Measurement of Bose-Einstein correlations with first CMS data

Bose-Einstein correlations have been measured using samples of proton-proton collisions at 0.9 and 2.36 TeV center-of-mass energies, recorded by the CMS experiment at the CERN Large Hadron Collider. The signal is observed in the form of an enhancement of pairs of same-sign charged particles with small relative four-momentum. The size of the correlated particle emission region is seen to increase significantly with the particle multiplicity of the event.


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In particle collisions, the space-time structure of the hadronization source can be studied using measurements of Bose-Einstein correlations (BEC) between pairs of identical bosons. Since the first observation of BEC fifty years ago in proton-antiproton interactions [1], a number of measurements have been made by several experiments using different initial states; a detailed list of the experimental results can be found in [2,3]. Boson interferometry at the Large Hadron Collider provides a powerful tool to investigate the space-time structure of the particle emission source on femtometric length scales at different center-of-mass energies and with different initial states, using the same detector. This letter reports the first measurement of BEC parameters in pp collisions at 0.9 and 2.36 TeV 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 between final-state particles is quantified by the Lorentz-invariant quantity Q = −(p 1 − p 2 ) 2 = M 2 − 4m 2 π , where M is the invariant mass of the two particles, assumed to be pions with mass m π . The BEC effect is observed as an enhancement at low Q of the ratio of the Q distributions for pairs of identical particles in the same event, and for pairs of particles in a reference sample that by construction is expected to include no BEC effect: which is then fitted with the parameterization In a static model of particle sources, Ω(Qr) is the Fourier transform of the spatial distribution of the emission region of bosons with overlapping wave functions, characterized by an effective size r. It is often parameterized as an exponential function, Ω(Qr) = e −Qr , or with a Gaussian form, Ω(Qr) = e −(Qr) 2 ( [4] and references therein). The parameter λ reflects the BEC strength for incoherent boson emission from independent sources, δ accounts for long-range momentum correlations, and C is a normalization factor.
The data used for the present analysis were collected by the CMS experiment in December 2009 from proton-proton collisions at center-of-mass energies of 0.9 and 2.36 TeV. A detailed description of the CMS detector can be found in [5]. The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a uniform magnetic field of 3.8 T. The inner tracking system is the most relevant detector for the present analysis. It is composed of a pixel detector with three barrel layers at radii between 4.4 and 10.2 cm and 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 pseudorapidity |η| = 2.5. The transverse-momentum (p T ) resolution, for 1 GeV 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 generated using PYTHIA (with D6T tune) [7] followed by full detector simulation based on the Geant4 program [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 > 200 MeV, which is sufficient for particles emitted from the interaction region to cross all three barrel layers of the pixel detector and ensure good two-track separation. Their pseudorapidity is required to satisfy |η track | < 2.4. To ensure high purity of the primary track selection, the trajectories are required to be reconstructed in fits with more than five degrees of freedom (dof) and χ 2 /N dof < 5.0. The transverse impact parameter with respect to the collision point is required to satisfy |d xy | < 0.15 cm. The innermost measured point of the track must be less than 20 cm from the beam axis , in order to reduce electrons and positrons from photon conversions in the detector material and secondary particles from the decay of long-lived hadrons (K 0 S , Λ, etc.). In a total of 270 472 (13 548) events selected at 0.9 (2.36) TeV center-of-mass energy, 2 903 754 (188 140) tracks are accepted by these selection criteria.
All pairs of same-charge particles with Q between 0.02 and 2 GeV are used for the measurement. The lower limit is chosen to avoid cases of tracks that are duplicated or not well separated, while the upper limit extends far enough beyond the signal region to verify a good match between signal and reference samples. A study with simulated data shows that the ratio of the tracking efficiencies of particle pairs in the signal and in the reference samples is independent of 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 (attraction), is corrected for by using Gamow factors [9]. As a cross-check, the enhancement in the production of opposite-charge particle pairs with small values of Q is measured in the data and is found to be reproduced by the Gamow factors to within ±15%.
Different methods are designed to pair uncorrelated charged particles and to define reference samples 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 in the same-charge combinations. Opposite-hemisphere pairs: tracks are paired after inverting in space the three-momentum of one of the two particles: (E, p) → (E, − p) ; this procedure is applied to pairs with same and opposite charges. Rotated particles: particle pairs are constructed after 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 are combined with the following methods: i) events are mixed at random; ii) events with similar charged particle multiplicity in the same η regions are selected; iii) events with an invariant mass 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 reference samples are shown in Fig. 1 both for data and simulation without BEC. A significant excess at small values of Q is observed in the data. Additional details are given in [10]. In order to reduce the bias due to the construction of the reference samples, a double ratio R is defined: where the subscripts "MC" and "MC,ref" refer to the corresponding distributions from the MC simulated data generated without BEC effects.
The results of fits of R(Q) based on the parameterization of Eq. (2) with Ω(Qr) = e −Qr are given in Table 1, both for 0.9 and 2.36 TeV data. In the case of the opposite-charge sample, it is found that the region with 0.6 < Q < 0.9 GeV, containing a sizeable contribution of pairs from ρ → π + π − decays, is not well described by the MC [10]. This region is therefore excluded from the fits with this reference sample and also with the combined sample defined below.
As a cross-check, the dE/dx [11] measurements of particles in the tracker are used to select a sample enriched in ππ pairs, and another sample with one of the particles not consistent with the pion hypothesis. Figure 2 presents the double ratios for these two samples at √ s = 0.9 TeV, 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, "combined" double ratio R comb is formed, where the data and MC distributions are obtained by summing the Q distributions of the seven corresponding reference samples.
The distributions of R comb for 0.9 and 2.36 TeV data are shown in Fig. 3, and the values of the fit parameters are given in Table 1. A large correlation is found between the parameters λ and r, as well as between δ and C (correlation coefficients of 0.82 and −0.97 at 0.9 TeV, respectively). The data are described by Eq. (2) with an exponential form for Ω(Qr), as shown by the solid lines in 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 describe the R(Q) distribution, as shown by the dashed lines in Fig. 3 and by a p value of 10 −21 . Gaussian shape fits also proved to offer a poor description of the data in previous measurements [12][13][14]. Although the values of r obtained in the exponential fits cannot be compared directly with results obtained with a Gaussian function, it should be noted for comparison purposes that the first moment of the Ω(Qr) distribution corresponds to 1/r for an exponential shape and to 1 r √ π for a Gaussian form. Alternative functions, as defined in [13,15,16] , also describe the data well with similar p values. In particular for the Lévy parameterization, Ω(Qr) = e −(Qr) α , the fitted values are λ = 0.93 ± 0.11, r = 2.46 ± 0.38 fm, and α = 0.76 ± 0.06, with a p value of 12.8%.  The leading source of systematic uncertainty on the measurements arises from the fact that none of the reference samples is expected to give a perfect description of the Q distribution in the absence of BEC, and that none of them can be preferred or discarded a priori. The corresponding contribution to the systematic error is computed as the r.m.s. spread between the results obtained for the different samples, i.e., ±7% for λ and ±12% for r. The systematic uncertainty related to the Coulomb corrections is computed by propagating the measured ±15% agreement margin, resulting in ±2.8% variation for λ and ±0.8% for r. The presence of a possible bias introduced by the track reconstruction and selection requirements was studied by comparing the results obtained at the generator and reconstruction levels in the MC simulation that incorporates BEC effects. The differences in the fitted parameter values for the different reference samples are smaller than the statistical errors and no systematic bias is observed for r. No correction is therefore applied and no additional systematic error is included. For the 2.36 TeV data the same relative systematic uncertainties as for the 0.9 TeV results are used, in view of the reduced size of the sample and the larger statistical uncertainties of the fit results.
The possible dependence of the BEC signal on various track and event observables has been studied. A significant dependence of r on the charged-particle multiplicity in the event is observed for all reference samples. Here, the only mixed-event reference sample used is the one constructed by combining charged particles from events in the same multiplicity range. The fit parameters for the combined reference sample are given in Table 2 and shown in Fig. 4 as a function of the track multiplicity for the 0.9 TeV data. As an example, the results for the opposite-hemisphere, same-charge reference sample are also shown in Fig. 4. The systematic errors on λ and r in each multiplicity bin are taken as the r.m.s. spread of the results obtained with the various reference samples. Due to the limited sample size of the 2.36 TeV data only two multiplicity bins are considered, one for multiplicities smaller than 20 tracks, the other for multiplicities between 20 and 60 tracks. The values measured for the parameters with the combined reference samples are λ = 0.65 ± 0.08 and λ = 0.85 ± 0.17, and r = 1.19 ± 0.17 fm and r = 2.85 ± 0.38 fm for these two multiplicity bins, where the errors are statistical only. For comparison, the values obtained for the same multiplicity bins at 0.9 TeV are λ = 0.65 ± 0.02 and λ = 0.63 ± 0.05, and r = 1.25 ± 0.05 fm and r = 2.27 ± 0.12 fm, respectively. These measurements are consistent within errors. The dependence of r on multiplicity was already observed in previous measurements as discussed in detail in [3].
In summary, Bose-Einstein correlations have been measured for the first time at the LHC by the CMS experiment in pp collisions at 0.9 and 2.36 TeV center-of-mass energies. Several reference samples were used to extract the signal. For all of them an exponential shape fits the data Table 2: Results of the fits to the double ratio R comb for the combined reference samples, using the parameterization of Eq. (2) with the exponential form, as a function of the charged-particle multiplicity in the event, for 0.9 TeV data. Errors are statistical only, except for λ and r where statistical (first error) and systematic uncertainties (second error) are given. significantly better than a Gaussian shape. An increase of the effective size of the emission region with charged-particle multiplicity in the event has been observed.