First Measurement of Bose-Einstein Correlations in Proton-Proton Collisions at s=0.9 and 2.36 TeV at the LHC

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First Measurement of Bose-Einstein Correlations in Proton-Proton Collisions at s=0.9 and 2.36 TeV at the LHC
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  EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP-2010-0102010/05/19 CMS-QCD-10-003 First Measurement of Bose–Einstein Correlations inproton-proton Collisions at √  s  = 0.9 and 2.36TeV at theLHC The CMS Collaboration ∗ Abstract Bose–Einstein correlations have been measured using samples of proton-proton colli-sions at 0.9 and 2.36TeV center-of-mass energies, recorded by the CMS experiment atthe CERN Large Hadron Collider. The signal is observed in the form of an enhance-ment of pairs of same-sign charged particles with small relative four-momentum. Thesize of the correlated particle emission region is seen to increase significantly with theparticle multiplicity of the event. ∗ See Appendix A for the list of collaboration members   a  r   X   i  v  :   1   0   0   5 .   3   2   9   4  v   1   [   h  e  p  -  e  x   ]   1   8   M  a  y   2   0   1   0  1 In particle collisions, the space-time structure of the hadronization source can be studied usingmeasurements of Bose–Einstein correlations (BEC) between pairs of identical bosons. Since thefirst observation of BEC fifty years ago in proton-antiproton interactions [1], a number of mea-surements have been made by several experiments using different initial states; a detailed listof the experimental results can be found in [2, 3]. Boson interferometry at the Large HadronCollider provides a powerful tool to investigate the space-time structure of the particle emis-sion source on femtometric length scales at different center-of-mass energies and with differentinitial states, using the same detector. This letter reports the first measurement of BEC param-eters in  pp  collisions at 0.9 and 2.36TeV with the CMS detector.Constructive interference affects the joint probability for the emission of a pair of identical bosons with four-momenta  p 1  and  p 2 . Experimentally, the proximity in phase space betweenfinal-state particles is quantified by the Lorentz-invariant quantity  Q  =   − (  p 1 −  p 2 ) 2 =    M 2 − 4 m 2 π  , where  M  is the invariant mass of the two particles, assumed to be pions withmass  m π  . The BEC effect is observed as an enhancement at low  Q  of the ratio of the  Q  distribu-tions for pairs of identical particles in the same event, and for pairs of particles in a referencesample that by construction is expected to include no BEC effect: R ( Q ) = ( d N  /d Q ) / ( d N  ref  /d Q ) , (1)which is then fitted with the parameterization R ( Q ) =  C  [ 1  +  λ Ω ( Qr )] · ( 1  +  δ Q ) . (2)Inastaticmodelofparticlesources, Ω ( Qr )  istheFouriertransformofthespatialdistributionof the emission region of bosons with overlapping wave functions, characterized by an effectivesize  r . It is often parameterized as an exponential function, Ω ( Qr ) =  e − Qr , or with a Gaussianform, Ω ( Qr ) =  e − ( Qr ) 2 ([4] and references therein). The parameter  λ  reflects the BEC strengthforincoherentbosonemissionfromindependentsources,  δ accountsforlong-rangemomentumcorrelations, and  C  is a normalization factor.The data used for the present analysis were collected by the CMS experiment in December2009 from proton-proton collisions at center-of-mass energies of 0.9 and 2.36TeV. A detaileddescription of the CMS detector can be found in [5]. The central feature of the CMS appa-ratus is a superconducting solenoid of 6 m internal diameter, providing a uniform magneticfield of 3.8 T. The inner tracking system is the most relevant detector for the present analy-sis. It is composed of a pixel detector with three barrel layers at radii between 4.4 and 10.2cmand a silicon strip tracker with 10 barrel detection layers extending outwards to a radius of 1.1 m. Each system is completed by two endcaps, extending the acceptance up to a pseudo-rapidity  | η |  =  2.5. The transverse-momentum (  p T ) resolution, for 1GeV charged particles, is between 0.7% at  η  =  0 and 2% at | η |  =  2.5. The events were selected by requiring activity in both beam scintillator counters [6]. A minimum-bias Monte Carlo (MC) sample was generatedusing PYTHIA (with D6T tune) [7] followed by full detector simulation based on the Geant4program [8]. Additional PYTHIA MC samples were generated to simulate BEC effects with both Gaussian and exponential forms of  Ω ( Qr ) .Charged particles are required to have  p T  >  200MeV, which is sufficient for particles emittedfrom the interaction region to cross all three barrel layers of the pixel detector and ensure goodtwo-track separation. Their pseudorapidity is required to satisfy | η track |  <  2.4. To ensure highpurity of the primary track selection, the trajectories are required to be reconstructed in fitswith more than five degrees of freedom (dof) and  χ 2 / N  dof   <  5.0. The transverse impact pa-rameter with respect to the collision point is required to satisfy | d xy | < 0.15 cm. The innermost  2 measured point of the track must be less than 20cm from the beam axis , in order to reduceelectrons and positrons from photon conversions in the detector material and secondary par-ticles from the decay of long-lived hadrons ( K  0 S , Λ , etc.). In a total of 270472 (13548) eventsselected at 0.9 (2.36)TeV center-of-mass energy, 2903754 (188140) tracks are accepted by theseselection criteria.All pairs of same-charge particles with  Q  between 0.02 and 2GeV are used for the measure-ment. The lower limit is chosen to avoid cases of tracks that are duplicated or not well sepa-rated, whiletheupperlimitextendsfarenoughbeyondthesignalregiontoverifyagoodmatch between signal and reference samples. A study with simulated data shows that the ratio of thetracking efficiencies of particle pairs in the signal and in the reference samples is independentof   Q  in the measurement region.Coulomb interactions between charged particles modify their relative momentum distribution.This effect, which differs for pairs with same charge (repulsion) and opposite charge (attrac-tion), is corrected for by using Gamow factors [9]. As a cross-check, the enhancement in theproduction of opposite-charge particle pairs with small values of   Q  is measured in the data andis found to be reproduced by the Gamow factors to within ± 15%.Different methods are designed to pair uncorrelated charged particles and to define referencesamples used to extract the distribution in the denominator of Eq. (1).  Opposite-charge pairs :this data set is a natural choice but contains resonances ( η ,  ρ , ...) which are not present inthe same-charge combinations.  Opposite-hemisphere pairs : tracks are paired after inverting inspace the three-momentum of one of the two particles:  ( E ,    p ) → ( E , −    p )  ; this procedure is ap-plied to pairs with same and opposite charges.  Rotated particles : particle pairs are constructedafter inverting the  x  and  y  components of the three-momentum of one of the two particles: (  p x ,  p  y ,  p  z )  →  ( −  p x , −  p  y ,  p  z ) .  Pairs from mixed events:  particles from different events arecombined with the following methods: i) events are mixed at random; ii) events with simi-lar charged particle multiplicity in the same  η  regions are selected; iii) events with an invariantmass of all charged particles similar to that of the signal are used to form the pairs.As an example, the ratios  R ( Q )  obtained with the opposite-hemisphere, same-charge referencesamples are shown in Fig. 1 both for data and simulation without BEC. A significant excess atsmall values of   Q  is observed in the data. Additional details are given in [10]. Q (GeV)00.20.40.60.811.21.41.61.82       R      (      Q      ) 11.11.21.31.41.51.61.7. DataMC Ref.: Opposite hem. same charge  = 0.9 TeVsCMS Figure 1: Ratios  R ( Q )  obtained with the opposite-hemisphere, same-charge reference samplesfor data (dots) and MC with no BEC effect (crosses).In order to reduce the bias due to the construction of the reference samples, a double ratio R isdefined: R ( Q ) =  RR MC =   d N  /d Q d N  ref  /d Q   d N  MC /d Q d N  MC,ref  /d Q  , (3)  3 Table 1: Results of fits to the double ratios R for several reference samples, using the parame-terization of Eq. (2) with the exponential form, for 0.9TeV data (top) and 2.36TeV data (bottom).Errors are statistical only, and quoted as if independent. Results of fits to 0.9TeV dataReference sample  p  value (%)  C  λ  r  (fm)  δ  (10 − 3 GeV − 1 )Opposite charge 21.9 0.988 ± 0.003 0.56 ± 0.03 1.46 ± 0.06  − 4 ± 2Opposite hem. same ch. 7.3 0.978 ± 0.003 0.63 ± 0.03 1.50 ± 0.06 11 ± 2Opposite hem. opp. ch. 11.9 0.975 ± 0.003 0.59 ± 0.03 1.42 ± 0.06 13 ± 2Rotated 0.02 0.929 ± 0.003 0.68 ± 0.02 1.29 ± 0.04 58 ± 3Mixed evts. (random) 1.9 1.014 ± 0.002 0.62 ± 0.04 1.85 ± 0.09  − 20 ± 2Mixed evts. (same mult.) 12.2 0.981 ± 0.002 0.66 ± 0.03 1.72 ± 0.06 11 ± 2Mixed evts. (same mass) 17.0 0.976 ± 0.002 0.60 ± 0.03 1.59 ± 0.06 14 ± 2Combined 2.9 0.984 ± 0.002 0.63 ± 0.02 1.59 ± 0.05 8 ± 2Results of fits to 2.36TeV dataReference sample  p  value (%)  C  λ  r  (fm)  δ  (10 − 3 GeV − 1 )Opposite charge 57 1.004 ± 0.008 0.53 ± 0.08 1.65 ± 0.23  − 16 ± 6Opposite hem. same ch. 42 0.977 ± 0.006 0.68 ± 0.11 1.95 ± 0.24 15 ± 5Opposite hem. opp. ch. 46 0.969 ± 0.005 0.70 ± 0.11 2.02 ± 0.23 24 ± 5Rotated 42 0.933 ± 0.007 0.61 ± 0.07 1.49 ± 0.15 58 ± 6Mixed evts. (random) 23 1.041 ± 0.005 0.74 ± 0.15 2.78 ± 0.36  − 40 ± 4Mixed evts. (same mult.) 35 0.974 ± 0.005 0.63 ± 0.10 2.01 ± 0.23 20 ± 5Mixed evts. (same mass) 73 0.964 ± 0.005 0.73 ± 0.11 2.18 ± 0.23 28 ± 5Combined 89 0.981 ± 0.005 0.66 ± 0.07 1.99 ± 0.18 13 ± 4 where the subscripts “MC” and “MC,ref” refer to the corresponding distributions from the MCsimulated data generated without BEC effects.The results of fits of   R ( Q )  based on the parameterization of Eq. (2) with  Ω ( Qr ) =  e − Qr aregiven in Table 1, both for 0.9 and 2.36TeV data. In the case of the opposite-charge sample, it isfound that the region with 0.6 < Q < 0.9GeV, containing a sizeable contribution of pairs from  ρ → π  + π  −  decays, is not well described by the MC [10]. This region is therefore excluded fromthe fits with this reference sample and also with the combined sample defined below.As a cross-check, the d E /d x  [11] measurements of particles in the tracker are used to select asample enriched in  ππ   pairs, and another sample with one of the particles not consistent withthe pion hypothesis. Figure 2 presents the double ratios for these two samples at √  s  =  0.9TeV,showing that an enhancement at small  Q  values is observed only in the case of identified  ππ  pairs.As none of the definitions of the reference samples is preferable  a priori , an additional, “com- bined” double ratio  R comb is formed, where the data and MC distributions are obtained bysumming the  Q  distributions of the seven corresponding reference samples.The distributions of  R comb for 0.9 and 2.36TeV data are shown in Fig. 3, and the values of the fitparameters are given in Table 1. A large correlation is found between the parameters  λ  and  r , aswell as between  δ  and  C  (correlation coefficients of 0.82 and − 0.97 at 0.9TeV, respectively). Thedata are described by Eq. (2) with an exponential form for Ω ( Qr ) , as shown by the solid linesin Fig. 3 and confirmed by the fit probability (  p  value) in Table 1. The fit with a Gaussian form, Ω ( Qr ) =  e − ( Qr ) 2 , which yields  λ  =  0.32 ± 0.01,  r  =  0.98 ± 0.03 fm, does not correctly describethe R ( Q )  distribution, as shown by the dashed lines in Fig. 3 and by a  p  value of 10 − 21 . Gaus-sian shape fits also proved to offer a poor description of the data in previous measurements[12–14].
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