, which should also coincide with the Λ end vertex. Lastly, to confirm that both particles come from the same mother, the MC key of their respective mothers must match. Below is the explicit code that ensures the satisfaction of the given conditions: ((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=13) | 114 a.3. background sources 101102103104105 counts Counter_for_Lambda0_Hlt1Global_TIS Counter_for_Lambda0_Hlt1Global_TOS Counter_for_Lambda0_Hlt1Phys_TIS Counter_for_Lambda0_Hlt1Phys_TOS Counter_for_Lambda0_Hlt1DiMuonHighMassDecision_TIS Counter_for_Lambda0_Hlt1DiMuonLowMassDecision_TIS Counter_for_Lambda0_Hlt1DiMuonLowMassDecision_TOS Counter_for_Lambda0_Hlt1SingleMuonNoIPDecision_TIS Counter_for_Lambda0_Hlt1SingleMuonHighPTDecision_TIS Counter_for_Lambda0_Hlt1TrackMuonDecision_TIS Counter_for_Lambda0_Hlt1TrackMuonDecision_TOS Counter_for_p_Hlt1Global_TIS Counter_for_p_Hlt1Global_TOS Counter_for_p_Hlt1Phys_TIS Counter_for_p_Hlt1Phys_TOS Counter_for_mu_Hlt1Global_TIS Counter_for_mu_Hlt1Phys_TIS Hlt1 Tis-Tos SignalLine 100101102103104105106107 counts Counter_for_Lambda0_Hlt1Global_TIS Counter_for_Lambda0_Hlt1Global_TOS Counter_for_Lambda0_Hlt1Phys_TIS Counter_for_Lambda0_Hlt1Phys_TOS Counter_for_Lambda0_Hlt1DiMuonHighMassDecision_TIS Counter_for_Lambda0_Hlt1DiMuonLowMassDecision_TIS Counter_for_Lambda0_Hlt1SingleMuonNoIPDecision_TIS Counter_for_Lambda0_Hlt1SingleMuonNoIPDecision_TOS Counter_for_Lambda0_Hlt1SingleMuonHighPTDecision_TIS Counter_for_Lambda0_Hlt1SingleMuonHighPTDecision_TOS Counter_for_Lambda0_Hlt1TrackMuonDecision_TIS Counter_for_Lambda0_Hlt1TrackMuonDecision_TOS Counter_for_p_Hlt1Global_TIS Counter_for_p_Hlt1Global_TOS Counter_for_p_Hlt1Phys_TIS Counter_for_p_Hlt1Phys_TOS Counter_for_pi_Hlt1Global_TIS Counter_for_pi_Hlt1Global_TOS Counter_for_pi_Hlt1Phys_TIS Counter_for_pi_Hlt1Phys_TOS Hlt1 Tis-Tos NormLine Figure A.2: Hlt1 Trigger Lines firing more often in Selected Events. SignalLine case is depicted in the left plot and NormLine in the right one. Missing lines have counter = 0 100101102103104105 counts Counter_for_Lambda0_Hlt2Global_TIS Counter_for_Lambda0_Hlt2Global_TOS Counter_for_Lambda0_Hlt2Phys_TIS Counter_for_Lambda0_Hlt2Phys_TOS Counter_for_Lambda0_Hlt2DiMuonJPsiDecision_TIS Counter_for_Lambda0_Hlt2DiMuonJPsiHighPTDecision_TIS Counter_for_Lambda0_Hlt2DiMuonPsi2SDecision_TIS Counter_for_Lambda0_Hlt2DiMuonBDecision_TIS Counter_for_p_Hlt2Global_TIS Counter_for_p_Hlt2Global_TOS Counter_for_p_Hlt2Phys_TIS Counter_for_p_Hlt2Phys_TOS Counter_for_mu_Hlt2Global_TIS Counter_for_mu_Hlt2Global_TOS Counter_for_mu_Hlt2Phys_TIS Hlt2 Tis-Tos SignalLine 101102103104105106107 counts Counter_for_Lambda0_Hlt2Global_TIS Counter_for_Lambda0_Hlt2Global_TOS Counter_for_Lambda0_Hlt2Phys_TIS Counter_for_Lambda0_Hlt2Phys_TOS Counter_for_Lambda0_Hlt2DiMuonJPsiDecision_TIS Counter_for_Lambda0_Hlt2DiMuonJPsiHighPTDecision_TIS Counter_for_Lambda0_Hlt2DiMuonPsi2SDecision_TIS Counter_for_Lambda0_Hlt2DiMuonBDecision_TIS Counter_for_p_Hlt2Global_TIS Counter_for_p_Hlt2Global_TOS Counter_for_p_Hlt2Phys_TIS Counter_for_p_Hlt2Phys_TOS Counter_for_pi_Hlt2Global_TIS Counter_for_pi_Hlt2Global_TOS Counter_for_pi_Hlt2Phys_TIS Counter_for_pi_Hlt2Phys_TOS Hlt2 Tis-Tos NormLine Figure A.3: Hlt2 Trigger Lines firing more often in Selected Events. SignalLine case is depicted in the left plot and NormLine in the right one. Missing lines have counter = 0 (Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=-13)) & abs(mu_MC_MOTHER_ID)=3122 & abs(p_MC_MOTHER_ID)=3122 & Lambda0_TRUEENDVERTEX_Z=mu_TRUEORIGINVERTEX_Z & p_TRUEORIGINVERTEX_Z=mu_TRUEORIGINVERTEX_Z & p_MC_MOTHER_KEY=mu_MC_MOTHER_KEY Selection requirements for Λ→𝑝𝜋− The requirements for selecting Λ→𝑝𝜋− in the MC samples are detailed in Tab. 115 appendix a. appendix Requirement Λ𝑝 𝜇− TRUE ID 3122 2212 13 TRUE ID CC -3122 -2212 -13 abs(MOTHER ID) 3122 3122 ORIGIN VERTEX ΛEnd Vertex ΛEnd Vertex MOTHER KEY ΛKEY ΛKEY Table A.3: Requirements to select signal in the MC samples. A.4. The TRUE ID of each particle should match the corresponding number code to ensure correct MC association. Both the proton and the pion are required to have a Λ as their mother particle. These two particles should originate from the same vertex, which should also coincide with the Λ end vertex. Lastly, to confirm that both particles come from the same mother, the MC key of their respective mothers must match. Requirement Λ𝑝 𝜋− TRUE ID 3122 2212 -211 TRUE ID CC -3122 -2212 211 abs(MOTHER ID) 3122 3122 ORIGIN VERTEX ΛEnd Vertex ΛEnd Vertex MOTHER KEY ΛKEY ΛKEY Table A.4: Requirements to select Λ→𝑝𝜋 − in the MC samples.Note that, in contrast to the muon, the sign of the negative pion is ’-’. Below is the explicit code that ensures the satisfaction of the given conditions: ((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=-211) | (Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=211)) & abs(mu_MC_MOTHER_ID)=3122 & abs(p_MC_MOTHER_ID)=3122 & Lambda0_TRUEENDVERTEX_Z=mu_TRUEORIGINVERTEX_Z & p_TRUEORIGINVERTEX_Z=mu_TRUEORIGINVERTEX_Z & p_MC_MOTHER_KEY=mu_MC_MOTHER_KEY Selection requirements for eDIF (Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇)) The requirements for selecting Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇) in the MC samples are detailed in Tab. A.5. The TRUE ID of each particle should match the corresponding number code to ensure correct MC association. The proton is required to have a Λ as its mother particle and the muon is required to have a pion as mother and a Λ as grandmother. The muon should not originate from the Λ end vertex . Lastly, to confirm that both particles come from the same mother, the MC key of the proton mother and muon grandmother must match. Below is the explicit code that ensures the satisfaction of the given conditions: 116 a.3. background sources Requirement Λ𝑝 𝜇− TRUE ID 3122 2212 13 TRUE ID CC -3122 -2212 -13 abs(MOTHER ID) 3122 211 abs(GRANDMOTHER ID) 3122 ORIGIN VERTEX not ΛEnd Vertex KEY REQUIREMENT mother = ΛKEY Grandmother = ΛKEY Table A.5: Requirements to select Λ→𝑝(𝜋−→𝜇−¯ 𝜈𝜇). ((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=13) | (Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=-13)) & abs(p_MC_MOTHER_ID)=3122 & abs(mu_MC_MOTHER_ID)=211 & abs(mu_MC_GD_MOTHER_ID)=3122 & p_MC_MOTHER_KEY=mu_MC_GD_MOTHER_KEY & Lambda0_TRUEENDVERTEX_Z≠mu_TRUEORIGINVERTEX_Z Selection requirements for 𝐾0 𝑆→𝜋+𝜋− The requirements for selecting 𝐾0 𝑆→ 𝜋+𝜋− in the MC samples are detailed in Tab. A.6. The TRUE ID of each particle should match the corresponding number code to ensure correct MC association. Both pions are required to have a 𝐾0 𝑆 as their mother particle. These two particles should originate from the same vertex, which should also coincide with the 𝐾0 𝑆 end vertex. This sample is only used to design the selection and reject this channel and to remove this kind of events from the combinatorial background sample. Requirements are looser to remove also mismatched 𝐾0 𝑆→𝜋+𝜋− from the combinatorial background sample. Requirement 𝐾0 𝑆𝜋+𝜋− TRUE ID 310 211 -211 abs(MOTHER ID) 310 310 ORIGIN VERTEX 𝐾0 𝑆End Vertex 𝐾0 𝑆End Vertex MOTHER KEY 𝐾0 𝑆KEY 𝐾0 𝑆KEY Table A.6: Requirements to select 𝐾0 𝑆→𝜋+𝜋−in the MC samples. Below is the explicit code that ensures the satisfaction of the given conditions: ((Lambda0_TRUEID=3122 & p_TRUEID=2212 & mu_TRUEID=13) | (Lambda0_TRUEID=-3122 & p_TRUEID=-2212 & mu_TRUEID=-13)) & abs(mu_MC_MOTHER_ID)=3122 & abs(p_MC_MOTHER_ID)=3122 & Lambda0_TRUEENDVERTEX_Z=mu_TRUEORIGINVERTEX_Z & p_TRUEORIGINVERTEX_Z=mu_TRUEORIGINVERTEX_Z & p_MC_MOTHER_KEY=mu_MC_MOTHER_KEY 117 appendix a. appendix Trig0x617d18a4/Reco18/30000000/LDST") MU DDDB: dddb-20170721-3 Condition DB: sim-20190430-vc-mu100 BKQuery("MC/2018/Beam6500GeV-2018-MagUp-Nu1.6-25ns-Pythia8/ Sim09k/ Trig0x617d18a4/Reco18/30000000/LDST") a.8.11 signal private production to correct stripping eff: YEAR: 2016 MD EventType=33512008 APPCONFIGOPTS_Gauss= /cvmfs/lhcb.cern.ch/lib/lhcb/DBASE/AppConfig/v3r395/options APPCONFIGOPTS_Boole= /cvmfs/lhcb.cern.ch/lib/lhcb/DBASE/AppConfig/v3r374/options APPCONFIGOPTS_Moore_1= /cvmfs/lhcb.cern.ch/lib/lhcb/DBASE/AppConfig/v3r297/options APPCONFIGOPTS_Moore_2= /cvmfs/lhcb.cern.ch/lib/lhcb/DBASE/AppConfig/v3r297/options APPCONFIGOPTS_Moore_3= /cvmfs/lhcb.cern.ch/lib/lhcb/DBASE/AppConfig/v3r355/options APPCONFIGOPTS_Brunel= /cvmfs/lhcb.cern.ch/lib/lhcb/DBASE/AppConfig/v3r401/options DECFILESROOT= /cvmfs/lhcb.cern.ch/lib/lhcb/DBASE/Gen/DecFiles/v30r57 LBPYTHIA8ROOT= /cvmfs/lhcb.cern.ch/lib/lhcb/GAUSS/GAUSS_v49r20/Gen/LbPythia8 GAUSS: source /cvmfs/lhcb.cern.ch/lib/LbEnv.sh -c x86\_64-slc6-gcc48-opt lb-run Gauss/v49r20 gaudirun.py \${APPCONFIGOPTS\_Gauss}/Gauss/Beam6500GeV-\ ${magnet}100-2016-nu1.6.py \${APPCONFIGOPTS\_Gauss}/Gauss/EnableSpillover-25ns.py \${APPCONFIGOPTS\_Gauss}/Gauss/DataType-\${year}.py \${APPCONFIGOPTS\_Gauss}/Gauss/RICHRandomHits.py \${DECFILESROOT}/options/\${EventType}.py \$LBPYTHIA8ROOT/options/Pythia8.py \${APPCONFIGOPTS\_Gauss}/Gauss/G4PL\_FTFP\_BERT\_EmNoCuts.py \${mainDir}/extraOptionsGauss.py BOOLE: source /cvmfs/lhcb.cern.ch/lib/LbEnv.sh -c x86\_64-slc6-gcc49-opt 124 a.8. davinci versions and tags lb-run Boole/v30r4 gaudirun.py \${APPCONFIGOPTS\_Boole}/ Boole/Default.py \${APPCONFIGOPTS\_Boole}/Boole/EnableSpillover.py \${APPCONFIGOPTS\_Boole}/Boole/DataType-2015.py \${APPCONFIGOPTS\_Boole}/Boole/Boole-SetOdinRndTrigger.py \${mainDir}/extraOptionsBoole.py MOORE L0: source /cvmfs/lhcb.cern.ch/lib/LbEnv.sh -c x86\_64-slc6-gcc48-opt lb-run Moore/v25r4 gaudirun.py \${APPCONFIGOPTS\_Moore\_1}/L0App/L0AppSimProduction.py \${APPCONFIGOPTS\_Moore\_1}/L0App/L0AppTCK-0x160F.py \${APPCONFIGOPTS\_Moore\_1}/L0App/ForceLUTVersionV8.py \${APPCONFIGOPTS\_Moore\_1}/L0App/DataType-2016.py \${APPCONFIGOPTS\_Moore\_1}/Persistency/Compression-ZLIB-1.py \${mainDir}/extraOptionsMooreL0.py MOORE HLT1: source /cvmfs/lhcb.cern.ch/lib/LbEnv.sh -c x86\_64-slc6-gcc48-opt \par lb-run Moore/v25r4 gaudirun.py \${APPCONFIGOPTS\_Moore\_2}/Moore/ MooreSimProductionForSeparateL0AppStep2015.py \${APPCONFIGOPTS\_Moore\_2}/Conditions/TCK-0x5138160F.py \${APPCONFIGOPTS\_Moore\_2}/L0App/DataType-2016.py \${APPCONFIGOPTS\_Moore\_2}/Persistency/Compression-ZLIB-1.py \${APPCONFIGOPTS\_Moore\_2}/Moore/MooreSimProductionHlt1.py \${mainDir}/extraOptionsMooreL1.py MOORE HLT2: source /cvmfs/lhcb.cern.ch/lib/LbEnv.sh -c x86\_64-slc6-gcc48-opt lb-run Moore/v25r4 gaudirun.p \${APPCONFIGOPTS\_Moore\_3}/Moore/ MooreSimProductionForSeparateL0AppStep2015.py \${APPCONFIGOPTS\_Moore\_3}/Conditions/TCK-0x6139160F.py \${APPCONFIGOPTS\_Moore\_3}/L0App/DataType-2016.py \${APPCONFIGOPTS\_Moore\_3}/Persistency/Compression-ZLIB-1.py \${APPCONFIGOPTS\_Moore\_3}/Moore/MooreSimProductionHlt2.py \${mainDir}/extraOptionsMooreL2.py 125 appendix a. appendix BRUNEL: source /cvmfs/lhcb.cern.ch/lib/LbEnv.sh -c x86\_64-slc6-gcc49-opt \par lb-run Brunel/v50r7 gaudirun.py \${APPCONFIGOPTS\_Brunel}/Brunel/DataType-2016.py \${APPCONFIGOPTS\_Brunel}/Brunel/MC-WithTruth.py \${APPCONFIGOPTS\_Brunel}/Brunel/SplitRawEventOutput.4.3.py \${mainDir}/extraOptionsBrunel.py Where basically the extraOptions file are: LHCbApp().DDDBtag = "dddb-20170721-3" LHCbApp().CondDBtag = "sim-20170721-2-vc-"+pol+"100" DAVINCI: DaVinci version: DaVinci/v44r10p5 tags: DaVinci().DDDBtag = "dddb-20170721-3" DaVinci().CondDBtag = "sim-20170721-2-vc-md100" \#dddb-20190206-3 \#cond-20191004-1 Particles: from StandardParticles import StdLooseProtons, StdAllLooseMuons \#StdAllNoPIDsProtons,StdAllNoPIDsMuons We are supposing that 𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆 𝑳𝒑𝒎𝒖 =𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆 𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫 ×𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆 𝑪𝒖𝒕𝒔𝑷𝑰 𝑫 , so we have to calculate each efficiency separately. The first one, 𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆 𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫 , can be obtained applying just the NoPID Stripping Line cuts: if ((((tReco.Lambda0_TRUEID==3122) and (tReco.p_TRUEID==2212) and (tReco.mu_TRUEID==13)) | ((tReco.Lambda0_TRUEID==-3122) and (tReco.p_TRUEID==-2212) and (tReco.mu_TRUEID==-13))) and (tReco.Lambda0_TRUEENDVERTEX_Z==tReco.mu_TRUEORIGINVERTEX_Z) 126 a.8. davinci versions and tags and ((tReco.p_TRUEORIGINVERTEX_Z==tReco.mu_TRUEORIGINVERTEX_Z))): if tReco.Lambda0_M<1141 and tReco.mu_TRACK_CHI2NDOF<3 and tReco.mu_IPCHI2_OWNPV>60 and tReco.mu_IP_OWNPV>1 and tReco.mu_TRACK_GhostProb<0.2 and tReco.p_TRACK_GhostProb<0.2 and tReco.p_TRACK_CHI2NDOF<3 and tReco.p_IPCHI2_OWNPV>16 and tReco.Lambda0_IP_OWNPV>0.2 and tReco.Lambda0_VCHI2NDOF<9 and tReco.Lambda0_AMAXDOCA<0.3 and tReco.Lambda0_BPVLTIME>0.009 and tRe\co.Lambda0_BPVVDCHI2>50 and tReco.Lambda0_MIPDV_PRIMARY>0.2: counterStrippingNoPID+=1 if tReco.mu_ProbNNmu>0.3 and tReco.mu_isMuon==True and tReco.mu_ProbNNpi<0.7 and tReco.mu_ProbNNk<0.7 and tReco.p_ProbNNp>0.3 and tReco.p_ProbNNmu<0.7 and tReco.p_ProbNNk<0.7: counterStrippingPID+=1 This can be done for Reconstructed tuples using as input for the CombineParticles StdLooseProtons and StdAllLooseMuons or StdAllNoPIDsProtons and StdAllNoPIDsMuons. The results are: NoPIDsParticles:𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆 𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫𝒔 =0.025189530 LooseParticles:𝝐𝑺𝒊𝒈𝒏𝒂𝒍𝑳𝒊𝒏𝒆 𝑪𝒖𝒕𝒔𝑵 𝒐𝑷𝑰 𝑫𝒔 =0.0089420 127 appendix a. appendix a.9 decfiles a.9.1 lppi: tightcut (33102103) # EventType: 33102103 # # Descriptor: [Lambda0 -> pip+]cc # # NickName: Lambda_ppi=PHSP,TightCut # # Cuts: LoKi::GenCutTool/TightCut # # Documentation: Lambda0 decay to p+ piwith phase space model, Tight cut. # * Lambda0 endvertex z in [-1m,0.8m] # * Lambda0 endvertex radial cut at 38mm # EndDocumentation # # CPUTime: < 1 min # # InsertPythonCode: # # # from Configurables import LoKi__GenCutTool # from Gauss.Configuration import * # gen = Generation() # gen.SignalPlain.addTool ( LoKi__GenCutTool , 'TightCut') # # # tightCut = gen.SignalPlain.TightCut # tightCut.Decay = '[^(Lambda0 => ^p+ ^pi-)]CC' # tightCut.Preambulo += [ # "from GaudiKernel.SystemOfUnits import meter, millimeter, GeV, MeV" , # "inAcc = in_range ( 0.005 , GTHETA , 0.400 ) " , # "inEta = in_range ( 1.95 , GETA , 5.050 ) " , # "goodTrack = inAcc & inEta" , # "GVX = LoKi.GenVertices.PositionX() " , # "GVY = LoKi.GenVertices.PositionY() " , # "GVZ = LoKi.GenVertices.PositionZ() " , # "vx = GFAEVX ( GVX, 100 * meter ) " , # "vy = GFAEVX ( GVY, 100 * meter ) " , # "rho2 = vx**2 + vy**2 " , # "rhoK = rho2 < (38 * millimeter )**2 " , # "decay = in_range ( -1 * meter, GFAEVX ( GVZ, 100 * meter ), 0.8 * meter ) ", # "goodpion = (GPZ > 0) & (GPT > 100*MeV ) & (GP > 3.0*GeV)", # "goodproton = (GPT > 275*MeV ) & (GP > 12.25*GeV)" # ] 128 a.9. decfiles # tightCut.Cuts = { # "[Lambda0]cc" : "decay & rhoK", # "[p+]cc" : "goodTrack & goodproton " , # "[pi-]cc" : "goodTrack & goodpion" # } # EndInsertPythonCode # # PhysicsWG: RD # Tested: Yes # Responsible: Alexandre Brea Rodriguez # Email: [email protected] # Date: 20201221 # Decay Lambda0sig 1.000 p+ piPHSP; Enddecay CDecay anti-Lambda0sig # End # a.9.2 lpmunu: tightcut shd (33512008) # EventType: 33512008 # # Descriptor: [Lambda0 -> p+ muanti-nu_mu]cc # # NickName: Lambda_pmunuSHD=TightCut # # Cuts: LoKi::GenCutTool/TightCut # # Documentation: Lambda0 decay to p+ muanti-nu_mu with SHD model. prob=0.615, probcos=0.366001501202 tight generator cut # * Lambda0 endvertex z in [-1m,0.8m] # * Lambda0 endvertex radial cut at 38mm # EndDocumentation # # CPUTime: < 1 min # # InsertPythonCode: # # # from Configurables import LoKi__GenCutTool # from Gauss.Configuration import * # gen = Generation() 129 appendix a. appendix # gen.SignalPlain.addTool ( LoKi__GenCutTool , 'TightCut') # # # tightCut = gen.SignalPlain.TightCut # tightCut.Decay = '[^(Lambda0 => ^p+ ^munu_mu~)]CC' # tightCut.Preambulo += [ # "from GaudiKernel.SystemOfUnits import meter, millimeter, GeV" , # "GY = LoKi.GenParticles.Rapidity () ## to be sure " , # "inY = in_range ( 1.9 , GY , 4.6 ) " , # "inAcc = in_range ( 0.005 , GTHETA , 0.400 ) " , # "inEta = in_range ( 1.95 , GETA , 5.050 ) " , # "goodTrack = inAcc & inEta" , # "GVX = LoKi.GenVertices.PositionX() " , # "GVY = LoKi.GenVertices.PositionY() " , # "GVZ = LoKi.GenVertices.PositionZ() " , # "vx = GFAEVX ( GVX, 100 * meter ) " , # "vy = GFAEVX ( GVY, 100 * meter ) " , # "rho2 = vx**2 + vy**2 " , # "rhoK = rho2 < (38 * millimeter )**2 " , # "decay = in_range ( -1 * meter, GFAEVX ( GVZ, 100 * meter ), 0.8 * meter ) ", # ] # tightCut.Cuts = { # "[Lambda0]cc" : "decay & rhoK", # "[mu-]cc" : "goodTrack " , # "[p+]cc" : "goodTrack " # } # EndInsertPythonCode # PhysicsWG: RD # Tested: Yes # Responsible: Alexandre Brea Rodriguez # Email: [email protected] # Date: 20190101 # #Alias MyLambda0 Lambda0 #Alias Myanti-Lambda0 anti-Lambda0 #ChargeConj MyLambda0 Myanti-Lambda0 Decay Lambda0sig 1.000 p+ muanti-nu_mu SHD; Enddecay CDecay anti-Lambda0sig # End 130 a.10. pidcalib2 a.10 pidcalib2 a.10.1 signal line In our case we should run the following commands: pidcalib2.make_eff_hists -c "Brunel_InMuonAcc == 1.0" --sample Turbo16 --magnet down --particle Mu_nopt --pid-cut "Brunel_MC15TuneV1_ProbNNmu>0.3 & Brunel_MC15TuneV1_ProbNNpi<0.7 & Brunel_MC15TuneV1_ProbNNk<0.7" --cut "Brunel_IsMuon & Brunel_TRCHI2NDOF<3 & Brunel_TRACK_GHOSTPROB<0.2 & Brunel_IPCHI2>60" --bin-var Brunel_P --bin-var Brunel_ETA --bin-var nSPDhits --binning-file binning-file_noPT.txt --output-dir pidcalib_output/ pidcalib2.make_eff_hists --sample Turbo16 --magnet down --particle P --pid-cut "Brunel_DLLp>-5 & Brunel_MC15TuneV1_ProbNNp > 0.3 & Brunel_MC15TuneV1_ProbNNmu < 0.7 & Brunel_MC15TuneV1_ProbNNk < 0.7" --cut "Brunel_PT>250 & Brunel_HasRich==1 & Brunel_TRCHI2NDOF<3 & Brunel_TRACK_GHOSTPROB<0.2 & Brunel_IPCHI2>16" --bin-var Brunel_P --bin-var Brunel_ETA --bin-var nSPDhits --binning-file proton_binning-file.txt --output-dir pidcalib_output/ Where the -c "InMuonAcc == 1.0" option was included because we want to separate the efficiency related to the Muon System acceptance and the muon PID efficiency, so the InMuonAcc cut was applied previously to the PIDCalib process. In our case we should also use the Mu_nopt instead of usual Mu, since the default muon calibration sample has a transverse momentum cut of 800 𝑴𝒆𝑽/𝒄 and a total momentum cut of 3 GeV/c. The Brunel prefix for the variables indicates that we are using the offline variables, since the aliases without this prefix are used for values at the trigger stages. Concerning the binning JSON file indicating the bin edges, it was designed taking into account the nSPDHits and the muon and proton ETA and P distributions after applying all the NoPID cuts detailed before (A.5). To compute the corrected efficiencies for the proton and the muon of the private Signal MC sample after the non-PID selection Cuts, the applied commands were: pidcalib2.ref_calib --sample Turbo16 --magnet down --ref-file data/LambdapmunuSIM_2016MD_NoPIDS_ETA_Cuts.root -t "T" --histo-dir pidcalib_output --bin-vars '{"Brunel_P": "P", "Brunel_ETA": "ETA", "nSPDhits": "nSPDHits"}'--ref-pars '{"mu": ["Mu_nopt", "Brunel_MC15TuneV1_ProbNNmu>0.3 & Brunel_MC15TuneV1_ProbNNpi<0.7 & Brunel_MC15TuneV1_ProbNNk<0.7"]}' --output-file mu_md_ntuple_PID_eff.root 131 appendix a. appendix Figure A.5: Distributions of the binning variables after the non-PID selection Cuts for muon and proton tracks. pidcalib2.ref_calib --sample Turbo16 --magnet down --ref-file data/LambdapmunuSIM_2016MD_NoPIDS_ETA_Cuts.root -t "T" --histo-dir pidcalib_output --bin-vars '{"Brunel_P": "P", "Brunel_ETA": "ETA", "nSPDhits": "nSPDHits"}'--ref-pars '{"p": ["P", "Brunel__DLLp > -5 & Brunel_MC15TuneV1_ProbNNp > 0.3 & Brunel_MC15TuneV1_ProbNNmu < 0.7 & Brunel_MC15TuneV1_ProbNNk < 0.7"]}' --output-file p_md_ntuple_PID_eff.root a.10.2 norm line In this case, the commands to create the efficiency histograms for the proton and the pion case should be: pidcalib2.make_eff_hists --sample Turbo18 --magnet down --particle Pi_KS 132 a.10. pidcalib2 Figure A.6: Distributions of the binning variables after the non-PID selection Cuts for pion and proton tracks. --pid-cut "Brunel_MC15TuneV1_ProbNNpi > 0.4 & Brunel_MC15TuneV1_ProbNNmu < 0.7 & Brunel_MC15TuneV1_ProbNNk < 0.7" --cut "Brunel_IsMuon!=1 & Brunel_TRCHI2NDOF<3 & Brunel_TRACK_GHOSTPROB<0.2 & Brunel_IPCHI2>60 & Brunel_HasRich==1" --bin-var Brunel_P --bin-var Brunel_ETA --bin-var nSPDhits --binning-file Pi_KS_binning-file_noPT.txt --output-dir pidcalib_output/ pidcalib2.make_eff_hists --sample Turbo18 --magnet down --particle P --pid-cut "Brunel_DLLp>-5 & Brunel_MC15TuneV1_ProbNNp > 0.3 & Brunel_MC15TuneV1_ProbNNmu < 0.7 & Brunel_MC15TuneV1_ProbNNk < 0.7" --cut "Brunel_PT>250 & Brunel_HasRich==1 & Brunel_TRCHI2NDOF<3 & Brunel_TRACK_GHOSTPROB<0.2 & Brunel_IPCHI2>16" --bin-var Brunel_P --bin-var Brunel_ETA --bin-var nSPDhits --binning-file proton_binning133