Precision measurement of the B0s–B0s oscillation frequency with the decay B0s →D−sπ+

PAPER Precision measurement of the B0 s– oscillation frequency with the decay B0 s→D− s π + To cite this article: R Aaij et al 2013 New J. Phys. 15 053021 View the article online for updates and enhancements. Related content CP violation at LHCb Olaf Steinkamp and the LHCb Collaboration - Measurements of B0 and B0s mixing frequencies at LHCb Giulia Tellarini - Very Rare Decays at LHCb Serena Oggero and the Lhcb Collaboration - Recent citations Updates and New Results in Models with Reduced Couplings S. Heinemeyer et al - Konstantin GizdovCP violation in twoand quasi-two-body charmless B decays at LHCb Emmy Gabriel and on behalf of the LHCb Collaboration - This content was downloaded from IP address 83.47.59.233 on 28/04/2020 at 11:14 Precision measurement of the B0 s–B0 soscillation frequency with the decay B0 s→D− sπ+ The LHCb Collaboration New Journal of Physics 15 (2013) 053021 (15pp) Received 18 April 2013 Published 14 May 2013 Online at http://www.njp.org/ doi:10.1088/1367-2630/15/5/053021 E-mail: [email protected] Abstract. A key ingredient to searches for physics beyond the Standard Model in B0 smixing phenomena is the measurement of the B0 s– B0 soscillation frequency, which is equivalent to the mass difference 1msof the B0 smass eigenstates. Using the world’s largest B0 smeson sample accumulated in a dataset, corresponding to an integrated luminosity of 1.0 fb−1, collected by the LHCb experiment at the CERN LHC in 2011, a measurement of 1msis presented. A total of about 34 000 B0 s→D− sπ+signal decays are reconstructed, with an average decay time resolution of 44 fs. The oscillation frequency is measured to be 1ms=17.768 ± 0.023 (stat) ±0.006 (syst) ps−1, which is the most precise measurement to date. New Journal of Physics 15 (2013) 053021 1367-2630/13/053021+15$33.00 © CERN 2013 for the benefit of the LHCb Collaboration, published under the terms of the Creative Commons Attribution 3.0 licence by IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Any further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation and DOI. 2 Contents 1. Introduction 2 2. The LHCb experiment 3 3. Signal selection and analysis strategy 4 4. Invariant mass description 5 5. Decay time description 6 6. Flavour tagging 7 7. Measurement of 1ms8 8. Systematic uncertainties 9 9. Conclusion 10 Acknowledgments 10 The LHCb Collaboration 10 References 14 1. Introduction The Standard Model (SM) of particle physics, despite its great success in describing experimental data, is considered an effective theory valid only at low energies, below the TeV scale. At higher energies, new physics phenomena are predicted to emerge. For analyses looking for physics beyond the SM (BSM), there are two conceptually different approaches: direct and indirect searches. Direct searches are performed at the highest available energies and aim at producing and detecting new heavy particles. Indirect searches focus on precision measurements of quantum-loop-induced processes. Accurate theoretical predictions are available for the heavy quark sector in the SM. It is therefore an excellent place to search for new phenomena [1,2], since any deviation from these predictions can be attributed to contributions from BSM. In the SM, transitions between quark families (flavours) are possible via the charged current weak interaction. Flavour changing neutral currents (FCNC) are forbidden at lowest order, but are allowed in higher order processes. Since new particles can contribute to these loop diagrams, such processes are highly sensitive to contributions from BSM. An example FCNC transition is neutral meson mixing, where neutral mesons can transform into their antiparticles. Particle–antiparticle oscillations have been observed in the K0–K0system [3], the B0–B0system [4], the B0 s–B0 ssystem [5,6] and the D0–D0system [7–10]. The frequency of B0 s– B0 soscillations is the highest. On average, a B0 smeson changes its flavour nine times between production and decay. This poses a challenge to the detector for the measurement of the decay time. Another key ingredient of this measurement is the determination of the flavour of the B0 smeson at production, which relies heavily on good particle identification and the separation of tracks from the primary interaction point. The observed particle and antiparticle states B0 sand B0 sare linear combinations of the mass eigenstates BHand BLwith masses mHand mLand decay widths 0Hand 0L, respectively [11]. The B0 soscillation frequency is equivalent to the mass difference 1ms=mH−mL. The parameter 1msis an essential ingredient for all studies of time-dependent matter–antimatter New Journal of Physics 15 (2013) 053021 (http://www.njp.org/) 3 asymmetries involving B0 smesons, such as the B0 smixing phase φsin the decay B0 s→ J/ψφ [12]. It was first observed by the Collider Detector at Fermilab (CDF) [6]. The Large Hadron Collider beauty experiment (LHCb) published a measurement of this frequency using a dataset, corresponding to an integrated luminosity of 37 pb−1, taken in 2010 [13]. This analysis complements the previous result and is obtained in a similar way, using a data sample, corresponding to an integrated luminosity of 1.0 fb−1, collected by LHCb in 2011. 2. The LHCb experiment The LHCb experiment is designed for precision measurements in the beauty and charm hadron systems. At a centre-of-mass energy of √s=7 TeV, about 3 ×1011 bb pairs were produced in 2011. The LHCb detector [14] is a single-arm forward spectrometer covering the pseudorapidity range from two to five. The excellent decay time resolution necessary to resolve the fast B0 s– B0 s oscillation is provided by a silicon-strip vertex detector surrounding the pp interaction region. At nominal position, the sensitive region of the vertex detector is only 8 mm away from the beam. An impact parameter (IP) resolution of 20 µm for tracks with high transverse momentum (pT) is achieved. Charged particle momenta are measured with the LHCb tracking system consisting of the aforementioned vertex detector, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 T m, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system has momentum resolution 1p/pthat varies from 0.4% at 5 GeV/cto 0.6% at 100 GeV/c. Since this analysis is performed with decays involving only hadrons in the final state, excellent particle identification is crucial to suppress background. Charged hadrons are identified using two ring-imaging Cherenkov detectors [15]. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The first stage of the trigger [16] is implemented in hardware, based on information from the calorimeter and muon systems, and selects events that contain candidates with large transverse energy and transverse momentum. This is followed by a software stage that applies a full event reconstruction. The software trigger used in this analysis requires a two-, threeor four-track secondary vertex with a significant displacement from the primary interaction, a large sum of pTof the tracks, and at least one track with pT>1.7 GeV/c. In addition, an IP χ2 with respect to the primary interaction greater than 16 and a track fit χ2per degree of freedom <2 is required. The IP χ2is defined as the difference between the χ2of the primary vertex reconstructed with and without the considered track. A multivariate algorithm is used for the identification of the secondary vertices. For the simulation, pp collisions are generated using Pythia 6.4 [17] with a specific LHCb configuration [18]. Decays of hadronic particles are described by EvtGen [19], in which final state radiation is generated using Photos [20]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [21,22], as described in [23]. New Journal of Physics 15 (2013) 053021 (http://www.njp.org/) 4 3. Signal selection and analysis strategy The analysis uses B0 scandidates reconstructed in the flavour-specific decay mode1B0 s→D− sπ+ in five D− sdecay modes, namely D− s→φ(K+K−)π−, D− s→K∗0(K+π−)K−, D− s→K+K−π− nonresonant, D− s→K−π+π−and D− s→π−π+π−. To avoid double counting, events that contain a candidate passing the selection criteria of one mode are not considered for the subsequent modes, using the order listed above. All reconstructed decays are flavour-specific final states; thus the flavour of the B0 scandidate at the time of its decay is given by the charges of the final state particles. A combination of tagging algorithms is used to identify the B0 sflavour at production. The algorithms provide for each candidate a tagging decision as well as an estimate of the probability that this decision is wrong (mistag probability). These algorithms have been optimized using large event samples of flavour-specific decays [24,25]. To be able to study the effect of selection criteria that influence the decay time spectrum, we restrict the analysis to those events in which the signal candidate passed the requirements of the software trigger algorithm used in this analysis. Specific features, such as the masses of the intermediate φand K∗0resonances or the Dalitz structure of the D− s→π−π+π−decay mode, are exploited for the five decay modes. The most powerful quantity to separate signal from background common to all decay modes is the output of a boosted decision tree (BDT) [26]. The BDT exploits the long B0 slifetime by using as input the IP χ2of the daughter tracks, the angle of the reconstructed B0 smomentum relative to the line between the reconstructed primary vertex, and the B0 svertex and the radial flight distance in the transverse plane of both the B0 sand the D− smesons. Additional requirements are applied on the sum of the pTof the B0 scandidate’s decay products as well as on particle identification variables, and on track and vertex quality. The reconstructed D− smass is required to be consistent with the known value [27]. After this selection, a total of about 47 800 candidates remain in the B0 s→D− sπ+invariant mass window of 5.32–5.98 GeV/c2. An unbinned likelihood method is employed to simultaneously fit the B0 sinvariant mass and decay time distributions of the five decay modes. The probability density functions (PDFs) for signal and background in each of the five modes can be written as P=Pm(m)Pt(t,q|σt, η) Pσt(σt)Pη(η), (1) where mis the reconstructed invariant mass of the B0 scandidate, tis its reconstructed decay time and σtis an event-by-event estimate of the decay time resolution. The tagging decision q can be 0 if no tag is found, −1 for events with different flavour at production and decay (mixed) or +1 for events with the same flavour at production and decay (unmixed). The predicted eventby-event mistag probability ηcan take values between 0 and 0.5. The functions Pmand Pt describe the invariant mass and the decay time probability distributions, respectively. Ptis a conditional probability depending on σtand η. The functions Pσtand Pηare required to ensure the proper relative normalization of Ptfor signal and background [28]. The functions Pσtand Pηare determined from data, using the measured distribution in the upper B0 sinvariant mass sideband for the background PDF and the sideband subtracted distribution in the invariant mass signal region for the signal PDF. This measurement has been performed ‘blinded’, meaning that during the analysis process the fitted value of 1mswas shifted by an unknown value, which was removed after the analysis procedure had been finalized. 1Unless explicitly stated, inclusion of charge-conjugated modes is implied. New Journal of Physics 15 (2013) 053021 (http://www.njp.org/) 5 ] 2 c) invariant mass [MeV/ + π − s (D 5350 5400 5450 5500 5550 ) 2 ccandidates / (15 MeV/ 0 2000 4000 data fit + π − s D→ 0 s B + K − s D→ 0 s B misid bkg. comb bkg. a) LHCb − πφ→ − s D ] 2 c) invariant mass [MeV/ + π − s (D 5350 5400 5450 5500 5550 ) 2 ccandidates / (15 MeV/ 0 2000 data fit + π − s D→ 0 s B + K − s D→ 0 s B misid. bkg. comb. bkg. − K*K→ − s D LHCb b) ] 2 c) invariant mass [MeV/ + π − s (D 5350 5400 5450 5500 5550 ) 2 ccandidates / (15 MeV/ 0 1000 2000 data fit + π − s D→ 0 s B + K − s D→ 0 s B misid. bkg. comb. bkg. − π − K + K→ − s D LHCb c) ] 2 c) invariant mass [MeV/ + π − s (D 5350 5400 5450 5500 5550 ) 2 ccandidates / (15 MeV/ 0 500 data fit + π − s D→ 0 s B + K − s D→ 0 s B misid. bkg. comb. bkg. − π + π − K→ − s D LHCb d) ] 2 c) invariant mass [MeV/ + π − s (D 5350 5400 5450 5500 5550 ) 2 ccandidates / (15 MeV/ 0 1000 data fit + π − s D→ 0 s B + K − s D→ 0 s B comb. bkg. − π − π + π→ − s D LHCb e) Figure 1. Invariant mass distributions for B0 s→D− sπ+candidates with the D− s meson decaying as (a) D− s→φ(K+K−)π−, (b) D− s→K∗0(K+π−)K−, (c) D− s→ K+K−π−nonresonant, (d) D− s→K−π+π−and (e) D− s→π−π+π−. The fits and the various background components are described in the text. Misidentified backgrounds refer to background from B0and 30 bdecays with one misidentified daughter particle. 4. Invariant mass description The invariant mass of each B0 scandidate is determined in a vertex fit constraining the D− s invariant mass to its known value [27]. The invariant mass spectra for the five decay modes after all the selection criteria are applied are shown in figure 1. The fit to the five distributions takes into account contributions from signal, combinatorial background and b-hadron decay backgrounds. The signal components are described by the sum of two Crystal Ball (CB) functions [29], which are constrained to have the same peak parameter. The parameters of the CB function describing the tails are fixed to values obtained from simulation, whereas the mean and the two widths are allowed to vary. These are constrained to be the same for all five decay modes. It has been checked on data that the mass resolution is compatible among all modes. The b-hadron decay background includes B0and 30 bdecays with one misidentified daughter particle. Their mass shapes are derived from simulated samples. The yields for the New Journal of Physics 15 (2013) 053021 (http://www.njp.org/) 6 Table 1. Number of candidates and B0 ssignal fractions in the mass range 5.32–5.98 GeV/c2. Decay mode (D− sπ+) candidates fB0 s→D− sπ+fB0 s→D∓ sK± D− s→φ(K+K−)π−14 691 0.834 ±0.008 D− s→K∗0(K+π−)K−10 866 0.857 ±0.009 D− s→K+K−π−nonresonant 11 262 0.595 ±0.009 D− s→K−π+π−4288 0.437 ±0.014 D− s→π−π+π−6674 0.599 ±0.008 0.019 ±0.010 Total 47 781 0.714 ±0.004 0.019 ±0.010 different b-hadron decay backgrounds are allowed to vary individually for each of the five decay modes. Another component originates from B0 s→D∓ sK±decays, in which the kaon is misidentified as a pion. This contribution is treated as a signal in the decay time analysis. The requirement that the invariant mass be larger than 5.32 GeV/c2rejects background candidates from B0 sdecays with additional particles in the decay not reconstructed, such as B0 s→D∗− sπ+(D∗− s→D− sπ0or D− sγ). The fitted number of signal candidates does not change with respect to a fit in a larger mass window. The high mass sideband region 5.55–5.98 GeV/c2 provides a sample of mainly combinatorial background candidates. The mass distribution is described by an exponential function, whose parameters are allowed to vary individually for the five decay modes. By including this region in the fit, we are able to determine the decay time distribution as well as the tagging behaviour of the combinatorial background. The number of used candidates along with the signal fractions extracted from the twodimensional fit in mass and decay time are reported in table 1. One complication arises from the fact that the shape of the invariant mass distribution of the B0 s→D∓ sK±events is very similar to that of the B0background. Therefore, the fraction of B0 s→D∓ sK±candidates has been determined in a fit to the D− s→π−π+π−mode only, in which no B0background is present. Subsequently this value is used for all the other modes. 5. Decay time description The decay time of a particle is measured as t=Lm p,(2) where Lis the distance between the production vertex and the decay vertex of the particle, mits reconstructed invariant mass and pits reconstructed momentum. We use the decay time calculated without the D− smass constraint to avoid a systematic dependence of the B0 sdecay time on the reconstructed invariant mass. The theoretical distribution of the decay time, t, ignoring the oscillation and any detector resolution, is Pt∝0se−0stcosh 10s 2tθ(t), (3) New Journal of Physics 15 (2013) 053021 (http://www.njp.org/) 7 where 0sis the B0 sdecay width and 10sthe decay width difference between the light and heavy mass eigenstates2. The value for 10sis fixed to the latest value measured by LHCb [12] 10s=0.106 ±0.011 ±0.007 ps−1. It is varied within its uncertainties to assess the systematic effect on the measurement of 1ms. The Heaviside step function θ(t)restricts the PDF to positive decay times. To account for detector resolution effects, the decay time PDF is convolved with a Gaussian distribution. The width σtis taken from an event-by-event estimate returned by the fitting algorithm that reconstructs the B0 sdecay vertex. Due to tracking detector resolution effects, σt needs to be calibrated. A data-driven method, combining prompt D− smesons from the primary interaction with random π+mesons, forms fake B0 scandidates. The decay time distribution of these candidates, each divided by its event-by-event σt, is fitted with a Gaussian function. The width provides a scale factor Sσt=1.37, by which each σtis multiplied, such that it represents the correct resolution. By inspecting different regions of phase space of the fake B0 scandidates, the uncertainty range on this number is found to be 1.25 <Sσt<1.45. The variation is taken into account as part of the 1mssystematic studies. The resulting average decay time resolution is Sσt×hσti=44 fs. Some of the selection criteria influence the shape of the decay time distribution, e.g. the requirement of a large IP for B0 sdaughter tracks. Thus, a decay time acceptance function Et(t) has to be taken into account. Its parametrization is determined from simulated data and the parameter describing its shape is allowed to vary in the fit to the data, while 0sis fixed to the nominal value [27]. Taking into account resolution and decay time acceptance, the PDF given in equation (3) is modified to Pt(t|σt)∝0se−0stcosh 10s 2tθ(t)⊗G(t;0,Sσtσt)Et(t)(4) with G(t;0,Sσtσt)being the resolution function determined by the method mentioned above. The decay time PDFs for the B0and 30 bbackgrounds are identical to the signal PDF, except for 10 being zero, and 0sbeing replaced by their respective decay widths [27]. The shape of the decay time distribution of the combinatorial background is determined with high mass sideband data. It is parametrized by the sum of two exponential functions multiplied by a second-order polynomial distribution. The exponential and polynomial parameters are allowed to vary in the fit and are constrained to be the same for the five decay modes. 6. Flavour tagging To determine the flavour of the B0 smeson at production, both opposite-side (OST) and sameside (SST) tagging algorithms are used. The OST exploits the fact that bquarks at the LHC are predominantly produced in quark–antiquark pairs. By partially reconstructing the second bhadron in the event, conclusions on the flavour at production of the signal B0 scandidate can be drawn. The OST has been optimized on large samples of B+→J/ψ K+, B →µ+D∗−X and B0→D−π+decays [24]. The SST takes advantage of the fact that the net strangeness of the pp collision is zero. Therefore, the squark needed for the hadronization of the B0 smeson must have been produced in association with an squark, which in about 50% of the cases hadronizes to form a charged kaon. 210sand 1msare measured in units with ¯ h=1 throughout this paper. New Journal of Physics 15 (2013) 053021 (http://www.njp.org/) 8 By identifying this kaon, the flavour at production of the signal B0 scandidate is determined. The optimization of the SST was performed on a data sample of B0 s→D− sπ+decays, which has a large overlap with the sample used in this analysis [25]. However, since the oscillation frequency is not correlated with the parameters describing tagging performance, this does not bias the 1ms measurement. The decisions given by both tagging algorithms have a probability ωto be incorrect. Each tagging algorithm provides an estimate for the mistag probability η; which is the output of a neural network combining various event properties. The true mistag probability ωcan be parametrized as a linear function of the estimate η[24,25]: ω=p0+p1×(η−hηi)(5) with hηibeing the mean of the distribution of η. This parametrization is chosen to minimize the correlations between p0and p1. The calibration is performed separately for the OST and SST. The sets of calibration parameters (p0,p1)OST and (p0,p1)SST are allowed to vary in the fit. The figure of merit of these tagging algorithms is called the effective tagging efficiency εeff. It gives the factor by which the statistical power of the sample is reduced due to imperfect tagging decisions. In this analysis, εeff is found to be (2.6±0.4)% for the OST and (1.2±0.3)% for the SST. Uncertainties are statistical only. 7. Measurement of 1m s Adding the information of the flavour tagging algorithms, the decay time PDF for tagged signal candidates is modified to Pt(t|σt)∝0se−0st1 2cosh 10s 2t+q[1−2ω(ηOST, ηSST)]cos(1mst)θ(t) ⊗G(t,Sσtσt)Et(t) , (6) where gives the fraction of candidates with a tagging decision. Signal candidates without a tagging decision are still described by equation (4) multiplied by an additional factor (1−) to ensure relative normalization. The information provided by the opposite-side and same-side taggers for the signal is combined to a single tagging decision qand a single mistag probability ω(ηOST,ηSST)using their respective calibration parameters p0OST/SST and p1OST/SST . The individual background components show different tagging characteristics for candidates tagged by the OST or SST. The bhadron backgrounds show the same opposite-side tagging behaviour (qand ω) as the signal, while the combinatorial background shows random tagging behaviour. For same-side tagged events, we assume random tagging behaviour for all background components. We introduce tagging asymmetry parameters to allow for different numbers of candidates being tagged as mixed or unmixed, and other parameters to describe the tagging efficiencies for these backgrounds. As expected, the fitted values of these asymmetry parameters are consistent with zero within uncertainties. All tagging parameters, as well as the value for 1ms, are constrained to be the same for the five decay modes. The result is 1ms=17.768 ±0.023 ps−1(statistical uncertainty only). The likelihood profile was examined and found to have a Gaussian shape up to nine standard deviations. The decay time distributions for candidates tagged as mixed or unmixed are shown in figure 2, together with the decay time projections of the PDF distributions resulting from the fit. 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