Measurement of CP Violation in B 0 s →J/ψϕ decays with the CMS detector
MMeasurement of CP Violation in B s → J / ψ φ decays with the CMS detector. Presented at the 8th International Workshop on the CKM Unitarity Triangle (CKM 2014),Vienna, Austria, September 8-12, 2014
Jacopo Pazzini on behalf of the CMS collaboration. Università di Padova, INFN sezione di Padova
Abstract.
The CP-violating weak phase φ s and the decay width difference ∆Γ s of B mesons are mea-sured by the CMS experiment at the LHC using a data sample of B → J/ ψ ( µµ ) φ ( KK ) decays. Theanalysed dataset corresponds to an integrated luminosity of about 20 fb − collected in pp collisionsat a centre-of-mass energy √ s = decays are used to extractthe values φ s and ∆Γ s by performing a time-dependent and flavour-tagged angular analysis of the µ + µ − K + K − final state. The weak phase is measured to be φ s = − ± ± mass eigenstates is ∆Γ s = ± ± − . Neutral B mesons are subject to mixing, i.e., oscil-lations from particle to antiparticle through flavourchanging neutral currents quark transition thatchange the meson flavour by two units, ∆ B = mixing is characterized by the mass differ-ence ∆ m s and by the decay width difference ∆Γ s be-tween the heavy (B H ) and light (B L ) mass eigen-states. A CP-violating phase φ s arise from the in-terference between direct B meson decays into ab → c¯cs CP eigenstate, and decays mediated by mix-ing to the same final state. The two correspond-ing phases φ D s and φ M s depend on the conventionof the CKM matrix parameterization. However,the difference φ s is phase-independent, and neglect-ing penguin diagram contributions, it is related tothe elements of the CKM matrix, as: φ s (cid:39) − β s ,where β s = arg ( − V ts V ∗ tb / V cs V ∗ cb ) . A value of φ s (cid:39) β s = + − rad, is predicted by the stan-dard model (SM), determined via a global fit to ex-perimental data [1]. Since the value is small andprecisely predicted, any deviation of the measuredvalue would be particularly interesting as a possiblehint of physics beyond the SM, contributing in theB mixing. The decay width difference ∆Γ s is pre-dicted to be non-zero in the SM, and the theoreticalprediction, assuming no new physics in B mixing,is ∆Γ s = ± − [2]. In this measure-ment the B → J/ ψ ( µµ ) φ ( KK ) decay channel hasa non-definite CP final state, and an angular anal-ysis is therefore applied to disentangle the CP-oddand CP-even components. A time-dependent angu-lar analysis is performed with the CMS detector [3] by measuring the decay angles of the final state par-ticles µ + µ − K + K − , and the proper decay length ofthe B . In this measurement the transversity basisis used [4]. The angles θ T and ϕ T are the polar andazimuthal angles of the µ + in the rest frame of theJ/ ψ , respectively, where the x axis is defined by thedirection of the φ ( ) meson in the J/ ψ rest frame,and the x - y plane is defined by the decay plane of the φ ( ) → K + K − . The helicity angle ψ T is the angleof the K + in the φ ( ) rest frame with respect tothe negative J/ ψ momentum direction. The differen-tial decay rate of the B → J/ ψ φ in terms of properdecay length and angular variables is represented ac-cording to Ref. [5], as: d Γ ( B ) d Θ dct = f ( Θ , α , ct ) ∝ ∑ i = O i ( α , ct ) · g i ( Θ ) , (1)where O i are the time-dependent functions, g i arethe angular functions, Θ represents the angles, and ct represents the proper decay length of the B me-son. A detailed description of the signal model canbe found in Ref. [6]. The analized events are selected with a trigger op-timized for the detection of b-hadrons decaying toJ/ ψ ( µ + µ − ) , with a dimuon invariant mass withinthe range [ − ] GeV, and transverse momen-tum ( p T ) greater than 6.9 GeV. The muon trajectoriesare fit to a common decay vertex, and the transversedecay length significance L xy / σ L xy is required to begreater than three, where L xy is the distance between a r X i v : . [ h e p - e x ] J a n he primary and secondary vertex in the transverseplane, and σ L xy is its uncertainty. The vertex fit prob-ability is required to be larger than 15%. Offline se-lection criteria requires the J/ ψ to be reconstructedusing muons with a transverse momentum greaterthan 4 GeV. The dimuon invariant mass is requiredto lie within 150 MeV from the world-average J/ ψ mass value [7]. Candidate φ ( ) mesons are re-constructed from pairs of oppositely charged trackswith p T > ψ . Each selected trackis assumed to be a kaon and the invariant mass thecandidate φ ( ) is required to be within 10 MeVof the world average meson mass [7]. B candidatesare formed by combining a J/ ψ with a φ ( ) can-didate. The two muons and the two kaons are fittedwith a combined vertex and kinematic fit, with a con-straint of the dimuon invariant mass to be the nom-inal J/ ψ mass [7]. A B candidate is retained if theJ/ ψ φ pair has an invariant mass between 5.20 and5.65 GeV and the χ vertex fit probability is largerthan 2%. For each selected event the primary ver-tex which minimises the angle between the flight di-rection and the momentum of the B candidate isselected. For events with more than one B candi-date, the candidate with the highest vertex fit prob-ability is selected. Simulated events are producedusing the PYTHIA 6.4 Monte Carlo event generatorand EVTGEN simulation package. The generatedevents are then passed through a full CMS detec-tor simulation using the GEANT package. SimulatedB → J/ ψ φ samples, validated through comparisonwith the data, are used to determine the signal recon-struction efficiencies, and to estimate the backgroundcomponents in the signal mass window. The angularefficiency correction (cid:101) ( Θ ) is obtained from simula-tions with a three-dimensional function of the angu-lar variables in order to take into account the corre-lation between the angular observables. The properdecay length, ct , is required to be larger than 200 µ min order to avoid a lifetime bias due to the turn-on curve of the trigger efficiency. The main back-ground for the B → J/ ψ φ decays originates fromnon-prompt J/ ψ arising from the decay of b-hadrons,such as B , B + and Λ b . The B c cross section is ex-pected to be very small and therefore B c decays arenot considered. The Λ b contribution to the selectedevents is also found to be very small and the massdistribution in the selected mass range is observed tobe flat. The mass distribution of the signal region isshown in Fig. 1. A flavour tagging algorithm is used to identify of theflavour of the B meson at production time, improv-ing the sensitivity on φ s phase. The flavour of the B KK invariant mass [GeV] ψ J/5.25 5.3 5.35 5.4 5.45 E v en t s / ( . G e V ) -1 =8 TeV L=20 fbs CMS Preliminary
DataTotal fitSignal fitBackground fit
Figure 1.
The mass distribution of the J/ ψ KK candidates.The full line is a fit to the data (solid markers), the dashedgreen line is the fitted signal and the dashed red line is thefitted background. is inferred on a statistical basis using the propertiesof the decay products of the opposite side B hadron,assuming the b ¯b production process occurred. Thetagging tool provides the inferred flavour of the B meson and the value of the mistag fraction ω , whichrepresents the fraction of incorrectly tagged events.The tagging efficiency ε tag and the mistag fraction ω are related to the effective tagging efficiency or tag-ging power, P tag = ε tag ( − ω ) . In the presentanalysis an opposite-side lepton ( µ , e ) tagger is used.For each event the lepton with the highest p T in theevent is selected. If no lepton information has beenretrieved the tag information is set to zero. The taglepton selection is optimized, using B simulations,so that the power of tagging P tag is maximized sepa-rately for electrons and muons. The flavour taggingis measured from data using the self-tagging chan-nel B + → J/ ψ K + . The B + signal is selected withcuts as similar as possible to those applied to the sig-nal sample. The tagging performance of simulatedB + and B events is compared with the B + data andfound to be consistent. In order to increase the sen-sitivity on φ s , the mistag fraction ω is binned andparametrized as a function of the transverse momen-tum of the lepton, as shown in Fig. 2. If multiple tagleptons are found in the event, the tagger with thelowest mistag is selected. The mistag fraction is as-signed to all the tagged events using the parametri-sations obtained for electrons and muons in B + data.The combined tagging performances evaluated ondata are ω = ( ± ) %, ε tag = ( ± ) %and P tag = ( ± ) %, where the reported un-certainties are statistical only. [GeV] T Tag muon p w W r ong t ag f r a c t i on CMS Preliminary = 8 TeVs -1 L = 20 fb simulation s B fit simulation + B fit data + B fit [GeV] T Tag electron p w W r ong t ag f r a c t i on CMS Preliminary = 8 TeVs -1 L = 20 fb simulation s B fit simulation + B fit data + B fit
Figure 2.
The mistag fraction ω as a function of the lep-ton transverse momentum for muons (top) and electrons(bottom). The points obtained from B simulation (red),B + simulation (blue) and B + data (black) are shown. Thecontinous lines describe are the relative parametrisations. An unbinned maximum likelihood fit to the data isperformed by including information on the invariantmass ( m ), proper decay length ( ct ), the three decayangles ( Θ ) of the reconstructed B candidates, andthe proper decay length uncertainty ( σ ct ) obtainedpropagating the uncertainties of the proper decaylength measurement. From this multi-dimensionalfit, the parameters of interest ∆Γ s , φ s , the B meanlifetime c τ , | A ⊥ | , | A | , | A S | , and the strong phases δ (cid:107) , δ ⊥ and δ S ⊥ are determined. The event likelihoodfunction L can be represented as described in Eq. 3,where L sig is the PDF that describes the B → J/ ψ φ signal model and L bkg describes the background con-tributions. L = L sig + L bkg (2) L sig = N S · (cid:0) ˜ f ( Θ , α , ct ) ⊗ G ( ct , σ ct ) · (cid:101) ( Θ ) (cid:1) · P S ( m B ) · P S ( σ ct ) · P S ( ξ ) L bkg = N BG · P BG ( cos θ T , ϕ T ) · P BG ( cos ψ T ) · P BG ( ct ) · P BG ( m B ) · P BG ( σ ct ) · P BG ( ξ ) The PDF ˜ f ( Θ , α , ct ) is the differential decay rate func-tion defined in Eq. 1 modified to include the flavourtagging information and the dilution term ( − ω ) .In the model ˜ f the longitudinal phase δ is set tozero, and the difference of phases δ S − δ ⊥ is fittedwith a unique variable δ S ⊥ to reduce the correlationamong the fitted parameters. Here (cid:101) ( Θ ) is the an-gular efficiency function and G is a Gaussian reso-lution function, which makes use of the event-by-event proper decay length uncertainty σ ct scaled bya factor κ , which is a function of ct . The κ factor isa scale factor introduced to correct the proper de-cay length uncertainty in order to resemble the ac-tual resolution. It is measured in simulated samplesassuming that the κ factor is the same as in data.For this assumption a systematic uncertainty is eval-uated. All the parameters of the PDFs are left free tofloat in the final fit, unless explicitly stated otherwise.The signal mass PDF P S ( m B ) is given by the sumof three Gaussian functions with a common mean;the two smaller widths, the mean and the fractionof the Gaussians are fixed to the values obtained ina one-dimensional mass fit. The background massdistribution P BG ( m B ) is described by an exponen-tial function. The background proper decay lengthcomponent P BG ( ct ) is described by the sum of twoexponential functions. The angular part of the back-ground PDFs, P BG ( cos θ T , ϕ T ) and P BG ( cos ψ T ) , aredescribed analytically by a series of Legendre poly-nomials for cos θ T and cos ψ T and sinusoidal func-tions used for the angle ϕ T . For the cos θ T and ϕ T variables a two-dimensional PDF is used to take intoaccount the correlation among the variables. Theproper decay length uncertainty signal PDF P S ( σ ct ) isa sum of two Gamma functions, where all the param-eters are fixed to the values obtained fitting a sampleof background-subtracted events. The proper decaylength uncertainty background PDF P BG ( σ ct ) is rep-resented by a single Gamma function, where all theparameters are fixed to the values obtained fitting themass peak sideband events. The P S ( ξ ) and P BG ( ξ ) are the flavour tag decision ξ PDFs which have beenobtained from the data sample.
The fit is applied to the sample of 70 000 events(49 000 signal candidates and 21 000 backgroundevents), selected in the mass range [ − ] GeVand proper decay length range [ − ] µ m. The ∆ m s has been constrained in the fit to the currentworld average value ( ± ) × ¯ h /s [7] bytaking a Gaussian distribution centred on the worldaverage with the uncertainty as the width. No directCP violation is assumed for this measurement, andtherefore | λ | is set to one, consistent with the results s ct (cm)0.05 0.1 0.15 0.2 0.25 0.3 E v en t s / ( . c m ) -1 =8 TeV L=20 fbs CMS Preliminary
DataTotal fitSignal fitBackground fit proper decay length [cm] s B0.05 0.1 0.15 0.2 0.25 0.3 pu ll -4-2024 Proper decay length uncertainty [cm]1 2 3 4 5 6 7 8 9 10 -3 × E v en t s / ( . - c m ) -1 =8 TeV L=20 fbs CMS PreliminaryCMS Preliminary
DataTotal fitSignal fitBackground fit
Figure 3.
The proper decay length distribution (top) andthe proper decay length uncertainty (bottom) of the B can-didates. The full line is a fit to the data (solid markers), thedashed green line is the fitted signal and the dashed redline is the fitted background. For the proper decay lengthdistribution the pull between the histogram and the fittedfunction is displayed in the histogram below. in Ref. [8]. The ∆Γ s is constrained to be positive as inRef. [9]. The observable distributions and the fit pro-jections are shown in Figs. 1, 3, and 4. The 68%, 90%and 95% Confidence Level (C.L.) likelihood contoursof the fit for φ s and ∆Γ s are shown in Fig. 5. The fitresults are presented in Table 1, where the uncertain-ties are statistical only. The systematic uncertainties are summarized in Ta-ble 2. The uncertainties of the φ s and ∆Γ s results aredominated by statistical uncertainties. The system-atic uncertainty associated with the hypothesis of aflat proper decay length efficiency is evaluated byfitting the data with the a proper decay length effi-ciency which takes into account a small contributionof the decay length significance cut at small ct and a T θ cos-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 E v en t s / ( . ) -1 =8 TeV L=20 fbs CMS Preliminary
DataTotal fitSignal fitBackground fit T ψ cos-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 E v en t s / ( . ) -1 =8 TeV L=20 fbs CMS Preliminary
DataTotal fitSignal fitBackground fit [rad] T ϕ -3 -2 -1 0 1 2 3 E v en t s / ( . r ad ) -1 =8 TeV L=20 fbs CMS Preliminary
DataTotal fitSignal fitBackground fit
Figure 4.
The angular distributions (cos θ T , cos ψ T , ϕ T ) ofthe B candidates. The full line is a fit to the data (solidmarkers), the dashed green line is the fitted signal, and thedashed red line is the fitted background. first order polynomial variations at high ct . The un-certainties associated with the variables of threedi-mensional angular efficiency function cos θ T , cos ψ T ,and ϕ T are propagated to the fit results by varyingthe corresponding parameters within their statisti-cal uncertainties and accounting for the covariancesamong the parameters. The systematic uncertaintydue to a small discrepancy in the kaon p T spectrumbetween the data and the simulations is evaluatedby reweighting the simulated kaon p T spectrum toagree with the data. The intrinsic biases of the fitmodel are taken into account as a systematic effect.The uncertainty in the proper decay length resolu-tion associated with the proper decay length uncer-tainty scale factor κ is propagated to the results. Sincethe κ ( ct ) factors are obtained from simulation, theassociated systematic uncertainty is assessed by us-ing a sample of prompt J/ ψ decays obtained withan unbiased trigger and comparing them to simi-larly processed simulated data. The likelihood doesParameter Fit result | A | ± | A S | ± | A ⊥ | ± δ (cid:107) [ rad ] ± δ S ⊥ [ rad ] ± δ ⊥ [ rad ] ± c τ [ µ m ] ± ∆Γ s [ ps − ] ± φ s [ rad ] -0.03 ± Table 1.
Results of the fit to the 2012 data. Only thestatistical uncertainties are shown. ource of uncertainty | A | | A S | | A ⊥ | ∆Γ s [ ps − ] δ (cid:107) [ rad ] δ S ⊥ [ rad ] δ ⊥ [ rad ] φ s [ rad ] c τ [ µ m ] Statistical uncertainty 0.0058 0.016 0.0077 0.0138 0.092 0.24 0.36 0.109 3.0Angular efficiency 0.0060 0.008 0.0104 0.0021 0.674 0.14 0.66 0.016 0.8 | λ | as a free parameter 0.0001 0.005 0.0001 0.0003 0.002 0.01 0.03 0.015 -Model bias 0.0008 - - 0.0012 0.025 0.03 - 0.015 0.4Kaon p T re-weighting 0.0094 0.020 0.0041 0.0015 0.085 0.11 0.02 0.014 1.1Proper decay length resolution 0.0009 - 0.0008 0.0021 0.004 - 0.02 0.006 2.9PDF modelling assumptions 0.0016 0.002 0.0021 0.0021 0.010 0.03 0.04 0.006 0.2Flavour tagging - - - - - - 0.02 0.005 -Background mistag modelling 0.0021 - 0.0013 0.0018 0.074 1.10 0.02 0.002 0.7Proper decay length efficiency 0.0015 - 0.0023 0.0057 - - - 0.002 1.0Total systematics 0.0116 0.022 0.0117 0.0073 0.684 1.12 0.66 0.032 3.5 Table 2.
Summary of the uncertainties. If no value is reported, then the systematic uncertainty is negligible with respectto the statistical and other systematic uncertainties. The total systematic uncertainty is the square root of sum of squaresof the listed systematic uncertainties. [rad] s f -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 ] - [ p s s GD CMS
CMS Preliminary -1 =8 TeV L=20 fbs 68% C.L.90% C.L.95% C.L.Standard Model Figure 5.
The 68%, 90% and 95% C.L. contours in the ∆Γ s versus φ s plane, together with the SM fit prediction. Un-certainties are statistical only. not contain a PDF model for the mistag distribution,therefore the systematic uncertainty arising from thissource is estimated. The systematic uncertainty dueto tagging is assessed by propagating the statisticaland systematic uncertainty of the ω parametrisationto the results. The various hypotheses that have beenassumed when building the likelihood function aretested by generating simulated pseudo-experimentswith different hypotheses in the generated samplesand fitting the samples with the nominal likelihoodfunction. Finally the | λ | = | λ | agrees with one within one standard de-viation. The differences found in the fit results with respect to the nominal fit are used as systematic un-certainties. Using the 2012 CMS data approximately 49000 B signal candidates were reconstructed and used to ac-curately measure the weak phase φ s and the decaywidth difference ∆Γ s . The analysis was performed byusing opposite-side lepton tagging of the B flavourat the production time. Both muon and the electrontags were used. The measured values for the weakphase and the decay width difference between the B mass eigenstates are: φ s = − ± ( stat. ) ± ( syst. ) rad (3) ∆Γ s = ± ( stat. ) ± ( syst. ) ps − (4)where the uncertainties of the φ s and ∆Γ s resultsare dominated by statistical uncertainties. The valueof φ s is in agreement with the previous measure-ments and with the SM fit prediction, and ∆Γ s is con-firmed to be non-zero. References [1] J. Charles et al., Phys. Rev. D
072 (2007)[3] R. Adolphi et al., JINST S08004 (2008)[4] A.S. Dighe et al., Eur. Phys. J. C
647 (1999)[5] A.S. Dighe et al., Phys. Lett. B
186 (2014)[9] R. Aaij et al., Phys. Rev. Lett.108