Measurement of the spectral function for the τ − → K − K S ν τ decay in BABAR experiment
SSciPost Physics Proceedings Submission
Measurement of the spectral function for the τ − → K − K S ν τ decay in BABAR experiment S. I. Serednyakov on behalf of the BABAR collaboration Novosibirsk State UniversityBudker Institute of Nuclear PhysicsNovosibirsk 630090 Russia* [email protected] 7, 2018
Proceedings for the 15th International Workshop on Tau Lepton Physics,Amsterdam, The Netherlands, 24-28 September 2018 scipost.org/SciPostPhysProc.Tau2018
Abstract
The decay τ − → K − K S ν τ has been studied using 430 × e + e − → τ + τ − eventsproduced at a center-of-mass energy around 10.6 GeV at the PEP-II collider andstudied with the BABAR detector. The mass spectrum of the K − K S systemhas been measured and the spectral function has been obtained. The measuredbranching fraction B ( τ − → K − K S ν τ ) = ( . ± . (stat . ) ± . . )) × − isfound to be in agreement with earlier measurements. The τ lepton provides a remarkable laboratory for studying many open questions in particlephysics. With a large statistics of about 10 τ s produced in e + e − annihilation at the BABARexperiment, various aspects can be studied, for example, improving the precision of spectralfunctions describing the mass distribution of the hadronic decays of the τ . In this work, weanalyze the τ − → K − K S ν τ decay and measure the spectral function of this channel definedas [1] V ( q ) = m τ πC ( q ) | V ud | B ( τ − → K − K S ν τ ) B ( τ − → e − ¯ ν e ν τ ) 1 N dNdq , (1)where m τ is the τ mass [2], q ≡ m K − K S is the invariant mass of the K − K S system, V ud is anelement of the CKM (Cabibbo-Kobayashi-Maskava) matrix [2], ( dN/dq ) /N is the normalized K − K S mass spectrum, and C ( q ) is the phase space correction factor given by the followingformula: C ( q ) = q ( m τ − q ) ( m τ + 2 q ) . (2)The branching fraction for the τ − → K − K S ν τ decay has been measured with relativelyhigh (3%) precision by the Belle experiment [3]. The K − K S mass spectrum was measured Throughout this paper, inclusion of charge-conjugated channels is implied. a r X i v : . [ h e p - e x ] D ec ciPost Physics Proceedings Submission m pp (GeV/c ) nu m b e r o f e v e n t s / ( M e V / c ) Figure 1: Schematic view of the τ decaychains in e + e − → τ + τ − events selected forthis analysis. Lepton l + can be electron ormuon. Figure 2: The π + π − mass spectrum for K S candidates in data (points with errors) andsignal simulation (histogram). Between thetwo vertical lines there is a signal region usedin the procedure of non- K S background sub-traction.by the CLEO experiment [4]. In the CLEO analysis, a data set of 2 . × produced τ pairswas used, and about 100 events in the decay channel τ − → K − K S ν τ were selected. In thiswork [5], using about ∼ τ leptons, we significantly improve upon the measurement of thespectral function for the τ − → K − K S ν τ decay. We analyze a data sample corresponding to an integrated luminosity of 468 fb − recorded withthe BABAR detector [6], [7] at the SLAC PEP-II asymmetric-energy e + e − collider. In thelaboratory frame, the energy of electron and positron beams is 9 and 3.1 GeV, respectively.For simulation of e + e − → τ + τ − events the KK2f Monte Carlo generator [8] is used, whichincludes higher-order radiative corrections to the Born-level process. Decays of τ leptons aresimulated using the Tauola package [9]. Two separate samples of simulated e + e − → τ + τ − events are used: a generic sample with τ decaying to all significant final states, and the signalchannel where τ + → l + ν l ¯ ν τ , l = e or µ and τ − → K − K S ν τ . To estimate backgrounds,we use a sample of simulated generic e + e − → τ + τ − events after excluding the signal decaychannel ( τ + τ − background) and a sample containing all events arising from e + e − → q ¯ q , q = u, d, s, c and e + e − → B ¯ B processes ( q ¯ q background). The q ¯ q background events with q = u, d, s, c are generated using the JETSET generator [10], while B ¯ B events are simulatedwith EVTGEN [11]. The detector response is simulated with GEANT4 [12]. The equivalentluminosity of the simulated sample is 2-3 times higher than the integrated luminosity in data.2 ciPost Physics Proceedings Submission We select e + e − → τ + τ − events with the τ + decaying leptonically ( τ + → l + ν l ¯ ν τ , l = e or µ )and the τ − decaying to K − K S ν τ . Such events referred to as signal events below. The K S candidate is detected in the K S → π + π − decay mode. The topology of events to be selectedis shown in Fig. 1. Unless otherwise stated, all quantities are measured in the laboratoryframe. The selected events must satisfy the following requirements:– The total number of charged tracks, N trk , must be four and the total charge of the eventmust be zero.– Among the four charged tracks there must be an identified lepton (electron or muon)and an identified kaon of opposite charge.– To reject non τ + τ − signal backgrounds, the lepton candidate must have a momentumabove 1.2 GeV/ c , the momentum in the center-of-mass frame (c.m. momentum) mustbe smaller than 4.5 GeV/ c , and the cosine of the lepton polar angle | cos θ l | must bebelow 0.9.– To suppress background from charged pions, the charged kaon candidate must have amomentum, p K , above 0.4 GeV/ c and below 5 GeV/ c , and the cosine of its polar anglemust lie between -0.7374 and 0.9005.– The two remaining tracks, assumed to be pions, form the K S candidate. The π + π − invariant mass must lie within 25 MeV/ c of the nominal K S mass, 497.6 MeV/ c .The K S flight length r K S , measured as the distance between the π + π − vertex and thecollision point, must be larger than 1 cm.– The total energy in neutral clusters, Σ E γ , must be less than 2 GeV. Here, a neutralcluster is defined as a local energy deposit in the calorimeter with energy above 20 MeVand no associated charged track.– The magnitude of the thrust [13, 14] for the event, calculated using charged tracks only,must be greater than 0.875.– The angle between the momentum of the lepton and the direction of the hadronic finalstate in the c.m. frame should be between 110 and 180 degrees.The chosen selection requirements are close to those used in previous τ studies in BABAR [15].As a result of applying these cuts the τ background is suppressed by 3.5 orders of magnitude,and the q ¯ q background by 5.5 orders. The detection efficiency obtained after applying the selection criteria is calculated using signalMonte Carlo simulation as a function of the true m K − K S mass. The efficiency is weaklydependent on m K − K S . The average efficiency over the mass spectrum is about 13%. Itshould be noted that the K − K S mass resolution is about 2-3 MeV/ c , significantly smaller3 ciPost Physics Proceedings Submission than the size of the mass bin (40 MeV/ c ) used in our analysis. Therefore, in the followingwe neglect the effects of the finite K − K S mass resolution.To correct for the imperfect simulation of the kaon identification requirement, the particleidentification PID efficiences have been compared for data and simulation on high puritycontrol samples of kaons from D (cid:63) + → π + D , D → K − π + decays [16]. We correct thesimulated efficiency using the measured ratios of the efficiencies measured in data and MonteCarlo, in bins of the kaon candidate momentum and polar angle. The resulting correctionfactor is small ∼
1% and weakly depends on m K − K S . K S background The π + π − mass spectra for K S candidates in data and simulated signal events are shown inFig. 2. The data spectrum consists of a peak at the K S mass and a flat background. Tosubtract the non- K S background, the following procedure is used. The signal region is setto π + π − masses within 0.0125 GeV/ c of the K S mass (indicated by arrows in Fig. 2), andthe sidebands are set to between 0.0125 and 0.0250 GeV/ c away from the nominal K S mass.Let β be the fraction of events with a true K S that fall in the sidebands, and let α be thefraction of non- K S events that fall in the sidebands. The total number of events in the signalregion plus the sidebands, N , and the number of events in the sidebands, N sb , depend on thenumber of true K S , N K S , and the number of non- K S background events, N b according to thefollowing relation : N = N K S + N b , (3a) N sb = α · N b + β · N K S (3b)Therefore: N K S = ( αN − N sb ) / ( α − β ) . (4)The value of β is determined using τ signal simulation. It is found to be nearly independentof the m K − K S mass and is equal to 0.0315 ± α is expected to be 0.5 fora uniformly distributed background. This is consistent with the value 0.499 ± τ + τ − background events. The non- K S background is subtracted in each m K − K S bin. Its fraction is found to be about 10% of the selected events with m K − K S near and below1.3 GeV/ c and increases up to 50% above 1.6 GeV/ c . τ -background with a π Although the studied process τ − → K − K S ν τ is not supposed to contain a π in the finalstate, some events from background processes with a π pass the selection criteria. In thefollowing, we describe how the π background contribution is subtracted.According to the simulation, the number of signal and τ -background events are of thesame order of magnitude. The τ + τ − background consists of events with the decay τ − → K − K S π ν τ (79%), events with a misidentified kaon from decays τ − → π − K S ν τ (10%) and τ − → π − K S π ν τ (3%), and events with a misidentified lepton mainly from the decays τ + → ciPost Physics Proceedings Submission m KKS (GeV/c ) e τ s MCdatam
KKS (GeV/c ) nu m b e r o f e v e n t s / M e V / c Figure 3: The probabilities (cid:15) s and (cid:15) b usedin Eqs. (5a, 5b) as functions of the K − K S mass, measured on simulated events. Figure 4: Measured m K − K S spectra forsignal events in comparison with the MonteCarlo simulation. π + ¯ ν τ and τ + → π + π ¯ ν τ (7%). Thus, more than 80% of the background events contain a π in the final state. The hadronic mass spectra for τ decays with a π are not well known, sowe use the experimental data to subtract this background.The τ background without a π ( τ − → π − K S ν τ , τ + → π + ¯ ν τ ) and q ¯ q background aresimulating well. Therefore, this background is subtracted using Monte Carlo simulation.To subtract the π background, the selected events are divided into two classes, withoutand with a π candidate, which is defined as a pair of photons with an invariant mass in therange 100 −
160 MeV/ c .On the resulting sample, the numbers of signal ( N s ) and background τ + τ − events con-taining a π candidate ( N b ) are obtained in each m K − K S bin: N π = (1 − (cid:15) s ) N s + (1 − (cid:15) b ) N b , (5a) N π = (cid:15) s N s + (cid:15) b N b , (5b)where N π and N π are the numbers of selected data events with zero and at least one π candidate, and (cid:15) s ( (cid:15) b ) is the probability for signal (background) τ + τ − events to be found inevents with at least one π candidate calculated using Monte Carlo simulation. The values (cid:15) s and (cid:15) b for each bin in m K − K S are measured in Monte Carlo by counting how many signal andbackground event candidates contain a π candidate. Figure 3 shows the (cid:15) s and (cid:15) b measuredin Monte Carlo as a function of m K − K S . These efficiencies are corrected to take into accountthe difference between data and Monte Carlo.With these corrected values for (cid:15) s and (cid:15) b we solve Eqs. (5a, 5b) for each K − K S mass binand obtain mass spectra for signal ( N s ) and background ( N b ). The efficiency corrected signalmass spectrum is shown in Fig. 4 in comparison with the simulation. We find a substantialdifference between data and simulation for the signal spectrum. The result is not affected byinaccuracies of the simulation since it doesn’t depend on the normalization of the simulated m K − K S spectrum. 5 ciPost Physics Proceedings Submission CLEOBaBarm
KKS (GeV/c ) / N d N / dq • m KKS (GeV/c ) V • Figure 5: Normalized K − K S invariantmass spectrum for the τ − → K − K S ν τ decaymeasured in this work (filled circles) com-pared to the CLEO measurement [4] (emptysquares). Only statistical uncertainties areshown. Figure 6: Measured spectral function forthe τ − → K − K S ν τ decay. Only statisticaluncertainties are shown. The uncertainty from non- K S background subtraction (0.4%) is estimated by varying thecoefficients of α and β within their uncertainties. This uncertainty is independent on the K − K S mass. The PID correction uncertainty due to data-Monte Carlo simulation differencein particle identification is taken to be 0.5%, independent of the K − K S mass. The uncertaintyon how well the Monte Carlo simulates the tracking efficiency is estimated to be 1%. We takethe observed difference between data and Monte Carlo near the end point M K − K S = m τ asan uncertainty on the q ¯ q background. This leads to an uncertainty on B ( τ − → K − K S ν τ ) of0.5%. The uncertainty associated with the subtraction of the τ + τ − background with π s isestimated to be 2.3%.The systematic uncertainties from different sources are combined in quadrature. The totalsystematic uncertainty for the branching fraction B ( τ − → K − K S ν τ ) is 2.7%. The systematicuncertainties for the mass spectrum are listed in Table 1. They gradually decrease from (cid:39) m K − K S = 1 GeV/ c to 1.5% at m K − K S = m τ . Near the maximum of the mass spectrum(1.3 GeV/ c ) the uncertainty is about 2.5%. 6 ciPost Physics Proceedings Submission Table 1: Measured spectral function (V) of the τ − → K − K S ν τ decay, in bins of m K − K S . The columns report: the range of thebins, the normalized number of events, the value of the spectralfunction. The first error is statistical, the second systematic. m K − K S (GeV/c ) N s /N tot × V × . − .
02 5 . ± . . ± . ± . . − .
06 26 . ± . . ± . ± . . − .
10 46 . ± . . ± . ± . . − .
14 70 . ± . . ± . ± . . − .
18 84 . ± . . ± . ± . . − .
22 92 . ± . . ± . ± . . − .
26 98 . ± . . ± . ± . . − .
30 98 . ± . . ± . ± . . − .
34 96 . ± . . ± . ± . . − .
38 90 . ± . . ± . ± . . − .
42 87 . ± . . ± . ± . . − .
46 65 . ± . . ± . ± . . − .
50 57 . ± . . ± . ± . . − .
54 38 . ± . . ± . ± . . − .
66 36 . ± . . ± . ± . . − .
78 6 . ± . . ± . ± . The branching ratio of the τ − → K − K S ν τ decay is obtained using the following expression: B ( τ − → K − K S ν τ ) = N exp LB lep σ ττ =(0 . ± . ± . × − , (6)where N exp = 223741 ± L = 468 . ± . − is the BABAR integrated luminosity [20], σ ττ =0 . ± .
003 nb is the e + e − → τ + τ − cross section at 10.58 GeV [8] and B lep =0.3521 ± τ lepton [2]. Thefirst uncertainty in (6) is the statistical, the second is systematic. Our result agrees well withthe Particle Data Group (PDG) value (0 . ± . × − [2], which is determined mainlyby the recent Belle measurement (0 . ± . ± . × − [3].The measured mass spectrum m K − K S for the τ − → K − K S ν τ decay is shown in Fig. 5 andlisted in Table 1. Our m K − K S spectrum is compared with the CLEO measurement [4]. TheBABAR and CLEO spectra are in good agreement. The spectral function V ( q ) calculatedusing Eq. (1) is shown in Fig. 6 and listed in Table 1. Due to the large error in the massinterval 1.66-1.78 GeV/c , which exceeds the scale of Fig. 6, the value of V ( q ) in this intervalis not shown in Fig. 6. 7 ciPost Physics Proceedings Submission The K − K S mass spectrum and vector spectral function in the τ − → K − K S ν τ decay havebeen measured by the BABAR experiment. The measured K − K S mass spectrum is far moreprecise than CLEO measurement [4] and the branching fraction (0 . ± . ± . × − is comparable to Belle’s measurement [3]. ACKNOWLEDGMENTS
The author of this talk is grateful to V. Druzhinin and A. Lusiani for useful discussions. Thiswork in part of data analysis is supported by the Russian Foundation for Basic Researches(grant No. 16-02-00327).
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