B+ Semileptonic Rare Decays in ATLASA. PolicicchioandG. CrosettiUniversity of Calabria and INFN Cosenza,Via P.Bucci, 87036 Arcavacata di Rende, Rende, ItalyWe discuss the latest studies on rare semileptonic decays of B+ mesonwith the ATLAS detector.1. IntroductionRare B-decays, produced by b→ s, d quark FCNC transitions, are ¡for-bidden at the tree level in the Standard Model (SM). These decays occurat the lowest order only through one-loop “penguin” and “box” diagrams.The branching ratios of these decays are very small and they vary between4×10−5 for rare radiative decay B0d → K∗γ down to 10−15 for rare Cabibbosuppressed leptonic decay B0d → e+e−.Rare B-decays careful investigation is mandatory for testing ground ofthe Standard Model and offer a complementary strategy in the search ofnew physics by probing the indirect effects of new interactions in higherorder processes. The probing of loop-induced couplings provide a means oftesting the detailed structure of the SM at the level of radiative corrections.In particular, FCNC involving b → s, d transitions, provide an excellentprobe of new indirect effects of New Physics by yielding informations on themasses and coupling of the virtual particles running in the loops and thisexplain the attention they have received in recent years. The study of suchdecays give also other opportunities: to measure the values of |Vts| and |Vtd|CKM matrix elements and to provide new informations on long-distanceQCD effects in matrix elements of the tensor current.In the last years the B-factories BaBar and Belle presented the firstresults for B → (K∗,K)l+l− branching ratios and forward-backward asym-metry (AFB) of these rare semileptonic decays ([1],[2],[3]). The experimental(1)ATL-PHYS-PUB-2007-01716 October 20072 B+ Semileptonic Rare Decays in ATLASbranching ratio values are consistent with SM predictions even if the statis-tical errors are very high. More precise measurements are also needed fordifferential dimuon invariant mass and forward-backward asymmetry distri-butions, in order to discriminate between SM and New Physics predictions.The interest in the rare short-distance FCNC contribution to the B →l+l−K decays demands that the mass of the dilepton system should notbe compatible with the mass of any hadronic source of dileptons, in par-ticular the J/ψ and the ψ(2S). This out of resonance requirements callfor a good mass resolution and thus a good momentum resolution of thetwo leptons. This cannot be fulfilled with electrons as the energy loss dueto Bremsstrahlung is too high. Moreover ATLAS trigger is favourable fordimuon channels, while it’s capacity for low PT dielectron channels is re-duced ([8]). Consequently we take into account only dimuon decays.In this report we will pay our attention to the semileptonic B+ →K+µ+µ− and B+ → K∗+ µ+µ− decays. We discuss the latest simulationresults at ATLAS detector.2. Theoretical DescriptionFrom the theoretical point of view, the b → q (q = s, d) transitions aredescribed using the effective HamiltonianHeff = −4GF√2VtbV∗tq10∑i=1Ci(µ)Oi(µ) (1)in the form of Wilson expansion (see e.g. [4]). The set of Wilson coef-ficients Ci(µ) depends on the current model and contains the lowest ordermodel contributions and perturbative QCD corrections. The scale param-eter µ is approximately equal to the mass of b-quark (∼ 5GeV ). Thisparameter separates the perturbative and nonperturbative contributions ofthe string interactions. The nonperturbative contribution is contained inthe matrix elements of basis operators Oi(µ) between the initial and finalhadronic states. For the calculation of these matrix elements it is necessaryto use different decay-specific nonperturbative methods: QCD Sum Rules,Heavy Quarks Effective Theory, Quark Models and Lattice calculations.The accuracy in nonperturbative calculations depends on a method, but itis not less than 15%. The accuracy of the Wilson coefficient for with NLOand NNLO QCD corrections ([5]) is not greater than 15% if µ parameterranges in [mb/2, 2mb].The branching ratios in SM of B+ → K+µ+µ− and B+ → K∗+ µ+µ−decays can be found in Table 1.B+ Semileptonic Rare Decays in ATLAS 3Decay channel Br. ratio Ref. Form Factors Wilson Coeff.B+ → K+µ+µ− 3.4× 10−7 [6] QCD LCSR NNLOB+ → K∗+ µ+µ− ∼ 10−6 [6] QCS LCSR NNLOTable 1. Branching ratios in SM of rare B+ decays with µ+µ− pair in final states.3. ATLAS Muon Trigger StrategyAt the start up, the target luminosity for the LHC will be 2×1033cm−2s−1,rising to the full design luminosity of 1034cm−2s−1 after few years of run-ning. There will be an average of 4.6 and 23 interactions per bunch crossingfor initial and design luminosity respectively. About 1% of collisions willproduce a bb¯ pair. The challenge for the trigger is to select those eventsof most interest for the ATLAS B-Physics program ([7]), within the lim-ited trigger and storage resources available. The ATLAS B-Physics trigger([8],[9],[10]) is based on a muon signature at the first level, which can beaccompanied by additional, lower transverse energy signature of leptons andjets. These signatures are refined in the higher trigger levels where specificdecays are reconstructed.For semileptonic dimuon decays, the trigger will be dominated by adimuon trigger. This is based on the detection of two muons found in thefirst trigger level with a transverse momentum (pT ) threshold of 6 GeVand 4 GeV respectively. At the second level, the muon pT measurementswill be confirmed in the muon precision chambers, the Tile Calorimeter andthen extrapolated to the Inner Detector in order to reject muons from pi/Kdecays. At the Event Filter level, oﬄine track quality reconstruction, vertexand mass cuts will be applied to select candidates for specific exclusive orsemi-inclusive decays such as J/Ψ → µ+µ− and B → µ+µ−(X). Thisstrategy can be used at low initial luminosity and also at nominal LHC1034cm−2s−1 luminosity.4. Signal Data SamplesThe data sample for the present studies have been produced in the frame-work of the DC3 production, using the final ATLAS detector layout, simu-lation based on Geant4 and new GRID-oriented software ([11], [12], [13]).The theoretical model for Monte Carlo generation of data samples isshown in Table 1. Pythia ([14]) and Evtgen ([15]) Monte Carlo softwarepackages have been used in the framework of ATLAS software for dataproduction.The vector meson K∗+, has been considered decaying into K0s + pi+4 B+ Semileptonic Rare Decays in ATLASwith K0s decaying into two charged pions. The resulting branching ratio forB+ → K∗+ µ+µ− decay with K∗+, decaying into K0s +pi+ and K0s decayinginto two charged pions is 4.4× 10−7.At the generation level, the first level trigger cuts have been applied onthe first and the second muon (pT > 6GeV and pT > 4GeV respectively).Also the Inner Detector acceptance cuts on pseudorapidity and on trans-verse momentum (|η| < 2.5 and pT > 0.5GeV ) have been applied on stablehadrons.Quantity Symbol ValueNominal luminosity L 1033 cm−2s−1Standard year t 107 sAnnual integrated luminosity L · t 10 fb−1bb¯ cross section σbb¯ 0.5 mbGeneration cut fraction T 0.01Probability of b¯→ B+ P 0.39Symmetry factor S 2BR(B → K+µ+µ−) BR1 0.34 × 10−6BR(B → K∗+µ+µ−, K∗+ → K0s + pi+,K0s → pi+pi−) BR2 0.44 × 10−6Table 2. Relevant assumption for the calculation of the signal yields.All numbers used to compute the signal yields are summarized in Table2. The standard year of running has been assumed 107 s at an averageluminosity of L = 1033 cm−2s−1 which corresponds to an integrated lumi-nosity of 10 fb−1. The bb¯ cross section is considered as an initial assumptionwhich will be revisited after the start of the LHC. The 0.5 mb value ([16]) is arenormalization constant and is thus not affected by errors. The hadroniza-tion fraction of the b-quark is taken from the PDG ([17]). The symmetryfactor takes into account the charge conjugate decays.The number of triggerable events expected in 3 years of LHC operationat L = 1033 cm−2s−1 (30 fb−1 integrated luminosity) has been found ∼40000 and ∼ 51000 for B → K+µ+µ− and B → K∗+µ+µ− respectively,and it has been calculated asNi = L · t · T · S · σbb¯ · P · BRi (2)Table 3 summarizes the number of simulated events and the number ofevents expected in 30 fb−1 integrated luminosity after cuts at the generationlevel for each decay channel.B+ Semileptonic Rare Decays in ATLAS 5Decay Triggerable events in 30 fb−1 Simulated eventsB → K+µ+µ− ∼40000 30000B → K∗+µ+µ− ∼51000 50000Table 3. Summary table for the B+ → K+µ+µ− and B+ → K∗+µ+µ− (followedby K∗+ → K0spi+,K0s→ pi+pi−) decays. From left, columns contain the decaychannel, the number of expected events after cuts at generation level in 30 fb−1and the number of simulated events.Below we introduce the basic results of the data analysis. A C++ codehas been written in the ATHENA framework for both the decay channels,in order to analyze the AOD reconstruction files ([18], [19]).5. Signal Reconstruction5.1. Selection StrategyThe key signature of B → µµK events is the presence of the oppositecharge muon pair. Due to long B lifetime, this dimuon pair is likely toform a secondary vertex which is detached from the primary vertex. Theidentification of this vertex, if particularly close to the interaction point,requires leptons which are well reconstructed.The event selection is done in the following order:• primary vertex reconstruction; if more than one primary vertex hasbeen reconstructed in the same event, only the one closer to the truevertex is taken into account.• muon and dimuon selection;• kaon reconstruction and selection;• B-meson reconstruction and selection.Thus the selection has to rely on topological variables as vertex qualityand vertex separation requirements. The vertex fitting routine used for thisanalysis is the CDF vertex fit routine ([20]).Common requirements for the two decay channels are explained in thefollowing:• The muon track candidates must fulfill the selection criteria of themuon identification MUID algorithm ([21]).6 B+ Semileptonic Rare Decays in ATLAS• The charged track selection for kaon reconstruction is done inside theInner Detector: the pT of the track must be above 0.5 GeV and thepseudorapidity |η| < 2.5. ATLAS cannot identify pions and kaons,therefore all charged particles in the Inner Detector, not identified asmuons or electrons, are taken into account.• Dimuons are formed by two opposite charge muon tracks satisfying theLVL1 trigger (pT (µ1) > 6 GeV , pT (µ2) > 4 GeV and |η(µ1, µ2)| < 2.5)request. They must fulfill the following requirements:- the dimuon vertex momentum must not point to primary vertex;- the dimuon vertex χ2/NDF must be lower than 10;- the dimuon invariant mass must be in the kinematic allowed win-dow: 2mµ < mµµ < mB+−mK+ and 2mµ < mµµ < mB+−mK∗+ respectively for the two decay channels.5.2. B+ → K+µ+µ−The B+ → K+µ+µ− decay is topologically very simple.After the dimuon selection, a positive charge particle is then searched inthe Inner Detector satisfying the charged track selection criteria. For eachfound dimuon, B+ candidates are formed using preselected positive chargetrack. The following final selection criteria are required for the B+ mesonreconstruction:• the B+ system must be made of one dimuon and one positive chargetrack;• the B+ vertex χ2/NDF must be lower than 5;• the B+ mass must be in a ±3σ window around PDG value;• the B+ proper time larger than 0.5 ps;• if more than one B+ has been reconstructed in the same event, onlythe one with better χ2/NDF is taken into account.The B+ mass and the B+ proper time resolution distributions of theseaccepted events (respectively without cut on B+ mass and proper time) areshown in Figure 1.The width of the Gaussian fit for the mass distribution is σ = 42 MeVand 80 fs for the proper time distribution. The B+ candidate requirementsare based on the knowledge of these value.B+ Semileptonic Rare Decays in ATLAS 7(MeV)+BM4800 5000 5200 5400 5600 5800 6000entries/20MeV02004006008001000mean 5279 MeV 42 MeVσ mass distribution+B(ps)+Bτ∆-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1entries/0.02ps0100200300400500600700mean 0 ps 0.08 psσ proper time resolution+BFig. 1. B+ mass and proper time resolution distributions: the mean value and thewidth of the distribution, resulting from a Gaussian fit, are shown.The most interesting distributions for the rare decay channel are thedimuon invariant mass spectrum and the forward-backward asymmetry (FBA).Experimentally this asymmetry is defined as ([22])AFB =NF [s1, s2]−NB [s1, s2]NF [s1, s2] +NB [s1, s2](3)where NF [s1, s2] and NB [s1, s2] are the number of positive muons (in-cluding the background ones) moving in the forward and backward direc-tions of the B-meson, respectively, in the range of the squared dimuon masss[s1, s2].These two distributions are shown in Figure 2 for true events and re-constructed events. The LVL1 trigger and the analysis cuts do not broughtsignificant changes.8 B+ Semileptonic Rare Decays in ATLAS2+B/M2-µ+µM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9FBA-0.4-0.3-0.2-0.1-00.10.20.30.4forward-backward asymmetry2+B/M2-µ+µM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1entries/0.0200.0050.010.0150.020.0250.030.035dimuon mass distributionFig. 2. B+ → K+µ+µ− differential FBA and normalized dimuon invariantmass distributions for true (triangles and solid line respectively) and reconstructed(squares and dotted line respectively) events. The horizontal bars in FBA differ-ential distribution represent the dimuon invariant mass bins and the vertical errorbars are the statistical errors on FBA.5.3. B+ → K∗+µ+µ−The B+ → K∗+µ+µ− (K∗+ → K0s +pi+, K0s → pi+pi−) decay requires amore complex analysis strategy with respect to the B+ → K+µ+µ− channeldue to the reconstruction of the two intermediate particles, K ∗+ and K0s .To reconstruct the K0s two opposite charge hadronic tracks are searchedin the Inner Detector to be passed at the vertex fit routine. The K 0s candi-dates have to fulfill the following requirements:• the K0s momentum have to point to the dimuon vertex;• the reconstructed K0s mass must be in a 3σ mass window around thePDG value;• the K0s vertex χ2/NDF lower than 10.B+ Semileptonic Rare Decays in ATLAS 9(MeV)s0KM300 350 400 450 500 550 600 650 700entries/5MeV02004006008001000mean 498 MeV 8.5 MeVσ mass distributions0K(MeV)*+KM800 820 840 860 880 900 920 940 960 980 1000entries/4MeV20406080100120140mean 892 MeV 26.5 MeVσ mass distribution*+KFig. 3. Mass distribution for K0sand K∗+ reconstruction: the mean value and thewidth of the distribution, resulting from a Gaussian fit, are shown.TheK0s mass distribution of events passing these selection criteria (with-out mass cut) is shown in Figure 3 (top). A Gaussian fit leads to a sigmaof 8.5 MeV .The K0s with a third positive charge track coming from dimuon ver-tex have to form the K∗+. The K∗+ candidates must fulfill the followingrequirements:• the K∗+ vertex χ2/NDF lower than 5;• the reconstructed K∗+ mass must be in a 3σ mass window around thePDG value.The K∗+ mass distribution of events passing these selection criteria10 B+ Semileptonic Rare Decays in ATLAS2+B/M2-µ+µM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7FBA-0.4-0.3-0.2-0.1-00.10.20.30.4forward-backward asymmetry2+B/M2-µ+µM0 0.1 0.2 0.3 0.4 0.5 0.6 0.7entries/0.02-310-210-110dimuon mass distributionFig. 4. B+ → K∗+µ+µ− normalized dimuon invariant mass and differentialFBA distributions for true (triangles and solid line respectively) and reconstructed(squares and dotted line respectively) events. The horizontal bars in FBA differ-ential distribution represent the dimuon invariant mass bins and the vertical errorbars are the statistical errors on FBA.(without mass cut) is shown in Figure 3 (bottom). A Gaussian fit leadsto a sigma of 26.5 MeV .For every dimuon, B candidates are formed using preselected kaons. Thefinal selection criteria required for B+ are the same as those in Subsection5.2. For this decay the B+ mass sigma has been found to be 44 MeV .The dimuon invariant mass and the FBA distributions are shown inFigure 4 both for true data and reconstructed ones. The LVL1 trigger andthe reconstruction analysis cuts do not change these two distributions.6. Background SourcesAll events containing two muons are a potential source of backgroundfor rare dimuonic beauty decays. Of course, the most dangerous are muonsoriginating from B-decays, as they have the same pT and the same impactB+ Semileptonic Rare Decays in ATLAS 11parameter spectrum as muons from rare decays.The most dangerous background sources have been found to be thefollowing ([23]):• B → ψX decays followed by ψ → µ+µ− have the same topologybut fixed dimuon masses. These decays can occur at tree level orthey are driven by the decay of the Z,W boson or γ in the box andpenguin diagrams into a resonant cc¯ pair. Their branching ratio isabout 102 times larger than the branching ratio of rare decays. Only acut in dimuon invariant mass can remove this background source.ψ →µ+µ−γ decays are a second order correction to the ψ → µ+µ− decays,but they can move out the muons from the ψ window and thereforethey have to be take into account as possible background source.• The b → µ−ν¯µc(c → µ+νµq) semileptonic decay chain, like B+ →D¯0µ+νµ followed by the decay D¯0 → K+µ−ν¯µ. The two muons seemto come from the same vertex when D does not have a long propertime or when the muon is emitted in the D direction. If the missedmass due to neutrinos is not large, these decays are a very dangerousbackground source. Vertex requirements and cuts around B-mesonmass are the basic tools to reduce this background.• b → µνµX semileptonic decays of both b and b¯ quarks. These eventsare less dangerous than the previous ones to represent a backgroundsource as the two muons are not correlated in position.Other rare semileptonic decays driven by b → sµ+µ− transition canbe in principle background sources for B+ → K(∗)+µ+µ− decays. Theirbranching ratio is of the same order of magnitude as the two signal channelsand their contribution to background is very poor. Same argumentation forthe rare decays given by b → dµ+µ− transitions: due to CKM matrixelement Vtd the branching ratios of these channels are approximately 10times smaller than B(B+ → K(∗)+µ+µ−).Decay BRB → J/ψX (J/ψ → µµ (γ)) 1.16% (5.88%)B → ψ(2S)X (ψ(2S) → µµ (γ)) 4.8× 10−3 (7.3 × 10−3)b→ µ−ν¯µc (c→ µ+νµq) ∼ 1%b(b¯) → µνµX ∼ 1.1%Table 4. Background sources for B+ → K(∗)+µ+µ− decays and their branchingratios.12 B+ Semileptonic Rare Decays in ATLAS6.1. Background Data SamplesThe B → ψX (ψ → µµ (γ)), b→ µ−ν¯µc (c→ µ+νµq) and b(b¯) → µνµXdecays have been generated together in a so-called bb¯→ µ(6GeV )µ(4GeV )Xsamples. All b and b¯ decay channels are left open and accessible in Pythia,but only events containing two muons satisfying the LVL1 trigger cuts arewritten into a permanent output file.Two samples of B+ → J/ψ K+ and B+ → ψ(2S) K+ with ψ → µ+µ−events have been produced including also radiative corrections on ψ decaysand LVL1 cuts on muons, in order to evaluate the cc¯ resonance width toperform cuts on dimuon invariant mass.The background sample production is summarized Table 5. Also thenumber of expected events in 30 fb−1 after LVL1 trigger cuts is shown.This number for bb¯→ µ(6GeV )µ(4GeV )X events can be computed asNbb¯→µ(6)µ(4)X = L · t · σbb¯ trig (4)where σbb¯ trig = 3.6× 10−5mb is the cross section of bb¯ events that havethe first level trigger as the Pythia output.Triggerable events SimulatedDecay in 30 fb−1 eventsB+ → J/ψK+ (J/ψ → µ+µ−) 6.2 × 106 5× 104B+ → ψ(2S)K+ (ψ(2S) → µ+µ−) 8× 105 5× 104bb¯→ µ(6GeV )µ(4GeV )X 1.08× 109 2.5× 105Table 5. Background sample production with relative expected number of events in30 fb−1 after LVL1 trigger cuts on muons.6.2. cc¯ ResonancesThe same analysis strategy for signal reconstruction described in Section5.2 has been applied on B+ → J/ψK+ and B+ → ψ(2S)K+ samples. Thegoal was to reconstruct the J/ψ and ψ(2S) resonances in order to evaluatetheir mass width. In Figure 5 the J/ψ and ψ(2S) mass distributions areshown.Requiring a good dimuon vertex reconstruction (χ2/NDF < 3), a cut ondimuon invariant mass 3σ around J/ψ and ψ(2S) PDG mass values allowsto cut off almost all the events coming from cc¯ resonant channels. This is offundamental importance for the background rejection discussed in the nextsection.B+ Semileptonic Rare Decays in ATLAS 13(MeV)-µ+µM3400 3500 3600 3700 3800 3900 4000entries/8MeV050100150200250mean 3687 MeV 37 MeVσ(2S) mass distributionψ(MeV)-µ+µM2800 2900 3000 3100 3200 3300 3400entries/8MeV050100150200250300350mean 3097 MeV 34 MeVσ mass distributionψ J/Fig. 5. J/ψ and ψ(2S) mass distributions: the mean value and the width of thedistributions, resulting from a Gaussian fit, are shown.7. Background RejectionThe background rejection has been performed using the same analysiscode and strategy as the signal reconstruction on bb¯→ µ(6GeV )µ(4GeV )Xreconstructed data samples. Cuts on the quantities already identified in thesignal reconstruction step have been tuned in order to reduce backgroundefficiency and obtain a signal/background ratio as high as possible. Thefollowing two subsections show the background rejection criteria for the twodecays.7.1. B+ → K+µ+µ−Dimuon Selection CutsAs anticipated in Section 6, the muon pT spectra for background andsignal events are similar and no cuts can be applied. Analogous motivationshave been adopted for the muon transverse impact parameter.The dimuon vertex have to be well reconstructed for the ψ resonancesrejection: it has been required to have a χ2/NDF lower than 3.14 B+ Semileptonic Rare Decays in ATLASFigure 6 shows the effect on signal and background dimuon invariantmass normalized distributions1 after the cut ±3σ around ψ resonance nom-inal mass values.(MeV)-µ+µM0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000entries/4MeV00.010.020.030.040.050.060.070.08dimuon invariant mass distribution(MeV)-µ+µM0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000entries/4MeV00.010.020.030.040.050.060.070.08(2S) cutψdimuon invariant mass distribution after (MeV)-µ +µM0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000entries/4MeV00.0050.010.0150.020.025 cutψdimuon invariant mass distribution after J/Fig. 6. Dimuon invariant mass normalized distribution after cuts on ψ resonancesfor signal (solid line) and background (dotted line).Kaon Selection CutsA cut on kaon pT > 1 GeV remove ∼ 90% of the background yieldkeeping ∼ 40% of signal events. It has been found the most incisive cut forbackground rejection.1 In the following normalized distribution is intended normalized to 1.B+ Semileptonic Rare Decays in ATLAS 15B+ Selection CutsThe cuts on B+ selection are: χ2/NDF < 1.2, mass in ±3σ aroundPDG value and proper time τB+ > 1ps.Final Signal and Background efficienciesA detailed cut description has been reported in Table 6. The final effi-ciency after the cut application in a sequence for the signal has been foundε = 10%.Using Eq.2 the number of signal expected events after 30 fb−1integrated luminosity can be determined as:N = L · t · T · S · σbb¯ · P · BR · ε (5)leading to 4000 expected events. Due to limited background MonteCarlostatistic, the efficiency for background has been found zero.Cut Signal eff. BG eff.basic cuts 0.73 0.104χ2/NDF (dimuon) < 3 0.92 0.84mµµ /∈ [mψ(2S) ± 3σ], σ = 37MeV 0.91 0.99mµµ /∈ [mJ/ψ ± 3σ], σ = 34MeV 0.93 0.79pT (K+) > 1GeV 0.37 0.06χ2/NDF (B+) < 1.2 0.28 0.04mB+ ∈ [mB+ ± 3σ], σ = 42MeV 0.49 0.40τB+ > 1ps 0.67 0.27Final efficiency(ε) 0.10 0Table 6. Cut description for B+ → K+µ+µ−, efficiency for background rejectionand expected events in 30 fb−1 of integrated luminosity. The so-called “basic cuts”summarize the vertex fit success requests, the cuts on muon and hadron tracks anddimuon mass in the kinematic allowed window. The original sample was the samplepassing the LVL1 trigger requirements.7.2. B+ → K∗+µ+µ−Dimuon Selection CutsCut on dimuon candidates are the same as those applied for B+ →K+µ+µ− background rejection (see Section 7.1).K0s Selection CutsA cut on K0s candidate transverse momentum has been added to the cutson vertex quality and invariant mass. The on K0s selection are χ2/NDF <10, mass in ±3σ around the PDG value and pT > 2 GeVK∗+ Selection Cuts16 B+ Semileptonic Rare Decays in ATLASThe cuts on K∗+ selection are χ2/NDF < 5, mass in ±3σ around thePDG value and pT > 3 GeVB+ Selection CutsThe cuts on B+ selection are χ2/NDF < 2, mass in ±3σ around thePDG value and proper time τB+ > 1 ps.Final Signal and Background efficienciesA detailed cut description has been reported in Table 7. Also finalefficiencies have been tabulated after the cut application in sequence. Thefinal efficiency for signal has been found ∼ 4.5% and this lead to an expectednumber of event after 30 fb−1 integrated luminosity of 2300. As for theB+ → K+µ+µ− decay, due to limited background MonteCarlo statistic,the efficiency for background has been found zero.Cut Signal eff. BG eff.basic cuts 0.47 0.25χ2/NDF (dimuon) < 3 0.92 0.84mµµ /∈ [mψ(2S) ± 3σ], σ = 37MeV 0.94 0.99mµµ /∈ [mJ/ψ ± 3σ], σ = 34MeV 0.93 0.75χ2/NDF (K0s ) < 89 0.89 0.93mK0s∈ [mK0s± 3σ], σ = 9MeV 0.37 0.16pT (K0s ) > 2GeV 0.41 0.16χ2/NDF (K∗+) < 5 0.81 0.87mK∗+ ∈ [mK∗+ ± 3σ], σ = 26MeV 0.56 0.46pT (K∗+) > 3GeV 0.43 0.16χ2/NDF (B+) < 2 0.52 0.55mB+ ∈ [mB+ ± 3σ], σ = 49MeV 0.66 0.55τB+ > 1ps 0.41 0.15Final Efficiency(ε) 0.045 0Table 7. Cut description for B+ → K∗+µ+µ− and efficiency for background rejec-tion. The so-called “basic cuts” summarize the vertex fit success requests, the cutson muon and hadron tracks and dimuon mass in the kinematic allowed window.The original sample was the sample passing the LVL1 trigger requirements.8. Expected Events and Background EstimationAs showed in the previous section, imposing smart cuts allows to removeall the background events coming from beauty decays.Compatibly whit the current MonteCarlo statistics, an estimate of thebackground produced in 30 fb−1 can be achieved by the following method.B+ Semileptonic Rare Decays in ATLAS 17The procedure will be explained in detail for B+ → K+µ+µ− decay, andthen applied also to B+ → K∗+µ+µ− channel.Without applying the cut on B+ mass, the mass distribution in therange 5000 − 5600 GeV is computed. Counting the events in the massregion, one can obtain the number of background eventsNBG = 7 events (6)Looking at the same mass window as the signal i.e. 250 MeV , one cancompute the number of background events asNB = rNBG (7)where r is the ratio of the window sizes:r =250 MeV600 MeV∼ 0.42 (8)Clearly the windows sizes and NBG have to be determined using muchlarger background samples than have been available for this study. Withthe current statistic, this calculation leads to 2.9 background events within250 MeV . The number of generated events that fulfills the LVL1 trigger is250000, and it leads to a fake reconstruction efficiency ofεfake = 1.2× 10−5 (9)The result leads to a total of B = L·t·σbb¯ trig ·εfake ∼ 12000 backgroundevents in 30 fb−1. In Figure 7 the mass spectrum for background eventsadded to signal events is plotted in the mass range 5000 − 5600 GeV . Thebackground is fluctuating around 2400 and on top of it the signal peak isclearly visible.To test whether the seen peak is a peak and not statistical fluctuationthe statistical significance is computed asSstat = Signal√Background=S√B(10)If significance is greater than 5, then the signal is observable. In theanalysis with a signal of ∼ 4000 events and a background of ∼ 12000 eventsin the signal mass window mB+ ± 3σ, a statistical significance of 35 iscomputed.For B+ → K∗+µ+µ− decay, the same procedure leads to ∼ 14000 back-ground events in 30 fb−1 in the signal mass window. The statistical signif-icance has been found Sstat = 19.These results are summarized in Table 8.18 B+ Semileptonic Rare Decays in ATLASM(MeV)5000 5100 5200 5300 5400 5500 5600Number of events/50MeV10001500200025003000350040004500Fig. 7. The B+ signal of B+ → K+µ+µ− decay after 30 fb−1 integrated luminosity.The background estimation is done on the available MonteCarlo statistic.Decay εi Si BiB+ → K∗+µ+µ− 0.045 2300 14000B+ → K+µ+µ− 0.10 4000 12000Table 8. Expected events for B+ → K(∗)+µ+µ− (Si) and background (Bi) in30 fb−1. Also the signal efficiency εi has been reported.9. Branching Ratio MeasurementsTo estimate the statistical error on an exclusive branching ratio mea-surement, it has been assumed that in 30 fb−1 integrated luminosity N¯ievents are observed in the B+ mass window, of which B¯i are backgroundand S¯i signal events2:2 Throughout this section X denote the random realization of a variable with mean X¯and following a Poissonian distribution with a large mean, thus σ2(X) = X¯.B+ Semileptonic Rare Decays in ATLAS 19N¯i = S¯i + B¯i (11)The estimates of the signal and background yields are given in table 8.Ni events are observed in a narrow B mass window and Pi events in awider window. The background in the narrow mass window isB¯i = rP¯i (12)where r is defined as in Eq. (8).S¯i will be determined asS¯i = N¯i − B¯i = N¯i − rP¯i (13)The numbers of events Ni and Pi observed after 30 fb−1 are randomrealizations of N¯i and P¯iNi = N¯i ± σ(Ni) σ2(Ni) ∼ N¯i ∼ Ni (14)Pi = P¯i ± σ(Pi) σ2(Pi) ∼ P¯i ∼ Pi (15)The statistical error on the number of events Si is thus given byσ2(Si) = σ2(Ni) + r2σ2(Pi) ∼ Ni + r2Pi (16)In the present case, Si and Bi are know form the previous section. UsingEq. (11) and (12), Eq. (16) can be rewritten asσ2(Si) ∼ Si + (1 + r)Bi (17)The yield Si has to be re-weighted by the corresponding selection effi-ciency εi, the generation cuts fraction T and the isospin weight ωiRi =ωiεiTSi = fiSi (18)The branching ratio is proportional to Ri, and thus the error isσ(BRi)BRi =σ(Ri)Ri(19)where σ(Ri) = fiσ(Si). The second term of the uncertainty dependingon σ(fi) is not taken into account as it enters the systematic uncertainty.Using values of εi and T given in Table 8 and 2 and 1 and 2.9 as isospinweights respectively forB+ → K+µ+µ− and B+ → K∗+µ+µ− decays, thestatistical error on branching ratio for the two decays, is then20 B+ Semileptonic Rare Decays in ATLASσ(BRi)BRi (B± → µµK±) ∼ 3.5% (20)σ(BRi)BRi (B± → µµK∗±) ∼ 6.5% (21)The statistical errors are much smaller than the current experimentaland theoretical ones. The systematic errors remain to be determined butthey are out of scope of this study. These measurements are interestinginputs to test the various theoretical models. They have a potential to beselective between the Standard Model and beyond SM theories.10. ConclusionsWith the present study on the B+ → K+µ+µ− and B+ → K∗+µ+µ−decays, many positive results have been achieved.All the software chain, from event generation to reconstruction and anal-ysis, has been tested using GRID facilities. The analysis strategy of the twodecay channels for the ATLAS data taking is ready. The analysis C++ codehas been implemented in the ATLAS official software framework.The most interesting quantities for the rare semileptonic beauty decaysare the differential dimuon invariant mass and the forward-backward asym-metry. New Physics might result in significant enhancement compared tothe Standard Model predictions and thus their measurement, as well as themeasurement of the branching ratio, provide an indirect search for NewPhysics. The study on simulated data shows that the trigger and the oﬄineanalysis cuts do not change the shape of the dimuon mass spectrum andthe FBA distribution.Also background rejection strategy is ready and it has been tested on250k background events. Due to limited background MonteCarlo statistics,only a preliminary background estimation has been done by extrapolatingbackground events from a wider mass window around PDG B+ mass value.The signal is clearly visible over the background level: the statistical signif-icance is very high for both decays.This method leads to an overestimate of the expected background yield.As shown in the ATLAS Technical Design Report ([7]), the expected numberof bb¯ background events after 30 fb−1 for the rare decay B0d → K∗0µ+µ− isabout 300, to be compared with the expected 2000 signal events. But, com-patibly with the low MonteCarlo available statistic, this is the only way todemonstrate the visibility of the decays over the background events and tohave some prediction on branching ratio measurements. The errors expectedon branching ratio measurements are ∼ 3.5% and ∼ 6.5% respectively forB+ Semileptonic Rare Decays in ATLAS 21B+ → K+µ+µ− and B+ → K∗+µ+µ− decays. These errors on the branch-ing ratio measurements are much smaller than the current experimental andtheoretical ones and this allows to conclude that these measurements are in-teresting inputs to test the SM versus SUSY theories predicting significantenhancements of these branching ratios.The present study is being refined by using more MonteCarlo data (back-ground), including also minimum bias pp events and considering pile-upeffects to evaluate the possibility to extend the ATLAS studies on raresemileptonic B-decays at high luminosity (L = 1034 cm−2s−1). The contri-bution of minimum bias events is expected to be poor with respect to thebackground taken into account, but an accurate estimation of backgroundyield is needed to perform precise measurements of the forward-backwardasymmetry and differential decay rate.REFERENCES[1] B. Aubert et al. (The BaBar Collaboration), Phys. Rev. D 73, 092001 (2006)[2] A. Ishikawa et al. (The Belle Collaboration), Phys. Rev. Lett. 96, 251801(2006)[3] K. Abe et al. (The Belle Collaboration), hep-ex/0410006 (2004)[4] G.Buchalla et al., Rev. Mod. Phys.68, 1125 (1996)[5] C. Bobeth et al., Nucl. Phys. B 574, 29 (2000)[6] A.Ali et al., Phys. Rev. D 66, 034002 (2002)[7] ATLAS Collaboration, ATLAS Detector and Physics Performance TechnicalDesign Report, CERN/LHCC/99-15 (1999)[8] S. George, ATL-DAQ-2004-004 (2004)[9] J. Baines et al., ATL-DAQ-COM-2002-013[10] M. Smizaˇnska´, Eur. Phys J C 34, 385-392 (2004)[11] D. Adams et al., ATL-SOFT-2004-007 (2005)[12] LCG Project Collaboration, CERN-LHCC-2005-024 (2005)[13] ATLAS Collaboration,http://atlas.web.cern.ch/Atlas/GROUPS/SOFTQARE/OO/architecture/General/Tech.Doc/Manual/2.0.0 DRAFT/AthenaUserGuide/pdf[14] M. Smizaˇnska´, ATL-COM-PHYS-2003-038 (2003)[15] M. Smizaˇnska´ and J. Catmore, ATL-COM-PHYS-2004-041 (2004)[16] S. Baranov and M. Smizaˇnska´, ATL-PHYS-98-133 (1998)[17] W.M. Yao et al., Journal of Physics G 33, 1 (2006)[18] J. Catmore et al., ATL-COM-PHYS-2006-013 (2006)[19] K.A. Assamagan et al., ATL-SOFT-2004-006 (2004)22 B+ Semileptonic Rare Decays in ATLAS[20] http://tarta.home.cern.ch/tarta/vtx/docu.html[21] D. Fassouliotis et al., ATL-COM-MUON-2003-003 (2003)[22] J. Baines et al., hep-ph/0003238 (2000)[23] D. Melikhov et al., Investigation of rare semimuonic B-decays, ATL-PHYS-96-083 (1996)

B+B^+B+ semileptonic rare decays in ATLAS

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$B^+$ semileptonic rare decays in ATLAS