Search for lepton flavour violation in the $e\mu$ continuum with the ATLAS detector in $\sqrt{s}$ = 7 TeV pp collisions at the LHC

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    a  r   X   i  v  :   1   2   0   5 .   0   7   2   5  v   2   [   h  e  p  -  e  x   ]   2   8   J  u  n   2   0   1   2 EUROPEANORGANISATIONFORNUCLEARRESEARCH(CERN) CERN-PH-EP-2012-108 Submittedto:EuropeanPhysicalJournalC Search for Lepton Flavour Violation in the  eµ  Continuum withthe ATLAS Detector in √  s  = 7  TeV  pp  Collisions at the LHC TheATLASCollaboration Abstract Thispaperpresentsasearchforthe  t -channelexchangeofan  R -parityviolatingscalartopquark( ˜ t )inthe  e ± µ ∓ continuumusing2.1fb − 1 ofdatacollectedbytheATLASdetectorin  √  s  = 7 TeV  pp collisionsattheLargeHadronCollider.DataarefoundtobeconsistentwiththeexpectationfromtheStandardModelbackgrounds.Limitson  R -parity-violatingcouplingsat95%C.L.arecalculatedasafunctionofthescalartopmass( m ˜ t ).Theupperlimitsontheproductioncrosssectionfor  pp  →  eµX  ,throughthe  t -channelexchangeofascalartopquark,rangesfrom170fbfor  m ˜ t  = 95 GeVto30fbfor  m ˜ t  = 1000 GeV.  EPJ manuscript No. (will be inserted by the editor) Search for Lepton Flavour Violation in the  eµ  Continuum withthe ATLAS Detector in √  s  = 7  TeV  pp  Collisions at the LHC The ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland e-mail:  atlas.publications@cern.ch June 29, 2012 Abstract.  This paper presents a search for the  t -channel exchange of an  R -parity violating scalar topquark (˜ t ) in the  e ± µ ∓ continuum using 2.1 fb − 1 of data collected by the ATLAS detector in  √  s  = 7 TeV  pp  collisions at the Large Hadron Collider. Data are found to be consistent with the expectation fromthe Standard Model backgrounds. Limits on  R -parity-violating couplings at 95% C.L. are calculated as afunction of the scalar top mass ( m ˜ t ). The upper limits on the production cross section for  pp  →  eµX  ,through the  t -channel exchange of a scalar top quark, ranges from 170 fb for  m ˜ t  = 95 GeV to 30 fb for m ˜ t  = 1000 GeV. 1 Introduction In the Standard Model (SM), direct production of   e ± µ ∓ ( eµ ) pairs is forbidden in  pp  collisions due to lepton flavourconservation. However, in many extensions of the SM, lep-ton flavour violation (LFV) is permitted. In particular, R -parity-violating (RPV) supersymmetric (SUSY) mod-els, LFV leptoquarks, and models with additional gaugesymmetry allow LFV. Previous searches by the CDF, D0,and ATLAS Collaborations [1–7] have focused on reso- nant production of a heavy neutral particle which decaysinto an  eµ  pair and have set limits on these models. Inaddition to resonant  eµ  production, RPV SUSY modelsalso allow for LFV interactions through the  t -channel ex-change of a scalar quark. The corresponding Lagrangianterm for these RPV processes [8] is  W   =  − λ ′ ijk ˜ u j  ¯ d k ℓ i ,where ˜ u  denotes the up-type squark field,  d  is the down-type quark field,  ℓ  represents the lepton field, and  λ ′ is thecoupling at the production vertex. The indices  i,j,k  referto fermion generations. This superpotential couples an up-type squark to a down-type quark and a lepton, allowingfor production of   eµ  pairs through the  t -channel exchangeof an up-type squark. This paper presents a search for thisprocess in the  eµ  continuum using 2.1 fb − 1 of   pp  collisiondata at  √  s  = 7 TeV collected by the ATLAS detector atthe Large Hadron Collider (LHC).The cross section for this process is expected to bedominated by the lightest up-type squark, which is takento be the scalar top quark (˜ t ) in this analysis. The Feyn-man diagram for the dominant process, d ¯ d → e − µ + throughthe  t -channel exchange of a ˜ t , is shown in Fig. 1. Theleading-order (LO) partonic differential cross section iscalculated as  d ˆ σ/d ˆ t  =  | λ ′ 131 λ ′ 231 | 2 ˆ t 2 / [64 N  c π ˆ s 2   ˆ t − m 2˜ t  2 ],where ˆ s  and ˆ t  are the usual Mandelstam variables in the d ¯ d  centre-of-mass frame,  N  c  = 3 is the colour factor,  m ˜ t  isthe scalar top mass, and  λ ′ 131  ( λ ′ 231 ) is the coupling for thevertex  d ˜ te − ( µ + ˜ t ¯ d ). The process where the final state lep-tons have opposite charges to those in Fig. 1 has the samecross section. Diagrams with the  d  and ¯ d  independentlyreplaced by  s  and ¯ s  quarks are also allowed. The formof the cross section for these diagrams is the same, butthe indices on the  λ ′ couplings are different. In the caseof   s ¯ s  →  µ ± e ∓ , the cross section depends on  | λ ′ 132 λ ′ 232 | .For  d ¯ s  →  µ + e − and  s ¯ d  →  µ − e + , the cross section de-pends on  | λ ′ 131 λ ′ 232 | . Lastly, diagrams with  s ¯ d  →  µ + e − and  d ¯ s → µ − e + depend on  | λ ′ 231 λ ′ 132 | .   t~dd - e + µ 131 ’ λ 231 ’ λ Fig. 1.  The Feynman diagram for  d ¯ d  →  e − µ + productionthrough the  t -channel exchange of a scalar top quark. Strong limits on RPV couplings have been obtainedfrom low-energy searches [9,10], such as  µ  →  eγ  ,  µ − e conversion on nuclei and  Z   →  eµ , where superparticlesappear in the intermediate state, often in loops. The pres-ence of multiple interfering amplitudes makes the extrac-tion of limits difficult, and it is usually assumed that asingle product of couplings dominates. The interferenceof different diagrams could weaken the limits on a spe-cific product of couplings. Also, these limits depend on  2 The ATLAS Collaboration: Search for Lepton Flavour Violation in the  eµ  Continuum unknown superparticle masses (including ones other thanthe scalar top), sometimes in a complex manner.The HERA experiments searched for an LFV lepto-quark in the process  ep  →  µX   [11, 12]. These studiesalso place limits on a potential RPV scalar top. At lowermasses (less than about 300 GeV), there would be copi-ous  s -channel production, and placing limits on specificcouplings depends on assumptions about the stop decays.At higher masses, the HERA searches are sensitive to  u -channel exchange, which can be directly compared to thisanalysis. The sensitivity of the measurement in this paperis slightly better than at HERA for masses above about300 GeV. The HERA experiments also searched for scalartop production in both the RPV and gauge boson decaychannels [13,14]. Such searches assumed the RPV couplinginvolved in the scalar top production,  λ ′ 131 , to be domi-nant and cannot be directly compared with the results of this paper.Direct searches at hadron colliders and at HERA forlepton-flavour-conserving scalar leptoquarks [15–24] are also relevant to the search here. The interpretation of suchresults as limits on a scalar top depends, as for the LFVleptoquarks, on the decay branching ratios to the leptonsand quarks and hence on assumptions about the otherpossible decays. Present limits on such leptoquarks at thescalar top masses considered here do not preclude the sig-nal sought in this analysis.The limits on the couplings associated with the  d ¯ s and  s ¯ d  processes are two orders of magnitude lower thanthose for the  d ¯ d  and  s ¯ s  couplings [9]. Therefore dominanceby same flavour quark scattering processes is assumed inthis analysis. As a result, the production cross section for  pp  →  eµX  , due to the  t -channel exchange of a scalar topquark, depends on  λ ′ 131 ,  λ ′ 231 ,  λ ′ 132 ,  λ ′ 232 , and  m ˜ t . 2 Detector and Data Sample The ATLAS detector [25] is a multi-purpose particle de-tector with a forward-backward symmetric cylindrical ge-ometry and almost 4 π  coverage in solid angle [26]. Theinner tracking detector (ID) covers  | η |  <  2 . 5 in pseudo-rapidity  η  and consists of a silicon pixel detector, a sili-con microstrip detector, and a transition radiation tracker.The ID is surrounded by a thin superconducting solenoidproviding a 2 T magnetic field and by a hermetic calorime-ter system, which provides three-dimensional reconstruc-tion of particle showers up to  | η |  = 4 . 9. The muon spec-trometer (MS) is based on one barrel and two endcap air-core toroids, each consisting of eight superconducting coilsarranged symmetrically in azimuth around the calorime-ter. Three layers of precision tracking stations, consistingof drift tubes and cathode strip chambers, allow precisemuon momentum measurement up to  | η | = 2 . 7. Resistiveplate and thin-gap chambers provide muon triggering ca-pability up to  | η | = 2 . 4.The  pp  collision data used in this analysis were recordedbetween March and August 2011 at a centre-of-mass en-ergy of 7 TeV. After applying data quality requirements,the total integrated luminosity of the dataset used in thisanalysis is 2.08 ± 0.08 fb − 1 [27]. Events are required to sat-isfy one of the single-lepton ( e  or  µ ) triggers. For electrons,the threshold on the transverse energy ( E  T ) is 20 GeVor 22 GeV depending on run periods, and for muons thethreshold on the transverse momentum (  p T ) is 18 GeV. 3 Event Preselection The event preselection requires a primary vertex with atleast three associated tracks with  p T  >  0 . 5 GeV and ex-actly one electron and one muon of opposite charge. Elec-tron candidates are selected from clustered energy de-posits in the electromagnetic calorimeter with an asso-ciated track reconstructed in the ID. They are requiredto have  E  T  >  25 GeV and to lie inside the pseudorapid-ity regions  | η |  <  1 . 37 or 1 . 52  <  | η |  <  2 . 47. Electronsare further required to satisfy a stringent set of identifica-tion requirements based on the calorimeter shower shape,track quality and track matching with the calorimeter en-ergy cluster, referred to as ‘tight’ in Ref. [28]. Muons arereconstructed by combining tracks in the ID and MS with  p T  >  25 GeV and  | η | <  2 . 4. Electrons are rejected if theyare located within a cone of   ∆R  =   ( ∆η ) 2 + ( ∆φ ) 2 = 0 . 2around a muon, where  ∆η  and  ∆φ  are the pseudorapid-ity and azimuthal opening angle difference between theelectron and muon.To suppress backgrounds from  W/Z  +jets and multi- jets, isolation requirements on tracks and calorimeter de-posits are applied to the leptons. The scalar sum of thetransverse momenta of tracks within a cone of   ∆R  = 0 . 2around the lepton must be less than 10% of the lepton’s  p T . Similarly, the transverse energy in the calorimeterwithin a cone of   ∆R  = 0 . 2 around the lepton are requiredto be less than 15% of the lepton’s transverse energy. Cor-rections are applied to account for energy leakage and en-ergy deposition inside the isolation cone due to additional  pp  collisions.Jets are reconstructed from calibrated clusters usingthe anti- k t  algorithm [29] with a radius parameter of 0.4.Jet energies are calibrated using  E  T - and  η -dependent cor-rection factors based on Monte Carlo (MC) simulationand validated by test beam and collision data studies [30].Only jets with  p T  >  30 GeV and  | η | <  2 . 5 are considered.If such a jet and an electron lie within  ∆R  = 0 . 2 of eachother, the jet is discarded.The measurement of missing transversemomentum [31]( E  missT  ) is based on the transverse momenta of the elec-tron and muon candidates, all jets, and all energy clusterswith  | η | <  4 . 5 not associated to such objects. 4 Background and Simulation The SM processes that can produce an  eµ  signature arepredominantly t ¯ t ,  Z/γ  ∗ → ττ  , diboson, single top,  W/Z  +jets, W/Z  + γ   and multijet events. All of these processes, ex-cept  W/Z  +jets and multijet production, are estimatedusing Monte Carlo samples generated at  √  s  = 7 TeV fol-lowed by a detailed  geant4 -based [32] simulation of the  The ATLAS Collaboration: Search for Lepton Flavour Violation in the  eµ  Continuum 3 ATLAS detector [33]. To improve the agreement betweendata and simulation, selection efficiencies are measuredin both data and simulation, and correction factors areapplied to the simulation. Furthermore, the simulation istuned to reproduce the calorimeter energy and the muonmomentum scale and resolution. Top production is gener-ated with mc@nlo [34] for  t ¯ t  and single top, the Drell-Yanprocess is generated with  pythia  [35], and the dibosonprocesses are generated with  herwig  [36]. The  W/Z   +  γ  background comes from the  W  ( →  µν  ) γ   and  Z  ( →  µµ ) γ  processes, which is estimated using events generated with madgraph  [37]. The simulation samples are normalizedto cross sections with higher-order corrections applied.The ˜ t  signal samples are produced with the  pythia event generator [35] with  | λ ′ 131 λ ′ 231 |  =  | λ ′ 132 λ ′ 232 |  = 0 . 05and the value of   m ˜ t  is varied from 95 GeV, which is themost stringent limit from previous experiments [38], to1000 GeV. The central CTEQ6L1 [39] parton distributionfunction (PDF) set is used. The LO cross section is 580 fbfor  m ˜ t  = 95 GeV and 0.33 fb for  m ˜ t  = 1000 GeV. 5 Data Analysis The production of   W/Z  +jets and multijets can give rise tobackgrounds due to jets misidentified as leptons or non-prompt leptons from heavy-quark decays in jets. Thesesources are referred to as fake background and are esti-mated from data. A looser lepton quality selection (called‘loose’ lepton here) is defined for each lepton type in addi-tion to the default tight quality selection. For loose muons,both the calorimeter and the track isolation requirementsare removed. For loose electrons, the ‘loose’ electron iden-tification criteria as defined in Ref. [28] are used and theisolation requirements are also removed. The fake back-ground is determined by weighting the events in the looselepton sample by the likelihood that the event came fromprocesses with at least one misidentified or non-promptlepton. These weights are obtained by solving a 4 × 4 ma-trix equation, constructed from the  E  T - or  p T -dependentprobabilities for a prompt or fake/non-prompt lepton thatpasses the loose lepton requirement to also pass the tightlepton requirement. More details about the 4 × 4 matrixmethod are given in Ref. [7].The middle column of Table 1 gives the number of events in the data and the estimated background contribu-tions with their total uncertainties after the event preselec-tion. A total of 5387  eµ  candidates are observed with 5300 ± 400 events expected from SM processes. The number of expected signal events is shown for  m ˜ t  = 95, 250, 500,and 1000 GeV, assuming  | λ ′ 131 λ ′ 231 |  =  | λ ′ 132 λ ′ 232 |  = 0 . 05.Figure 2 shows the comparison between data and the ex-pected SM background for the dilepton invariant mass( m eµ ), their azimuthal opening angle ( ∆φ eµ ),  E  missT  andthe number of jets. A good description of the data by theexpected SM background is observed.To increase the signal purity, the preselected events arerequired to have zero jets,  m eµ  >  100 GeV,  ∆φ eµ  >  3 . 0rad and  E  missT  <  25 GeV. This selection was optimizedusing the signal sample with  m ˜ t  = 95 GeV which is the Table 1.  Number of events observed in data, the estimatedbackgrounds, and expected number of signal events, assuming | λ ′ 131 λ ′ 231 | = | λ ′ 132 λ ′ 232 | = 0 . 05, with their combined systematicand statistical uncertainties for the preselected sample and thefinal selected sample. The number of signal and backgroundevents has been rounded.Process Preselection Final selection WW   640  ±  50 23.4  ±  3.3 Z/γ  ∗ → ττ   1210  ±  110 10  ±  4Fake Background 290  ±  40 9.6  ±  1.9 WZ   36  ±  4 0.76  ±  0.31 t ¯ t  2800  ±  400 0.25  ±  0.17Single top 270  ±  40 0.22  ±  0.20 W/Z   +  γ   20  ±  7 0.04  ±  0.04 ZZ   4.0  ±  0.4 0.042  ±  0.028Total background 5300  ±  400 44  ±  6Data 5387 39Signal ( m ˜ t  = 95 GeV) 240  ±  15 67  ±  5Signal ( m ˜ t  = 250 GeV) 23.7  ±  1.4 9.3  ±  0.6Signal ( m ˜ t  = 500 GeV) 3.05  ±  0.18 1.28  ±  0.08Signal ( m ˜ t  = 1000 GeV) 0.305  ±  0.018 0.124  ±  0.008 most demanding in terms of signal-to-background ratiowhen setting limits. After applying the full selection, 39events are observed with 44  ±  6 SM events expected. Abreakdown of the SM background composition is given inthe last column of Table 1. In order of importance, thedominant contributions stem from  WW  ,  τ  -pair and fakebackground. The  m eµ  distribution of the selected eventsis shown in Fig. 3.Systematic uncertainties on the SM background esti-mation arise from uncertainties in the estimation of thefake background (15%), the integrated luminosity (3.7%),and lepton trigger, reconstruction and identification effi-ciencies (1–2%). Uncertainties from lepton energy/momentumscale and resolution (0.5–1%),  E  missT  modelling (12%), and jet energy scale and resolution [40] (3.6%) are also in-cluded. The SM background uncertainty in the shape of the  m eµ  distribution used to extract the signal is esti-mated by comparing the default  WW   distribution gener-ated with  herwig  [36] to those obtained with  alpgen  [41](interfaced with  jimmy  [42]) and  sherpa  [43]. A 13%uncertainty is assigned. The uncertainties on the  t ¯ t  andsingle-top cross sections are 10% [44] and 9% [45], re- spectively. The theoretical uncertainties assigned to the W/Z   +  γ  ,  Z/γ  ∗ → ττ  ,  WW  ,  WZ  , and  ZZ   cross sectionsare 10%, 5%, 7%, 7%, and 5% respectively; these arisefrom the choice of PDFs, the factorization and renormal-ization scale dependence, and  α s  variations. 6 Limit Setting Since no excess is observed in data, the  m eµ  distributionin Figure 3, with a single bin for  m eµ  >  400 GeV to re-duce sensitivity to statistical fluctuations, is used to setlimits on the production cross section of   eµ  pairs through  4 The ATLAS Collaboration: Search for Lepton Flavour Violation in the  eµ  Continuum     E  v  e  n   t  s   /   2   5   G  e   V 110 2 10 3 10     E  v  e  n   t  s   /   2   5   G  e   V 110 2 10 3 10 = 95 GeV) t~ Signal (mTotal BackgroundTop ττ→ * γ  Z/ Fake BackgroundDiboson ATLAS  1  Ldt = 2.1 fb ∫   [GeV] µ e m 01002003004005006007008009001000    D  a   t  a   /   S 0.511.5    /   1   6   )      π     E  v  e  n   t  s   /   ( 10 2 10 3 10 4 10    /   1   6   )      π     E  v  e  n   t  s   /   ( 10 2 10 3 10 4 10 = 95 GeV) t~ Signal (mTotal BackgroundTop ττ→ * γ  Z/ Fake BackgroundDiboson ATLAS  1  Ldt = 2.1 fb ∫   [rad] µ e, φ∆ 00.511.522.53    D  a   t  a   /   S 0.511.5     E  v  e  n   t  s   /   1   0   G  e   V 110 2 10 3 10     E  v  e  n   t  s   /   1   0   G  e   V 110 2 10 3 10 = 95 GeV) t~ Signal (mTotal BackgroundTop ττ→ * γ  Z/ Fake BackgroundDiboson ATLAS  1  Ldt = 2.1 fb ∫   [GeV] missT E 050100150200250300350400    D  a   t  a   /   S   M 0.511.5       E  v  e  n   t  s 10 2 10 3 10 4 10     E  v  e  n   t  s 10 2 10 3 10 4 10 = 95 GeV) t~ Signal (mTotal BackgroundTop ττ→ * γ  Z/ Fake BackgroundDiboson ATLAS  1  Ldt = 2.1 fb ∫   Number of Jets 0123>=4    D  a   t  a   /   S   M 0.511.5 Fig. 2.  Observed distributions of dilepton invariant mass ( m eµ ), dilepton azimuthal opening angle ( ∆φ eµ ),  E  missT  and numberof jets after object selection (‘preselection’). The expected SM contributions, obtained as described in the text, with combinedstatistical and systematic uncertainties, are shown. In addition, the expected signal for  m ˜ t  = 95 GeV is overlaid. For eachcase, a plot of the ratio of observed events to the expected background is shown. The error bars on these points represent thestatistical errors on the data points and the hashed boxes represent the total error (statistical and systematic) on the expectedbackground. t -channel exchange of  ˜ t  in RPV SUSY models. A mod-ified frequentist approach, using a binned log-likelihoodratio (LLR) of the signal-plus-background hypothesis tothe background only hypothesis [46], is used to set the95% confidence level (CL) upper limits. Confidence lev-els, CL s+b  and CL b , are defined by integrating the nor-malized probability distribution of LLR values from theobserved LLR value to infinity for the two hypotheses.Since no data excess is observed, the production cross sec-tion is excluded at 95% CL when 1 − CL s+b / CL b  = 0 . 95.The limits take into account systematic uncertainties byconvolving the Poisson probability distributions for sig-nal and background with the probability distributions forthe corresponding uncertainty, which are assumed to beGaussian.The upper limit on the production cross section for  pp  →  eµX   through the  t -channel exchange of a ˜ t  at 95%CL is shown in Fig. 4(a). For a ˜ t  with mass of 95 GeV(1000 GeV), the limit on the production cross sectionis 170 (30) fb which is in agreement with the expectedlimit of 180 +80 − 60  (30 +11 − 10 ) fb. The theoretical cross sectionfor  | λ ′ 131 λ ′ 231 |  =  | λ ′ 132 λ ′ 232 |  = 0 . 05 is also shown to illus-trate the sensitivity.The fraction of events produced by the  d ¯ d  →  eµ ( s ¯ s  →  eµ ) process is predicted to be  f  d ¯ d  = 0 . 72 ( f  s ¯ s  =0 . 28) using the pythia generator with the central CTEQ6L1PDF set and with  m ˜ t  = 95 GeV. The cross section for thesignal process is hence proportional to the PDF-weightedsum of the RPV couplings, which is  f  d ¯ d  ×| λ ′ 131 λ ′ 231 | 2 + f  s ¯ s  ×| λ ′ 132 λ ′ 232 | 2 . The cross section limits set above canbe interpreted as a limit on the plane spanned by the sumof couplings and  m ˜ t . The resulting two-dimensional 95%confidence limit is shown in Fig. 4(b).
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