Measurement of the ϒ ( 1 S ) production cross-section in pp collisions at s = 7 TeV in ATLAS

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Measurement of the ϒ ( 1 S ) production cross-section in pp collisions at s = 7 TeV in ATLAS
    a  r   X   i  v  :   1   1   0   6 .   5   3   2   5  v   1   [   h  e  p  -  e  x   ]   2   7   J  u  n   2   0   1   1 CERN-PH-EP-2011-083 Measurement of the  ϒ ( 1 S  )  Production Cross-Section in  pp  Collisions at √  s  =  7 TeV in ATLAS The ATLAS Collaboration Abstract A measurement of the cross-section for  ϒ ( 1 S  ) → µ  + µ  −  production in proton-proton collisions at centreof mass energy of 7 TeV is presented. The cross-section is measured as a function of the  ϒ ( 1 S  )  transversemomentum in two bins of rapidity, |  y  ϒ ( 1 S  ) | <  1 . 2 and 1 . 2  < |  y  ϒ ( 1 S  ) | <  2 . 4. The measurement requires thatboth muons have transverse momentum  p µ  T   >  4 GeV and pseudorapidity  | η µ  | <  2 . 5 in order to reducetheoretical uncertainties on the acceptance, which depend on the poorly known polarization. The resultsare based on an integratedluminosity of 1.13 pb − 1 , collected with the ATLAS detector at the LargeHadronCollider. The cross-section measurementis comparedto theoretical predictions: it agrees to within a factorof two with a prediction based on the NRQCD model including colour-singlet and colour-octet matrixelements as implemented in P YTHIA  while it disagrees by up to a factor of ten with the next-to-leadingorder prediction based on the colour-singlet-model. 1. Introduction The production of   J  / ψ   and  ϒ  mesons has beenstudied since their discovery in the 1970s [1, 2],and even today there is no conclusive coherent the-oreticalpictureofJ/  ψ   and  ϒ hadroproduction. Therearemajorquestionsassociatedwith the consistencyof measurements made at the Tevatron, HERA andfixed target experiments [3]. In particular it is dif-ficult to reconcile the cross section measurementswith those of the spin alignment [3], and there aresignificant disagreements between the two Teva-tron experiments on the measurement of the spinalignment in the case of   ϒ  production [4, 5]. It isthusimportantfortheLHC experimentstomeasurethe productionof these mesons in orderto shed fur-ther light on the puzzle.The CMS collaboration has recently presenteda measurement of   ϒ  production [6], correcting forthe detector acceptance of the two daughter muonsin both angular and momentum range. This ap-proach was also adopted in the ATLAS  J  / ψ   cross-section publication [7]. Correction of the data inthis way introduces uncertainties due to the poorlyknown spin alignment of the  ϒ  (or  J  / ψ  ).With that in mind, a somewhat different ap-proachto the measurementof the  ϒ ( 1 S  )  productioncross-section is adopted in this analysis. The resultis presentedas a functionof transverse momentum,  p T  , and rapidity,  y , of the  ϒ ( 1 S  ) , corrected for de-tector response and efficiencies but defined withina restricted range of muon kinematics where bothmuons have  p µ  T   greater than 4 GeV and absolutepseudorapidity 1 ,  | η µ  | , less than 2.5. The relativefraction of   ϒ ( 1 S  )  mesons where both muons fulfillthe kinematic requirements compared to all  ϒ ( 1 S  ) mesons depends strongly on the spin alignment of the  ϒ ( 1 S  ) . For instance, assuming full transverseor longitudinal spin alignment versus unpolarisedproduction changes this fraction by typically 30%.By quoting the measurement in a restricted regionof phase space where muons are detected, uncer-tainties due to the  ϒ  spin alignment on the mea-surement are almost eliminated so that the quotedcross section is free of any assumptions about thisproperty.A single muon trigger with a threshold of   p µ  T   > 4 GeV is used. This limits the dataset used for thismeasurementto the low luminosityperiodsof 2010correspondingtoanintegratedluminosityof1 . 13 ± 0 . 04 pb − 1 . 1 ATLAS uses a right-handed coordinate system with its ori-gin at the nominal interaction point (IP) in the centre of the de-tector and the  z -axis along the beam pipe. The  x -axis pointsfrom the IP to the centre of the LHC ring, and the  y  axis pointsupward. Cylindrical coordinates  ( r  , φ  )  are used in the trans-verse plane,  φ   being the azimuthal angle around the beam pipe.The pseudorapidity is defined in terms of the polar angle  θ   as η  = − lntan ( θ  / 2 ) . Preprint submitted to Physics Letters B June 28, 2011  In the following sections, a brief description of the ATLAS detector is given with emphasis on theaspects most relevant to this analysis. Next themeasurementstrategyis outlined,followedbya de-scription of the Monte Carlo simulation used. Theevent selection and the determination of the num-ber of   ϒ ( 1 S  )  events are then described before theresults are presented, and a conclusion is given. 2. The ATLAS Detector The ATLAS detector [8] consists of an innertracker, a calorimeter and a muon system. The in-ner detector (ID) directly surrounds the interactionpoint; it includes a silicon pixel detector (Pixel), asilicon strip detector (SCT) and a transition radia-tiontracker(TRT),andisembeddedinansolenoidal2 T magnetic field. The ID covers the range | η | < 2 . 5 and is enclosed by a calorimeter system con-taining electromagneticand hadronicsections. Thecalorimeter is surrounded by a large muon spec-trometer(MS)inside an air-coretoroidmagnetsys-temwhichcontainsacombinationofmonitoreddrifttubes (MDT) and cathode strip chambers (CSC),designed to provide precise position measurementsin the bending plane and covering the range | η | < 2 . 0 and 2 . 0  < | η | <  2 . 7, respectively. In addition,resistive plate chambers (RPC) and thin gap cham-bers (TGC) with a coarse position resolution buta fast response time are used primarily to triggermuons in the rapidity ranges | η | < 1 . 05 and 1 . 05 < | η | <  2 . 4, respectively. Momentum measurementsin the MS are based on track segments formed sep-arately in at least two of the three station layers of the MDT and the CSC. TheRPC and TGC are usedto improve the pattern recognition and track recon-struction in the non-bending plane. They do notimprove the position measurement in the bendingplane.Thefirst level muontriggerlooksfor hit coinci-dences within different RPC or TGC detector lay-ers inside programmed geometrical windows thatdefinethemuon  p T   andprovidea roughestimate of their positions [9]. The lowest available  p T   thresh-old is used for this analysis. In addition, muonsare required to pass a high-level trigger selectionsimilar to that of the offline reconstruction and atransverse momentum threshold of   p µ  T   >  4 GeV. 3. Outline of the Measurement The differential  ϒ ( 1 S  )  cross-section is given asd 2 σ  d  p T  d  y × BR (  ϒ ( 1 S  ) → µ  + µ  − ) =  N   ϒ ( 1 S  )   L   d t  × ∆  p T  × ∆  y ,  (1)where   L   d t   is the integrated luminosity, and  ∆  p T  and  ∆  y  are the bin sizes in  p  ϒ ( 1 S  ) T   and  y  ϒ ( 1 S  ) , re-spectively.  N   ϒ ( 1 S  )  is the corrected number of   ϒ ( 1 S  ) mesons. It is determined with an unbinned maxi-mum likelihood fit to the dimuon mass distributionafter applying a weight to each candidate that isthe inverse of its selection efficiency as describedin Section 5. The cross section is defined withinthe fiducial cuts  p µ  T   >  4 GeV and  | η µ  | <  2 . 5 onboth muons, where the  µ   kinematics are those be-fore any final state QED radiation.The key aspects of this measurement are the ef-ficiency determination and the fit to extract  N   ϒ ( 1 S  ) .These are described in detail in Sections 5 and 6,respectively.The effect of bin migrations due to finite detec-tor resolution and final state photon radiation hasbeen studied. Given the good muon momentumresolution of   σ  (  p T  ) /  p T   <  0 . 5% in the momentumrange relevant for this analysis [10] and the rela-tively coarse binning used for this measurement,the bin migrations due to detector resolution andfinal state radiation are smaller than 2% in all bins.This 2% also accountsfor the migrationsacross the  p µ  T   and  η µ  cuts. This small effect is not correctedfor and therefore considered as part of the system-atic uncertainty, which is discussed in Section 7.Any residual impacts of the assumption on the  ϒ polarization have also been assessed and are withinthis 2% uncertainty. 4. Monte Carlo Simulation In this analysis, all efficiency factors are deter-mined directly from the data. The differentialcrosssection expressed in Eq. 1 does not need any largeacceptance corrections which would require a de-tailed modelling of the kinematic properties of theevents. Monte Carlo (MC) simulation is only usedto construct templates for the likelihood fits to thedimuon mass distribution, and to assess the correc-tions due to migrations between  p  ϒ ( 1 S  ) T   and  y  ϒ ( 1 S  ) bins.MC events are generated using P YTHIA 6[11]with the ATLAS MC09 tune[12] and MRST2  LO ⋆ [13] parton distribution functions. Theyare simulated with the ATLAS simulation frame-work [14] using G EANT 4 [15] and fully recon-structed with the same software that is used to pro-cess the data from the detector.For the  ϒ  MC samples, P YTHIA 6’s implemen-tation of   ϒ  production subprocesses using the non-relativisticQCD(NRQCD)[16]frameworkandtheparameters recommended in Ref. [17] are used.In this model, quarkonium is produced in both acolour-singlet and a colour-octet state, and evolvesnon-perturbativelyinto physical quarkonium. Each  ϒ ( nS  )  state is generated separately and includes di-rect production from the hard interaction, as wellas production through radiative feed-down from  χ  b ( nP ) →  ϒ ( nS  ) γ   decays. The samples are gen-erated without polar or azimuthal anisotropy in thedecay of the  ϒ  (the default in P YTHIA ).Background contributions come mainly fromopen production of charm and bottom quarks withsubsequent decay of the  c - or  b -hadron to a muon.A further, much smaller contribution comes fromDrell-Yan production. These continuum back-groundsaredescribedusingtheminimum-biaspro-cesses in P YTHIA . In order to avoid double-counting, any generated minimum bias events con-taining  ϒ -mesons are explicitly removed from thesample. This backgroundsampleis onlyusedtoes-timate a systematic uncertainty on the backgroundmodelling.In all samples final state QED radiation is con-sidered using P HOTOS  [18] interfaced to P YTHIA . 5. EventSelectionandEfficiencyDetermination Selected events are first requested to satisfy asinglemuontriggerwithathresholdof   p µ  T   > 4GeV.Then two offline muons are required with  p µ  T   > 4 GeV and | η µ  | <  2 . 5.Reconstructed muons that combine a track re-constructed in the MS with a track reconstructedin the ID are referred to as  combined muons  [8].In order to recover efficiency for muons with lowmomenta,  tagged muons  extrapolate an ID track to the muon system and attach MS track segmentsthat are not associated to any MS track. For bothcategories of muons in this analysis, the kinematicpropertiesof the muons are solely determinedfromthe parameters of the ID tracks associated with themuons. At least one of the two offline muons mustbe a combined muon,and at least one of them mustmatch geometrically to a trigger muon. At lowdimuon  p T   about 60% of the events have two com-bined muons, and at high  p T   this fraction increasesto about 90%. Since the measurement is restrictedto |  y  ϒ ( 1 S  ) | <  2 . 4 and  p µ  T   > 4 GeV at least one of thetwo decaymuons is within the trigger pseudorapid-ity acceptance.Both muon tracks are required to have at leastone pixel hit and six SCT hits. Since the  ϒ  is pro-ducedpromptly,backgroundfromheavyflavourde-cays is suppressed by requiring the muons to srci-nate from the primaryvertex. Cuts requiring | d  0 | < 150  µ  m and |  z 0 | sin θ   <  1 . 5 mm are applied where d  0  (  z 0 ) is the impact parameter with respect to theevent vertex in the transverse (longitudinal) direc-tion. The event vertex is required to have at leastthree associated tracks to reject background due tocosmic ray muons. The two selected muons arefurther required to have opposite electric charge.The muon trigger and reconstruction efficien-cies are determined using the high statistics  J  / ψ  data sample [19] as a function of   p µ  T   and  η µ  . Fora singlemuon,the triggerefficiencyvariesbetween40%and90%overtherelevant  p µ  T   and η µ  range[19,9]. Using the single muon trigger, this results in anaverage trigger efficiency for the selected dimuonevents between 80% and 95% in any measurementbin. Within the kinematic range considered in thismeasurement, the offline muon reconstruction ef-ficiency varies with  p µ  T   and  η µ  between 80% and100%. The small gaps in the muon acceptance atcertain  η  regions (mostly at | η |≈ 0 and | η |≈ 1 . 3)are correctedfor as part of the efficiency correctionassuming the nearly flat  η  dependence predictedby the simulation, and represent a small fractionof the total angular range. The efficiency of thepixel and SCT hit requirements has been measuredusing  J  / ψ   mesons as 99 . 5 ± 0 . 5% per track, andthe efficiency of the primary vertex requirement is > 99 . 9%. The  z 0 sin θ   cutefficiencyis nearly100%in both data and MC.Theefficienciesofthetransverseimpactparam-etercutaredeterminedusingtwoindependentmeth-ods. Theimpactparameterresolutionis sensitivetothe alignment of the ID and to the multiple scatter-ing in the ID volume. The former dominates theresolution at high  p µ  T   while the latter dominates atlow  p µ  T  . The primary method to determine the res-olution uses muons from  J  / ψ   decays and fits theimpact parameter distribution using templates con-structed from prompt and non-prompt  J  / ψ   MC.In order to allow for small deviations of the ob-served resolution with respect to the MC, an ad-ditional  d  0  resolution smearing parameter is intro-duced. This smearing parameter is of order 10 µ  mdueto imperfectionsinthe materialdescriptionandtracker alignment. The efficiency determined with3  this method agrees well with the simulation and isabout 99.5% in the central region, decreasing to96.5% at the highest  η µ  and lowest  p µ  T  . The sec-ond method uses  Z  -bosons to determine the impactparameter resolution at high  p µ  T  , and translates itto the low  p µ  T   region using the known dependenceof the resolution on  p µ  T   also taking into accountthe uncertainty on the material distribution withinthe ID [20]. The efficiencies measured using the  J  / ψ  → µ  + µ  −  decaysareusedforthecentralvalue,and the differencebetween the two methods is con-sideredasasystematicuncertaintyonthemuonim-pact parameter cut efficiency. It is less than 1% for | η µ  | <  2, and 1 . 5 − 2 . 5% for  | η µ  | >  2 dependingon  p µ  T  .The efficiencies are accounted for in the crosssection measurement by applying a weight to eachcandidate. The weight is given by the inverse of the event selection efficiency,  w  =  1 / ε  µµ  , which isevaluated from the single-muon trigger and recon-struction efficiencies as ε  µµ   =  ε  trig ε  reco  (2)where the individual terms are given by ε  trig  =  1 − ( 1 − ε  + trig )( 1 − ε  − trig )  (3) ε  rec  =  ε  + cb || tag ε  − cb || tag − ε  − tag ε  + tag  (4)Here  ε  + trig  and  ε  − trig  are the trigger efficienciesfor a positively and negatively charged muon, re-spectively.  ε  + cb || tag  ( ε  − cb || tag )  and  ε  + tag  ( ε  − tag )  give thesingle muon reconstruction efficiencies for a com-binedor taggedor just a taggedmuon, respectively,forpositively(negatively)chargedmuons. Foreachmuon the efficiency is determined as a function of   p T  ,  η  and the electric charge. The final weightsspan the range from about 1.4 at low  p T   to 1.1 athigh  p T  . 6. DeterminationoftheNumberof   ϒ ( 1 S  ) Events Thenumberof   ϒ ( 1 S  ) eventsis determinedfroman unbinned maximum likelihood fit to the dimuonmassdistributionsineachbinin  p µµ  T   and  y µµ  where  p µµ  T   (  y µµ  ) is the  p T   (  y ) of the dimuon system. Thedistributionsandcorrespondingfitresultsareshownfor four representative kinematic bins in Fig. 1.The shape of these distributions is rather com-plex. The background varies substantially over theconsidered mass range and its shape changes sig-nificantly depending on the kinematic bin. At low  p µµ  T   , the background increases sharply with  m µµ  and is significant in the  ϒ ( 1 S  )  mass range. At high  p µµ  T   , the background is nearly independent of thedimuon mass and also relatively low compared tothe signal. Additionally, the  ϒ ( 1 S  )  signal is notwell separated from the  ϒ ( 2 S  )  and  ϒ ( 3 S  ) , partic-ularly in the forward region (1 . 2  < |  y µµ  |  <  2 . 4),due to the limited track momentumresolution [21].Resolving the  ϒ ( 2 S  )  and  ϒ ( 3 S  )  is even more dif-ficult, and thus measurements of   ϒ ( 2 S  )  and  ϒ ( 3 S  ) production are not presented in this letter.A template based likelihood fit method is em-ployed where four parameters are fitted indepen-dently in each kinematic bin: the numbers of   ϒ ( 1 S  ) ,  ϒ ( 2 S  )  and  ϒ ( 3 S  )  mesons, and a backgroundnormalisation parameter. The three  ϒ  signal tem-plates aretakenfromthecorresponding  ϒ MC sam-ples. The background templates are constructedfrom data by pairing a muon with a track recon-structed in the ID of opposite electric charge (OS)that passes the ID track selection requirements de-scribedinSection5andthekinematicrequirementsof   p T   >  4 GeV and | η | <  2 . 5. This template (de-noted as “OS  µ  +track”) gives an adequate descrip-tion of the background since its shape is primar-ily determined by the kinematic selection require-ments. The  ϒ  signal contamination in this sampleis expected to be negligible.The fit results for  N   ϒ ( 1 S  )  are given in Fig. 1 forfourkinematic bins. The goodnessof fit is assessedby a  χ  2 test comparingthe data to the template dis-tributions using the normalisations determined bythe likelihoodfit to thedata. Inall binsthe  χ  2 prob-ability is  >  5%.Alternative templates for the shape of the back-ground are constructed using dimuon events in  b ¯ b and  c ¯ c  MC or  µ  +track events with the same elec-tric charge (SS  µ  +track). A comparison of thesealternative background templates shapes is shownin Fig. 2 for two representative bins. The shapesof the alternative templates are similar to the de-fault template at both low and high  p T  , and anydifferences are considered as part of the systematicuncertainty, as discussed in Section 7.The momentum resolution is determined fromcosmic rays,  J  / ψ   and  Z   mass distributions[21] andthe central mass value for the  ϒ ( 1 S  )  is fixed to theexpectedvalue[22]. The validityoffixingthe massresolution and the overall mass scale is consideredas part of the systematic uncertainty, as describedin Section 7. 7. Systematic Uncertainties The followingsystematic uncertaintiesare con-sidered:4   [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   1   0   0   M  e   V 020406080100120140 [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   1   0   0   M  e   V 020406080100120140 Data 2010Fit result(1S)  ϒ (2S)  ϒ (3S)  ϒ Background -1  L dt = 1.13 pb ∫  ATLAS   25 ± = 246 (1S)  Υ N /ndf = 43.3/52 2 χ  < 4 GeV µµ T  2 GeV < p| < 1.2 µµ |y (a)  [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   2   0   0   M  e   V 010203040506070 [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   2   0   0   M  e   V 010203040506070 Data 2010Fit result(1S)  ϒ (2S)  ϒ (3S)  ϒ Background -1  L dt = 1.13 pb ∫  ATLAS   11 ± = 70 (1S)  Υ N /ndf = 36.3/31 2 χ  < 18 GeV µµ T 14 GeV < p| < 1.2 µµ |y (b)  [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   1   0   0   M  e   V 0102030405060708090100 [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   1   0   0   M  e   V 0102030405060708090100 Data 2010Fit result(1S)  ϒ (2S)  ϒ (3S)  ϒ Background -1  L dt = 1.13 pb ∫  ATLAS   30 ± = 238 (1S)  Υ N /ndf = 55.5/53 2 χ  < 4 GeV µµ T  2 GeV < p| < 2.4 µµ 1.2 < |y (c)  [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   2   0   0   M  e   V 05101520253035404550 [GeV] µµ m678910111213    W  e   i  g   h   t  e   d  e  n   t  r   i  e  s   /   2   0   0   M  e   V 05101520253035404550 Data 2010Fit result(1S)  ϒ (2S)  ϒ (3S)  ϒ Background -1  L dt = 1.13 pb ∫  ATLAS   12 ± = 71 (1S)  Υ N /ndf = 37.3/31 2 χ  < 18 GeV µµ T 14 GeV < p| < 2.4 µµ 1.2 < |y (d)Figure 1: Dimuon mass distributions for four representative bins in  y µµ  and  p µµ  T   . The data (filled circles) are shown together withthe result of the unbinned maximum likelihood fit (histogram) as explained in the text. The shaded histogram shows the backgroundcontribution, and the three other histograms show the contributions from the three  ϒ  states. All histograms are normalised by thefactor determined in the fit. In the individual plots, the fitted  N   ϒ ( 1 S  )  yield with its statistical uncertainty, the  χ  2 and the number of degrees of freedom are also given. It should be noted that this is simply a binned graphical representation of the fit; the actual fit isunbinned and interpolates the template histograms to obtain the input probability density function. 5
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