Due to the possibility to produce $B^0$, $B_s^0$ and $\lambda_b$ hadrons in the proton-proton collisions at the LHC, the mass peaks of many two-body $B$ decays overlap. For this reason, the particle identification capabilities of the LHCb detector will play a crucial role in the measurements related to these decay modes. In this document we propose a method for combining different observables provided by the LHCb particle identification system into a single generalized discriminating variable, useful when performing the statistical separation of the various channels in event-by-event fits

Carbone, A

Perazzini, S

Vagnoni, V

CERN Document Server

LHCb-PUB-2009-03213/01/2010LHCb-PUB-2009-032January 13, 2010Particle identification for charmlesstwo-body B decays at LHCbA. Carbone, S. Perazzini, V. Vagnoni.Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, ItalyAbstractDue to the possibility to produce B0, B0s and Λb hadrons in the proton-protoncollisions at the LHC, the mass peaks of many two-body B decays overlap. Forthis reason, the particle identification capabilities of the LHCb detector will play acrucial role in the measurements related to these decay modes. In this document wepropose a method for combining different observables provided by the LHCb particleidentification system into a single generalized discriminating variable, useful whenperforming the statistical separation of the various channels in event-by-event fits.1 IntroductionThe large beauty production cross section σbb¯ ' 500 µb expected at the LHC [1] will allowthe LHCb detector [2] to reconstruct some 105 Hb → h+h′− events per year, where h andh′ stand for a pion, kaon or proton. Due to the production of B0, B0s and Λb hadrons inthe 14 TeV proton-proton collisions, the mass peaks of many two-body B decays overlap(see Fig. 1) and an excellent control of the particle identification (PID) observables isrequired in order to isolate the various decay modes.PID at LHCb is based on the information provided by the RICH system [3], theelectromagnetic and hadronic calorimeters [4], including pre-shower and scintillator paddetectors, and the muon chambers [5]. The variable used to discriminate between differentparticle hypotheses is ∆ logLAB, that for each track is defined as:∆ logLAB = logLA − logLB, (1)where LA and LB are the likelihoods for particle hypotheses A and B, respectively.For each track, the PID system gives an answer in terms of the four observables∆ logLepi, ∆ logLµpi, ∆ logLKpi and ∆ logLppi. In the studies presented in this document,we only consider the two observables ∆ logLKpi and ∆ logLppi. These observables aresufficient to discriminate particles coming from all the Hb → h+h′− decays, since signaldecays contain neither electrons nor muons.The ∆ logLKpi and ∆ logLppi distributions for true pions, kaons and protons from asample of oﬄine selected Hb → h+h′− events, including all the different decay modes, areshown in Fig. 2. The oﬄine event selection is described in Ref. [6].2 Combining ∆ logLKpi and ∆ logLppiAs is apparent from Fig. 3, the ∆ logLKpi and ∆ logLppi variables are strongly corre-lated. Hence the employment of such observables in order to discriminate between thevarious mass hypotheses in event-by-event fits would require the use of 2-dimensionaljoint probability density functions (p.d.f.’s) of ∆ logLKpi and ∆ logLppi, properly takinginto account the correlation between the two. Although this is formally simple to state,it would considerably complicate the calibration of such distributions from data, since itwould require a two-dimensional analysis. We propose instead to merge the informationof the ∆ logLKpi and ∆ logLppi observables into a single observable ∆, defined below.The exponentiation of the ∆ logLhpi gives by definition the ratio of the likelihoods Lhand Lpi, i.e.: LKLpi = e∆logLKpi (2)and LpLpi = e∆ logLppi . (3)1]2 [GeV/cpipiM5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8Counts0100020003000400050006000700080009000−pi +pi → 0B−pi + K→ 0B− K+ K→ s0B− K+pi → s0B− p K→ bΛ−pi p → bΛ]2 [GeV/cpipiM5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8Counts10210310410 −pi +pi → 0B−pi + K→ 0B− K+ K→ s0B− K+pi → s0B− p K→ bΛ−pi p → bΛFigure 1: Invariant mass distribution, under the pi+pi− hypothesis, for all the decay modesafter the oﬄine event selection: linear scale (top) and logarithmic scale (bottom). Thehistograms of the various channels are cumulatively added up to form the overall massline shape. Background events are not included. See Ref. [6] for details on the eventselection procedure.2dllK_truePipiKlogL∆-150 -100 -50 0 50 100 150Events / ( 3 )01000200030004000500060007000dllK_truePidllp_truePiEntries  42958Mean    -38.9RMS     26.88piplogL∆-150 -100 -50 0 50 100 150Events / ( 3 )05001000150020002500dllp_truePidllK_trueKpiKlogL∆-150 -100 -50 0 50 100 150Events / ( 3 )01000200030004000500060007000dllK_trueKdllp_trueKpiplogL∆-150 -100 -50 0 50 100 150Events / ( 3 )0500100015002000250030003500dllp_trueKdllK_truePpiKlogL∆-150 -100 -50 0 50 100 150Events / ( 3 )050010001500200025003000dllK_truePdllp_truePpiplogL∆-150 -100 -50 0 50 100 150Events / ( 3 )02004006008001000dllp_truePFigure 2: Distributions of ∆ logLKpi (left) and ∆ logLppi (right) for pions (top), kaons(middle) and protons (bottom) from a sample of oﬄine selected Hb → h+h′− eventsincluding all the different decay modes.One can then define the confidence level for a given particle to be a pion, kaon or proton,respectively, as:Ppi =LpiLpi + LK + Lp =11 + e∆ logLKpi + e∆ logLppi, (4)PK =LKLpi + LK + Lp =e∆logLKpi1 + e∆logLKpi + e∆logLppi(5)3∆logLppi∆logL Kpi-140-120-100-80-60-40-2002040-140 -120 -100 -80 -60 -40 -20 0 20 40∆logLppi∆logL Kpi-40-20020406080100120-100 -80 -60 -40 -20 0 20 40 60 80∆logLppi∆logL Kpi-20-10010203040-20 0 20 40 60 80 100Figure 3: Distributions of ∆ logLKpi versus ∆ logLppi for pions (top left), kaons (top right)and protons (bottom) from a sample of oﬄine selected Hb → h+h′− events including allthe different decay modes.andPp =LpLpi + LK + Lp =e∆ logLppi1 + e∆ logLKpi + e∆ logLppi. (6)The three confidence levels are not independent, since by construction their sum is iden-tically equal to 1. The distributions of Ppi, PK and Pp for pions, kaons and protons fromoﬄine selected Hb → h+h′− decays are shown in Fig. 4. As expected, the distributionsare peaked at 1 when the corresponding mass hypothesis is correct, while they are peakedat 0 otherwise.4PpiArbitrary units10 310 410 50 0.2 0.4 0.6 0.8 1PKArbitrary units10 210 310 410 50 0.2 0.4 0.6 0.8 1PpArbitrary units10 210 310 410 50 0.2 0.4 0.6 0.8 1PpiArbitrary units10 210 310 410 50 0.2 0.4 0.6 0.8 1PKArbitrary units10 310 410 50 0.2 0.4 0.6 0.8 1PpArbitrary units10 210 310 410 50 0.2 0.4 0.6 0.8 1PpiArbitrary units11010 210 310 40 0.2 0.4 0.6 0.8 1PKArbitrary units11010 210 310 40 0.2 0.4 0.6 0.8 1PpArbitrary units1010 210 310 40 0.2 0.4 0.6 0.8 1Figure 4: Distributions of Ppi, PK and Pp for pions (top), kaons (middle) and protons(bottom) from a sample of oﬄine selected Hb → h+h′− events including all the differentdecay modes.We can now define a generalized PID discriminating variable ∆ as follows:∆ = 2− Ppi + Pp, (7)which by construction lies between 1 and 3. As it is apparent in Fig. 5, the distributionof ∆ is peaked at 1 for true pions, at 2 for true kaons, and at 3 for true protons.In order to characterize the ∆ observable, Fig. 6 shows the efficiencies and misidenti-fication probabilities achievable by cutting on ∆, as a function of the cut value C∆. The5∆Arbitrary units10 210 310 410 51 1.25 1.5 1.75 2 2.25 2.5 2.75 3∆Arbitrary units10 210 310 410 51 1.25 1.5 1.75 2 2.25 2.5 2.75 3∆Arbitrary units11010 210 310 41 1.25 1.5 1.75 2 2.25 2.5 2.75 3Figure 5: Distributions of ∆ for pions (top left), kaons (top right) and protons (bottom)from a sample of oﬄine selected Hb → h+h′− events including all the different decaymodes.cut for true pions, kaons or protons has been defined differently in order to have the samerange in each of the three cases:• when calculating the efficiency for the identification of pions, the event is acceptedif (∆− 1) ≤ 2 · C∆ AND |∆− 2| > 0.05 AND (3−∆) > 0.05;• when calculating the efficiency for the identification of kaons, the event is acceptedif (∆− 1) > 0.05 AND |∆− 2| ≤ C∆ AND (3−∆) > 0.05;6C∆Efficiency or Misid. probability00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1C∆Efficiency or Misid. probability00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1C∆Efficiency or Misid. probability00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Figure 6: Efficiency and misidentification probabilities as functions of the cut value C∆ forpions (top left), kaons (top right) and protons (bottom) from a sample of oﬄine selectedHb → h+h′− events including all the different decay modes. As a reference, the dottedlines indicate the points where the efficiency reaches 80% and 90%.• when calculating the efficiency for the identification of protons, the event is acceptedif (∆− 1) > 0.05 AND |∆− 2| > 0.05 AND (3−∆) ≤ 2 · C∆.With these definitions, C∆ always lies in the range between 0 and 1, with C∆ = 0 corre-sponding to the minimum efficiency and C∆ = 1 to the maximum efficiency. We emphasizethat the efficiencies are calculated for samples which span a significant range in momentumfor the particles in question, from a few GeV/c up to more than 100 GeV/c.73 ConclusionsWe have derived a method to combine different correlated ∆ logL variables coming fromthe PID system of the LHCb detector into a single variable, so-called ∆. Such a reductionof the dimensionality of the PID parameter space simplifies in a considerable way theemployment of the PID information in maximum likelihood fits including all the two-body B decay modes, as discussed in Ref. [6].8References[1] P. Nason et al., arXiv:hep-ph/0003142.[2] A. A. Alves et al. [LHCb Collaboration], JINST 3 (2008) S08005.[3] [LHCb Collaboration], CERN-LHCC-2000-037.[4] [LHCb Collaboration], CERN-LHCC-2000-036.[5] [LHCb Collaboration], CERN-LHCC-2001-029, CERN-LHCC-2003-002, CERN-LHCC-2005-012.[6] B. Adeva et al. [LHCb Collaboration], LHCb-PUB-2009-029 [arXiv:0912.4179].9

Particle identification for charmless two-body B decays at LHCb

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