The possibility of improving the limit on the branching fraction of the lepton flavor violating decay τ ± → µ±µ±µ∓ at LHCb is discussed. It is shown that a simple, cut-based analysis is sufficient to improve the upper limit on this branching fraction within the lifetime of LHC

Keune, A.

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ISSN 1063-7788, Physics of Atomic Nuclei, 2012, Vol. 75, No. 9, pp. 1085–1087. c© Pleiades Publishing, Ltd., 2012.ELEMENTARY PARTICLES AND FIELDSExperimentThe Lepton Flavor Violating Decay τ± → μ±μ±μ∓ at LHCb*A. Keune**Laboratoire de Physique des Hautes Energies, Ecole Polytechnique Fe´de´rale de Lausanne, SwitzerlandReceived November 15, 2011Abstract—The possibility of improving the limit on the branching fraction of the lepton ﬂavor violatingdecay τ± → μ±μ±μ∓ at LHCb is discussed. It is shown that a simple, cut-based analysis is suﬃcient toimprove the upper limit on this branching fraction within the lifetime of LHCb.DOI: 10.1134/S10637788120900741. INTRODUCTIONLepton ﬂavor conservation is explicitly assumed inthe Standard Model. However, with the discovery ofneutrino oscillations, establishing that lepton ﬂavorsmix in the neutral sector, it is conceivable to havelepton ﬂavor violating charged lepton decays. Leptonﬂavor conservation in the charged sector is measuredto a high precision, but is not a consequence of aknown gauge symmetry; almost every model beyondthe Standard Model predicts lepton ﬂavor violation.With the known neutrino oscillation contribution im-measurably small, any observation of lepton ﬂavorviolation would imply New Physics.The lepton ﬂavor violating decay τ± → μ±μ±μ∓ isan ideal decay mode for LHCb to probe. The muonsare easily identiﬁed and triggered upon. The modecan be reconstructed with high eﬃciency and preci-sion, using the vertex detector which is speciﬁcallydesigned to identify secondary vertices. This resultsin a precise determination of the τ-vertex locationand an excellent τ-mass resolution (σ), since thereis no missing neutrino. As most τ ’s come from b andc hadrons, its vertex will be suﬃciently displaced topass the impact parameter requirements, designed toselect B mesons in the LHCb trigger.2. NEW PHYSICS PREDICTIONSAND CURRENT LIMITSThe τ± → μ±μ±μ∓ branching fraction throughneutrino oscillation is proportional to the term(mν/mW )4 ∼ 10−50, where mν and mW are theneutrino and W mass, respectively. This allowedbranching fraction is thus undetectable. Its decay di-agram is depicted in Fig. 1. New Physics models, like∗The text was submitted by the author in English.**E-mail: anne.keune@epfl.chmediating boson models or supersymmetry (SUSY)models, predict much higher branching fractions.The nonuniversal Z ′ model predicts a branchingfraction of the order 10−8 [1], whereas the minimalsupersymmetric model predicts it to be 10−9 [2].These decay diagrams are depicted in Figs. 2 and 3,respectively.Upper limits on the branching fraction have beenset by BaBar and Belle. BaBar has obtained a limit of3.3× 10−8 [3], but the strongest limit of 2.1× 10−8 [4]is currently set by Belle at a 90% conﬁdence limit.These limits are in the range of many New Physicspredictions and any improvement will have a directeﬀect on the understanding of New Physics.3. τ± → μ±μ±μ∓ SIGNALAND BACKGROUND AT LHCbThe total τ cross section at LHCb is estimated tobe ∼111 μb at √s = 14 TeV. A nominal year (107 s)of data taking yields 2 fb−1 of data and 2.22 × 1011 τparticles will be produced. The geometrical eﬃciencyof the tauons decaying to three muons, i.e. all threedaughters are in the acceptance of LHCb (10 < θ <400 mrad), is estimated from the Monte-Carlo (MC) τ – μ – μ – μ + ν τ ν μ W – Z 0 / γFig. 1. Feynman diagram of the lepton ﬂavor violatingdecay τ± → μ±μ±μ∓ through neutrino oscillation.10851086 KEUNEsimulation to be ∼19.5%. The branching fraction ofthis decay is currently known to be smaller than 2.1×10−8 (Belle’s limit). There are therefore less than910 signal events in LHCb per nominal year. Thereconstruction eﬃciency, with minimal pre-selection,is ∼25%, resulting in less than 228 signal eventsbefore applying any selection criteria.Around half, 52% of the signal, of τ ’s comefrom prompt Ds mesons, 34% come directly fromB mesons and the remaining 14% come from Dsmesons through B-meson decays. The main sourceof background originates from di-muons producedin b and b¯ quark decays associated with one randomtrack. Other sources of background considered arethe light quark events and inclusive cc¯ events. Anoptimal selection can be made using diﬀerent selec-tion methods for the diﬀerent τ sources, however, dueto the similar τ property distributions, all τ sourceswill initially be treated simulatenously. In addition,it is noted that the di-muon background samplemost resembles the signal. A selection strategy thatfully suppresses this source is suﬃcient to remove allevents from other background types, as was checkedin MC simulation.For this study a background sample of ∼15M di-muon events with candidates within a mass windowof ∼10σ (Δmτ = 200 MeV) are considered. Thissample is equivalent to 1/377 of a nominal year ofdata. The normalization factor needed for the signalevents depends on the unknown branching fraction.It is 0.0104 for a branching fraction of 1× 10−8.4. A CUT-BASED SELECTIONRough initial cuts are made on individual kine-matic and geometrical variables, assuming zero cor-relation between them. The cuts are tuned to op-timize the signal signiﬁcance, deﬁned as s/√s + b,where s and b are the number of selected signal andbackground events, both normalized to the same sizedata set. For the uncorrelated variables this is indeed τ – μ – μ – μ + Z '/ H 0Fig. 2. The decay diagram of τ± → μ±μ±μ∓ througha mediating anomalous Z′ boson or Higgs as predictedby the nonuniversal Z′ model or any mediating Higgsmodel. τ – μ – μ – μ + τ Z 0 / γ ~ μ ~ χ 0 ~Fig. 3. The decay diagram of τ± → μ±μ±μ∓ throughslepton mixing as predicted by the minimal supersym-metric model. 101650 1700Events/MeV m τ , MeV0203040501750 1800 1850 1900Fig. 4. The mass distributions of the MC true signalcandidates (gray) and the background candidates (black)before the particle identiﬁcation cut.the optimal cut value. For the variables that exhibitsome interdependence, these cuts are loosened byexploiting their relative correlations.The strongest cuts are made on the χ2 of the τend-vertex and the particle identiﬁcation likelihoodof each muon. Both variables are uncorrelated toany other. The mass distributions of the signal andbackground candidates before the particle identiﬁca-tion cut are shown in Fig. 4. The third strongestcut is made on the χ2 of the muon impact parameter.This variable is highly correlated to the actual impactparameter of the muon and the ﬂight distance of the τ(especially for the signal candidates).5. FIRST RESULTSBy applying the selection cuts, an eﬃciency of∼5% is obtained. Candidates in events, which havenot passed the L0 hardware trigger, are also excludedfrom the selection.This simple selection leaves 526 signal events and1 background event in a wide mass window (Δmτ =200 MeV). Selecting a smaller signal mass windowPHYSICS OF ATOMIC NUCLEI Vol. 75 No. 9 2012THE LEPTON FLAVOR VIOLATING DECAY 1087of ∼2σ (Δmτ = 40 MeV) there are 511 signal eventsleft; the background is scaled linearly to 1/5 = 0.2of expected background events. As the normaliza-tion factor for the di-muon sample is 377, the totalexpected background in this mass window is 75.4 +2√75.4  93 candidates. Although the selection wasonly done using the di-muon sample, it has beenveriﬁed that the same event selection has also cutaway 100% of the available minimum bias and in-clusive c backgrounds. As the normalization factorof the signal is 0.0104 for a branching fraction of1× 10−8, an upper limit on the branching fraction of3.2× 10−8 can be set within one nominal year of datataking with a conﬁdence level of 90%. This numbermatches BaBar’s current limit, but would not be animprovement on Belle’s limit.Within the lifetime of LHCb, which corresponds to10 fb−1, the branching fraction can be probed downto 1.3× 10−8. Thus, it is seen that even with a simpleselection procedure an improved limit on the τ± →μ±μ±μ∓ branching fraction will be set within thelifetime of LHCb.6. FURTHER WORKThe single background candidate left in the selec-tion consists of one muon coming from a Ds decay,a second muon from a D± decay and one ghosttrack. A better choice of cut variables, for instanceconsidering vertex isolation, may also eliminate thelast background candidate.An improved selection eﬃciency of 8% using moreadvanced selection methods is considered realistic.The current upper limit on the branching fractionwould then be reached within one nominal year ofLHCb data taking.Using the ﬁrst data the detector eﬀects are cur-rently being studied and the event generator tuned.Following this work, the selection on the simulationcan be further reﬁned.7. CONCLUSIONA simple, cut-based selection is suﬃcient to showthat within the lifetime of LHCb new limits will be seton the τ± → μ±μ±μ∓ branching fraction.REFERENCES1. C. Yue, Y. Zhang, and L. Liu, Phys. Lett. B 547, 252(2002).2. A. Pilaftsis, Phys. Rev. D 65, 115013 (2002).3. J. P. Lees et al. (BaBar Collab.), Phys. Rev. D 81,111101(R) (2010), arXiv: 1002.4550 [hep-ex].4. Y. Miyazaki et al. (Belle Collab.), Phys. Lett. B 660,154 (2008).PHYSICS OF ATOMIC NUCLEI Vol. 75 No. 9 2012

The lepton flavor violating decay τ ± → µ±µ±µ∓ at LHCb

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The lepton flavor violating decay τ ± → µ±µ±µ∓ at LHCb

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