Pion-kaon femtoscopy and the lifetime of the hadronic phase in Pb − Pb collisions at s NN − − − √ = 2.76 TeV
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN-EP-2020-1268 July 2020© 2020 CERN for the benefit of the ALICE Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.
Pion–kaon femtoscopy and the lifetime of the hadronic phase in Pb − Pbcollisions at √ s NN = 2.76 TeV ALICE Collaboration * Abstract
In this paper, the first femtoscopic analysis of pion–kaon correlations at the LHC is reported. Theanalysis was performed on the Pb–Pb collision data at √ s NN = .
76 TeV recorded with the ALICEdetector. The non-identical particle correlations probe the spatio-temporal separation between sourcesof different particle species as well as the average source size of the emitting system. The sizes ofthe pion and kaon sources increase with centrality, and pions are emitted closer to the centre of thesystem and/or later than kaons. This is naturally expected in a system with strong radial flow and isqualitatively reproduced by hydrodynamic models. ALICE data on pion–kaon emission asymmetryare consistent with (3+1)-dimensional viscous hydrodynamics coupled to a statistical hadronizationmodel, resonance propagation, and decay code THERMINATOR 2 calculation, with an additionaltime delay between 1 and 2 fm / c for kaons. The delay can be interpreted as evidence for a significanthadronic rescattering phase in heavy-ion collisions at the LHC. * See Appendix A for the list of collaboration members a r X i v : . [ nu c l - e x ] J u l ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration The main goal of the heavy-ion programme at the Large Hadron Collider (LHC) is to study the deconfinedstate of strongly interacting matter. This state, where the relevant degrees of freedom are quarks andgluons, is called the quark-gluon plasma (QGP). Experimental results from RHIC suggest that the QGPbehaves as a fluid with small specific viscosity [1–4]. The characteristics in momentum space can beaccessed from radial and elliptic flow, transverse momentum spectra or from event-by-event fluctuations.The space-time structure, relevant for the size and pressure gradients of the system, can be accessed usingtwo-particle correlations.Non-identical particle correlations are sensitive to the relative space-time emission shifts of differentparticle species [5–7].The difference between mean emission space-time coordinates of two particle species at freeze-out is calledemission asymmetry. It occurs as a consequence of the collective expansion of the system, the presenceof short-lived resonances decaying into the considered particles, the radial flow of these resonances,and the possibility of having additional rescattering between the chemical and kinetic boundaries ofthe evolution of the system [7]. Measurements of correlations of non-identical particles in low-energyheavy-ion collisions allowed one to establish an emission time ordering of the nuclear fragments [8, 9]. Inrelativistic heavy-ion collisions they provided independent evidence of collective transverse expansion inAu–Au collisions at √ s NN =
130 GeV at the Relativistic Heavy Ion Collider (RHIC) [10].The Hanbury Brown and Twiss (HBT) [11–16] pion correlation radii are a measure of the source sizeof pions of a given momentum. Together with measurements of the elliptic flow and the transversemomentum spectra of identified particles they have been fundamental in identifying the relevant stagesof ultra-relativistic heavy-ion collisions and their properties [17]. Furthermore, a recent measurement ofthe kaon HBT radii in Pb–Pb collisions [18] showed that (when compared for the same event centralityand pair m T ) they are systematically larger than the ones from pions and those predicted by models basedon a hydrodynamic evolution coupled to statistical hadronization. Only after including the hadronicrescattering phase could the model [19] reproduce the data for pions and kaons simultaneously. Themean emission time of kaons (11.6 fm / c ) and of pions (9.5 fm / c ) were reported [18]. The difference isattributed to the rescattering through the K ∗ resonance.Particle yields and spectra add further support to models which include the formation of a dense hadronicphase in the final stages of the evolution of the fireball created in heavy-ion collisions. The suppression orthe enhancement of the yield (with respect to pp collisions) of short-lived resonances due to rescattering(suppression) or regeneration (enhancement) in the hadronic phase has been proposed as an observable forthe estimation of the lifetime and properties of the hadronic phase [20–22]. The measurements of severalresonances, from the very short-lived ρ meson ( τ = . / c ), K ∗ ( τ = / c ), Λ ( ) ( τ =
10 fm / c )to longer-lived φ ( τ =
46 fm / c ), demonstrate strong suppression of short-lived resonances in centralcollisions [23–25]. The observed suppression can result from a long-lasting hadronic rescattering phase.Recently, pion–kaon correlations were studied theoretically with a (3+1) viscous hydrodynamic model [26],coupled to the statistical hadronization, resonance decay, and propagation code THERMINATOR 2 [28].The model uses a parameterisation of the equation of state interpolating between the lattice results [27]for high temperatures and the hadron gas equation of state at low temperatures. The hadronisation occursvia the Cooper-Frye formalism without distinction between chemical and kinetic freeze-out. No furtherinteractions between the hadrons are considered, however, the emission time of each species can bedelayed by hand, mimicking the effect of rescattering. The femtoscopic emission asymmetry was shownto be highly sensitive to this delay. Moreover, it can be decoupled from other mechanisms like flow orresonance contributions present at freeze-out, including the K ∗ resonance [28]. This approach has beenexplored for pion–kaon pairs. Detailed predictions for different emission scenarios for the pion–kaon radiiand their emission asymmetry as a function of the source volume have been made for Pb–Pb collisions at3ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration √ s NN = 2.76 TeV in [28].In this work π + K + , π − K + , π + K − , and π − K − momentum correlations are analysed using the femtoscopytechnique. Two methods are used to evaluate the emission asymmetry in order to strengthen theresults. The first method decomposes the correlations into terms of one dimensional spherical harmonic(SH) coefficients [29] while the second one is based on the Cartesian representation of the correlationfunction [5]. The source size parameter R out and the emission asymmetry µ out are measured as a functionof the cube root of the average charged-particle multiplicity density (cid:104) d N ch / d η (cid:105) / . Finally, the obtainedresults are compared with detailed model calculations [28] assuming the previously found delayed kaonemission [18]. In this paper, pion–kaon correlation results obtained with Pb–Pb collisions at √ s NN = 2.76 TeV arepresented. This measurement used 40 million events collected by ALICE in 2011. A detailed descriptionof the ALICE detector and its performance in the LHC Run 1 (2009–2013) is given in [30, 31].Events were classified according to their centrality determined using the measured signal amplitudes in theV0 detectors [32]. Three trigger configurations were used: minimum bias, semi-central (10–50% collisioncentrality), and central (0–10% collision centrality) [32]. The analyses were performed in six centralityclasses: (0–5%), (5–10%), (10–20%), (20–30%), (30–40%), and (40–50%), separately for positive andnegative magnetic field polarity. The reconstructed primary vertex is required to lie within ± χ of the track fit,normalized to the number of degrees of freedom, is required to be χ / ndf <
2. The distances of closestapproach (DCA) of a track to the primary vertex in the transverse (DCA xy ) and longitudinal (DCA z )directions are required to be less than 2.4 cm and 3.2 cm, respectively. These selections are imposed toreduce the contamination from secondary tracks originating from weak decays and from interaction withthe detector material. The transverse momenta and pseudorapidities of pions and kaons were restricted to0 . < p T < . / c and | η | < .
8. All selections are summarized in Table 1.The charged-particle tracks are identified as pions and kaons using the combined information of theirspecific ionization energy loss (d E / d x ) in the TPC and the time-of-flight information from the Time-Of-Flight (TOF) detectors [34]. For each reconstructed particle, the signals from both the TPC and the TOF(d E / d x and time of flight, respectively) are compared with the ones predicted for a pion or kaon. A value N σ is assigned to each track denoting the number of standard deviations between the measured trackd E /d x or time of flight and the expected one. For pions, the signal (d E / d x for p T <
500 MeV / c , combinedd E / d x and time of flight above this value) is allowed to differ from the calculation by 3 σ . For kaons, fiveselections were used, as detailed in Table 1, together with variations used for uncertainty estimation. Theselection criteria are optimised to obtain a high-purity sample while maximising efficiency, especially inthe regions where separating kaons from other particle species is challenging. The purity was estimatedfrom Monte Carlo simulations using the HIJING [35] event generator coupled to the GEANT3 [36]transport package and was found to be above 98% for both the pion and kaon samples.The identified tracks from each event are combined into pairs. Two-particle detector acceptance effects,including track splitting, track merging, as well as effects coming from γ → e + e − conversion, contribute4ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration Table 1:
Single particle selection criteria, together with particle identification variations used for uncertaintyestimation.
Track selection p T . < p T < . c | η | < . transverse to primary vertex < . longitudinal to primary vertex < . N σ , TPC (for p < . c ) < < . < N σ , TPC (for 0 . < p < .
45 GeV/ c ) < < < N σ , TPC (for p > .
45 GeV/ c ) < < < N σ , TOF (for 0 . < p < . c ) < < < N σ , TOF (for 0 . < p < . c ) < . < . < . N σ , TOF (for 1 . < p < . c ) < < < N σ , TPC (for p < . c ) < < < . (cid:113) N σ , TPC + N σ , TOF (for p > . c ) < < < . | ∆ η | < . + e − pairs originating from photon conversions can be misidentified as areal pion–kaon pair and it is necessary to remove spurious correlations arising from such pairs. Thesepairs are removed if their invariant mass, assuming the electron mass for both particles, is less than 0.002GeV / c , and the relative polar angle, ∆ θ , between the two tracks is less than 0.008 rad. The femtoscopic correlation function C ( kkk ∗ ) , as a function of the pion and kaon relative three-momenta kkk ∗ = ( ppp ∗ π − ppp ∗ K ) , is constructed as C ( kkk ∗ ) = N A ( kkk ∗ ) B ( kkk ∗ ) , (1)where A ( kkk ∗ ) is the distribution defined in the pair rest frame (PRF) constructed from the same event and B ( kkk ∗ ) is the reference distribution from particles belonging to different events using the event mixingmethod [37]. The normalization constant N is used to ensure that the ratio reaches unity outside themomentum range where the correlation function is affected by final state interactions, i.e. 0 . < k ∗ < . / c , where k ∗ = | kkk ∗ | .The first and second moments of the distribution of the spatio-temporal separation of emission points in thePRF can be obtained from correlation functions either in the three-dimensional Cartesian representation [5]or using its decomposition into spherical harmonics (SH) [29, 38]. The three-momentum and positiondifferences can be projected onto the out-side-long orthogonal axes, where the long axis is the beam axis,the out axis is in the direction of the transverse pair velocity in the laboratory system, while the side axisis perpendicular to the long and out axes [39, 40]. At midrapidity, the emission asymmetry – displacementbetween pion and kaon sources – can exist only in the out direction [28]. In this work, the emissionasymmetry in the out direction is obtained with two different methods and they are explained hereafter.5ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE CollaborationThe SH decomposition allows one to project the three-dimensional information contained in the correlationfunction into a set of one-dimensional distributions. The method applied here uses the direct decompositionof A ( kkk ∗ ) and B ( kkk ∗ ) during the filling of the discrete distributions [29]. The numerator can be written as A ( kkk ∗ ) = √ π ∞ ∑ l = l ∑ m = A ml ( k ∗ ) Y ml ( θ , ϕ ) , (2)where Y ml ( θ , φ ) are the spherical harmonics and A ml ( k ∗ ) = π ´ π A ( k ∗ ) Y ml ∗ ( θ ∗ , ϕ ∗ ) d Ω . A similar defini-tion is valid also for the denominator. The l < Y ml ( θ , ϕ ) weight for its θ and ϕ angles in the PRF. From these one-dimensional distributions, the components of the correlation functioncan be calculated following the method introduced in [29].The femtoscopic information relevant for the emission asymmetry measurement is contained in twoone-dimensional correlation functions, C and the real part of C , where C ij is defined as A ij / B ij . The C and ℜ C functions are mostly sensitive to the source size and the emission asymmetry, respectively [29].Additionally, the values of C (asymmetry in the long direction) and ℑ C are checked for zero emissionasymmetry. Their deviations from zero may indicate track reconstruction problems in the detector. Higherorder components are small and irrelevant for this analysis. The C , ℜ C , and ℑ C components of thecorrelation function in the SH representation are shown in Fig. 1 for the different pairs.For the Cartesian representation analysis, the correlation function was obtained as a function of pionmomentum in the PRF. The reconstructed pairs were divided into two different correlation functions,namely C + ( k ∗ ) and C − ( k ∗ ) , where the sign reflects the sign of k ∗ out . These correlation functions representtwo different scenarios where the first particle (by construction the pion) is faster or slower than the secondone (the kaon). The difference between them reflects the space-time emission asymmetry.It can be observed from Fig. 2 that the correlation function is not exactly equal to unity at large values of k ∗ , but has some intrinsic slope mainly due to the presence of elliptic flow, resonance decays, and dueto global conservation of energy and momentum. These background correlations have to be subtractedbefore fitting the correlation functions in both the SH and Cartesian representations. The procedure toestimate the non-femtoscopic background is described in detail in [41], where it is shown that for π ± K ± pairs the non-femtoscopic baseline can be parameterised by a common 6 th order polynomial function forall pair combinations. The same approach is used to correct the effect of non-femtoscopic background inthe present analysis and the resulting background estimation is shown in Fig. 2 as a solid black line forthe C and ℜ C components of pion–kaon pairs of different charge sign combinations. The experimental correlation functions in both representations are compared to theoretical functionscalculated with the software package CorrFit [42]. These functions are calculated as C ( kkk ∗ ) = ´ S ( r ∗ , KKK ∗ ) | Ψ π K ( r ∗ , kkk ∗ ) | d r ∗ ´ S ( r ∗ , KKK ∗ ) d r ∗ , (3)where the four-vector r ∗ = x ∗ π − x ∗ K is the space-time position difference of a pion and a kaon, S ( r ∗ , KKK ∗ ) isthe source emission function which is the probability of emitting a pair of particles at a given positiondifference and total momentum KKK ∗ . The possible dependence of the source on kkk ∗ has been neglected.This approximation has been proven for radii larger than 1–2 fm [15]. Ψ π K is the pion–kaon pair wavefunction. It accounts for the Coulomb and strong final-state interactions (FSI), the former being dominantfor the correlation effect [28]. 6ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration * ) k ( C = 2.76 TeV NN s Pb - ALICE Pb10% centrality - h , | c < 1.5 GeV/ T p * ) k ( C ´ - - ) c * (GeV/ k * ) k ( C ` - - + K + p - K - p - K + p + K - p Figure 1:
The C (top panel), ℜ C (middle panel), and ℑ C (bottom panel) SH components of the charged pion–kaon femtoscopic correlation functions for Pb–Pb collisions at √ s NN = 2.76 TeV in the 5–10% centrality class,positive field polarity. The different charge combinations of pions and kaons are shown with different colours andmarkers. The statistical and systematic uncertainties are shown as vertical bars and boxes, respectively. In order to be able to compare the resulting radii to those obtained from identical-particle femtoscopy, weparameterise the source in the longitudinally comoving coordinate system (LCMS), defined for each pairsuch that the longitudinal pair momentum vanishes. The relative two-particle source can be expressed as S ( rrr ) ∝ exp (cid:32) − [ r out − µ out ] R − r R − r R (cid:33) , (4)where R out , R side , and R long are the sizes of the system in the three directions and µ out is the emissionasymmetry. In order to avoid a large set of fitting parameters, the relations R side = R out and R long = . R out are used, which are based on measured system sizes from identical pion femtoscopy from the sameexperimental data [16]. In this approach only two independent parameters are needed to characterisethe correlation function for the whole system: µ out and R out . In order to (numerically) compute the fit7ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration * ) k ( C NN s Pb - ALICE Pb10% centrality - h , | c < 1.5 GeV/ T p ) c * (GeV/ k * ) k ( C ´ - - + K + p - K - p - K + p + K - p Background fit
Figure 2:
The C (top panel) and ℜ C (botton panel) components of the pion–kaon correlation functions inthe 5–10% centrality class showing the non-femtoscopic background in the spherical-harmonic representation,positive field polarity. The background fit corresponds to a 6 th order polynomial function common for all chargecombinations. The two structures visible in the correlation function at 0.11 GeV / c and at 0.28 GeV / c correspondto the remaining effect from track merging and the K ∗ resonance, respectively. The statistical and systematicuncertainties are shown as vertical bars and boxes, respectively. function corresponding to Eq. 3, the relative positions between pions and kaons are sampled from Eq. 4,while their momenta are sampled from the respective experimental distributions from the same data set.The positions and momenta are then boosted from the LCMS to the PRF. The fit value is the mean wavefunction squared in the PRF.The fitting procedure also accounts for the purity of the sample, defined as the percentage of the properlyidentified primary particle pairs originating from the 3D Gaussian profile, referred to as the “Gaussiancore”. Products of decays of long lived resonances are considered as not correlated. Following the methodproposed in [7], the values for the purity parameter depend on the misidentification ( p ), on the secondary8ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration ) c * (GeV/ k * ) k ( C = 2.76 TeV NN s Pb - ALICE Pb 10% - Centrality 5 | < 0.8 h , | c < 1.5 GeV/ T p ) c * (GeV/ k * ) k ( C ´ - K - p Fit ) c * (GeV/ k * ) k ( C = 2.76 TeV NN s Pb - ALICE Pb 10% - Centrality 5 | < 0.8 h , | c < 1.5 GeV/ T p ) c * (GeV/ k * ) k ( C ´ - - - - + K - p Fit
Figure 3:
The C ( k ∗ ) and ℜ C ( k ∗ ) parts of the correlation function for (left) π − K − and (right) π − K + pairs, shownas markers for the 5–10% centrality, with the corresponding fits calculated using the CorrFit package shown asdashed lines. Only half of the statistics is used, corresponding to one magnetic field (positive field polarity). Thestatistical and systematic uncertainties are shown as vertical lines and boxes, respectively. contamination from weak decays ( f ), and on the percentage of pions and kaons that come from stronglydecaying resonances constituting the long-range tails in the source distribution, outside the Gaussian core( g ). The purity is evaluated independently for each centrality class and magnetic field polarity and isdefined as: P π ± K ± = p π ± · p K ± · f π ± · f K ± · g . (5)All parameters except g are obtained from a detailed simulation of the detector response obtained with theHIJING Monte Carlo model with particle transport performed by GEANT3. The g values are taken froma calculation in [7] following the methodology used in [28]. The total value of the primary fraction is 0.73for the 0–5% centrality class and decreases smoothly to 0.61 for the 40–50% centrality class.The experimental finite momentum resolution has been incorporated in the fitting procedure. The idealthree-momenta of 20 000 randomly selected pairs from analysed data per k ∗ bin used in the fitting routinewere smeared by the momentum-dependent experimental momentum and angular resolutions. These wereobtained from Monte Carlo simulations using a detailed description of the experimental set-up.Each of the correlation functions obtained for the six event centralities, four charge combinations, andtwo polarities of the electric field have been fitted independently. The values of the radii and emissionasymmetry are obtained using a χ minimization in the R out − µ out plane. The fitting is done in the range0 < k ∗ < . / c using the CorrFit package [42]. A fit example of the C ( k ∗ ) and ℜ C ( k ∗ ) parts ofthe correlation function for π − K − and π − K + is shown in Fig. 3.To include variations due to statistical uncertainty, as well as possible correlation between parameters, thesystematic uncertainty is estimated using the covariance ellipses method. For each of the eight fit results(pair combinations and magnetic field polarities) as well as for each systematic variation, 10 points aregenerated following a two-dimensional Gaussian distribution in the R out – µ out space, where the mean and9ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration - * ) k ( C + K + p = 2.76 TeV NN s Pb - ALICE Pb - datafit - K - p - Centrality 5 | < 0.8 h , | c < 1.5 GeV/ T p - ) c * (GeV/ k · *) out k sign( * ) k ( C - K + p - ) c * (GeV/ k · *) out k sign( + K - p Figure 4:
Pion–kaon correlation functions in the Cartesian representation for all charge combinations. The C − ison the negative side of the k ∗ axes while C + is on the positive. The femtoscopic fits are shown as a solid blue lineand were computed using the CorrFit package. The statistical and systematic uncertainties are shown as verticallines and boxes, respectively. covariance are taken from the fit. The covariance ellipses are calculated from the sample of generatedpoints in each centrality bin. The systematic uncertainties used for the final result are obtained using 1 σ covariance ellipses. Negligible correlation between R out – µ out parameters is observed.The systematic uncertainties are estimated by varying the particle identification and selection, thenormalisation range of the correlation functions, the background fit range of the polynomial that is used forestimation of non-femtoscopic contributions, the fit range, and the momentum resolution parameters usedfor smearing. Values of these variations and their individual contributions to the systematic uncertainty aresummarized in Table 2. All the systematic uncertainties are evaluated independently for each centralityclass and the maximum value is reported in the table. The primary pair fractions are treated separately.They introduce a significant and correlated systematic error for all centralities. Additionally, the analysiswas done in the Cartesian representation using the projected C + and C − correlation functions shown inFig. 4. The results of this analysis are fully compatible with those from SH within uncertainties. However,these results are not incorporated as another source of systematic uncertainty since the Cartesian methodyields significantly smaller statistical sensitivity to the µ out parameter.Fits to correlation functions considering only Coulomb interaction show a systematic and centrality-dependent decrease for R out of the order of 33% with a significantly reduced χ of the fit. For this reasonthese are not included in the evaluation of the uncertainties. However, the effect on the asymmetryparameter, supporting the prediction made in [28], is about 9%, in line with other variations and10ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration Table 2:
Input parameters to CorrFit used to fit the correlation functions and variation of relevant parameters andranges used for the evaluation of the systematic uncertainties.The uncertainties were estimated for all the centralityranges independently and maximum value is reported. The variation of primary pair fractions was not included inthe covariance ellipse calculation and is shown separately as a correlated model-dependent systematic uncertaintyindicated with a † symbol. Uncertainties from fits using only Coulomb interaction, indicated with symbol ‡, are notincluded in the final systematic uncertainty. The ranges indicated with § symbol include exclusion of 0.1–0.125GeV/ c and 0.265–0.315 GeV/ c , to account for splitting effects and K ∗ resonance. Uncertainty source
Default value Variations max R out (%) max µ out (%)PID Default in Tab. 1 Loose and strict inTab. 1 3.0 12.0Background fit range ( k ∗ in GeV/ c ) 0.0–0.5 § § ,0.125–0.5 § k ∗ in GeV/ c ) 0–0.1 0–0.08/0.12,0.005–0.1 3.7 13.4Normalization range ( k ∗ inGeV/ c ) 0.15–0.2 0.1–0.12, 0.18–0.21 3.3 18.0Momentum resolution Procedure from[30, 31] +
12% 3.6 10.3Primary fraction† In Sec. 4 ±
10% 15.0† 20.0†Analysis type SH Cartesian coordinates 1.6 3.1 Ψ π K ‡ Strong andCoulomb Coulomb only 33.0‡ 8.7‡demonstrating the prevalence of the Coulomb interaction for the emission asymmetry measurement. The final extracted radii, R out , and emission asymmetry, µ out , are calculated as a weighted averagesbetween the values obtained from the analysis of correlation functions corresponding to two magnetic fieldpolarities and four possible charge combinations of charged pion–kaon pairs, using the SH representation.One single value of R out and µ out is extracted for each centrality. The obtained values are shown asa function of (cid:104) d N ch / d η (cid:105) / in Fig. 5. The radius increases smoothly from 4 fm to 9 fm when goingfrom the 40–50% centrality interval to 0–5%. At the same time, the emission asymmetry evolves froma starting value of µ out = − . µ out = − / c extra emission time.This delay reduces the asymmetry produced naturally which originates from the collective behaviour ofthe expanding system created in the collisions modelled with THERMINATOR 2 [43]. The agreementbetween the measured and predicted radii is good for peripheral events but measurements are larger by1.5 fm for the most central events. On the other hand, the emission asymmetry measurement follows thepredicted trends for all centralities. The data points lie between the curves corresponding to time delaysof 1.0 and 2.1 fm / c .The model-dependent systematic errors of 15% and 20% for the radii and asymmetry, respectively,are present also in the theoretical prediction, as the same values for the fraction of particles withinthe Gaussian core are used to obtain the radii and emission asymmetry [7]. Therefore, this additionalsystematic uncertainty would synchronously move the results up and down and the prediction lines withoutchanging their interpretation. 11ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration æh /d ch N d Æ ( f m ) ou t R THERMINATOR-2 default c = 2.0 fm/ t s , c = 1.0 fm/ tD c = 2.0 fm/ t s = 2.1 fm/c, tD c = 2.0 fm/ t s , c = 3.2 fm/ tD = 2.76 TeV NN s Pb - ALICE Pb | < 0.8 h , | c < 1.5 GeV/ T p – æh /d ch N d Æ ( f m ) ou t m -
20% corr. unc. – Figure 5:
Pion–kaon source size (upper panel) and emission asymmetry (lower panel) for Pb–Pb collisions at √ s NN = 2.76 TeV as a function of (cid:104) d N ch / d η (cid:105) / . The solid lines show predictions from calculation of source size andemission asymmetry using the THERMINATOR 2 model with default and selected values of additional delay with amean time of ∆ τ and width σ t for kaons [28]. The statistical and systematic uncertainties are combined and shownas square brackets. The uncertainty related to the fraction of primary pairs is reported separately as a correlatedmodel-dependent systematic uncertainty of ±
15% (20%).
In this work the first femtoscopy analysis of pion–kaon pairs is presented. The collective behaviour ofthe matter created in Pb–Pb collisions generates a natural asymmetry in the emission of pions and kaonsdue to their different masses. This is related to the kaon emission distribution, which is more stronglyinfluenced by flow than pions [7]. The analysis was implemented using the spherical harmonics andthe Cartesian representation of the femtoscopic correlation function. The non-femtoscopic backgroundpresent in the raw ratios was subtracted using a combined fit to the four possible charge combinations.The final results are compared to state-of-the-art hydrodynamical calculations where an additional delayfor kaons was introduced to mimic the behaviour during the hadron rescattering phase.The radii values predicted by the theoretical calculation [28] have several assumptions included in theparticle distributions which are different from the experiment. One of them is that the presence of thestrong interaction does not modify the emission asymmetry visible in the correlation functions. Ouranalysis confirms this statement; removal of strong interaction from the fit has significant influence onthe radii (33%) but moderate influence on the emission asymmetry (9%). Even though pions and kaons12ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE Collaborationhave been selected according to ALICE acceptance and momentum ranges, the optimisation of the purityof the data sample modified the transverse momentum distribution. This experimental effect biases thedistributions towards lower momentum values, hence it increases the source radii.The obtained width of the relative pion–kaon source, R out , can be compared to the pion and kaon sourceradii extracted from identical-particle correlation analyses added in quadrature. The pion–kaon pairs usedin the current analysis are predominantly composed of soft pions (0 . ≤ m T ≤ . c ) and hard kaons(1 . ≤ m T ≤ . c ). The pion and kaon source radii measured for these ranges of transverse mass( m T ) in 0–10% central collisions were 7–8.5 fm and 4–5 fm, respectively [18]. Added in quadrature, thisyields 8–10 fm, well in agreement with the most central pion–kaon point in Fig. 5. Similarly, for 30–50%centrality class, the pion and kaon sources are 4–4.5 fm and 2–3 fm, respectively, and their combinationyields 4.5–5.5 fm, again in reasonable agreement with the average of two most peripheral intervals inFig. 5.The emission asymmetry presented here coincides with the predictions calculated including a delay of thekaon emission of 1.0–2.1 fm / c . These values are in line with those predicted by the hydrokinetic model[19], the broken m T scaling of the radii of kaons with respect to pions observed in [18], and from theshort-lived resonances measured by ALICE [23–25]. This measurement is another confirmation of thehadron rescattering phase.In order to better understand the relevant effects influencing the emission asymmetry, it would be naturalto continue the studies measuring other systems. It would be especially interesting to measure the π p andKp systems and probe the validity of the relation µ π pout = µ π Kout + µ Kpout [7]. Final-state interactions such asthe ones taking place in a long-lasting rescattering phase might modify or distort this picture.In summary, the first measurement of the emission asymmetry of pions and kaons for different centralitiesat the LHC has been performed. R out was measured to be 9 fm for central collisions and decreases as afunction of centrality to 4.5 fm for more peripheral collisions. At the same time, the magnitude of theemission asymmetry changed from µ out = − . µ out = − / c for kaons in order to reproduce the measured trend. This observation isin agreement with a hydrodynamic evolution of the expanding system and favors a stronger radial flowin central collisions together with a dense and long-lasting hadronic rescattering phase at the end of theevolution of the fireball at LHC energies. Acknowledgements
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluablecontributions to the construction of the experiment and the CERN accelerator teams for the outstandingperformance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources andsupport provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration.The ALICE Collaboration acknowledges the following funding agencies for their support in building andrunning the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia;Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung fürForschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies,National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico eTecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa doEstado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil;Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and13ion–kaon femtoscopy in Pb − Pb collisions at √ s NN = 2.76 TeV ALICE CollaborationNational Natural Science Foundation of China (NSFC), China; Ministry of Science and Education andCroatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear(CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, CzechRepublic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN andDanish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland;Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physiquedes Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France;Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry ofEducation, Research and Religions, Greece; National Research, Development and Innovation Office,Hungary; Department of Atomic Energy Government of India (DAE), Department of Science andTechnology, Government of India (DST), University Grants Commission, Government of India (UGC)and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science,Indonesia; Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and IstitutoNazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , NagasakiInstitute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science andTechnology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; ConsejoNacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Cienciay Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA),Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The ResearchCouncil of Norway, Norway; Commission on Science and Technology for Sustainable Development inthe South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science andHigher Education, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science andTechnology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministryof Education and Scientific Research, Institute of Atomic Physics and Ministry of Research andInnovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR),Ministry of Education and Science of the Russian Federation, National Research Centre KurchatovInstitute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry ofEducation, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundationof South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation(KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University ofTechnology (SUT), National Science and Technology Development Agency (NSDTA) and Office of theHigher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency(TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology FacilitiesCouncil (STFC), United Kingdom; National Science Foundation of the United States of America (NSF)and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. References [1]
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34 ,59 , S. Klein , C. Klein-Bösing , M. Kleiner , T. Klemenz , A. Kluge ,M.L. Knichel , A.G. Knospe , C. Kobdaj , M.K. Köhler , T. Kollegger , A. Kondratyev ,N. Kondratyeva , E. Kondratyuk , J. Konig , S.A. Konigstorfer , P.J. Konopka , G. Kornakov ,L. Koska , O. Kovalenko , V. Kovalenko , M. Kowalski , I. Králik , A. Kravˇcáková , L. Kreis ,M. Krivda
64 ,111 , F. Krizek , K. Krizkova Gajdosova , M. Krüger , E. Kryshen , M. Krzewicki ,A.M. Kubera , V. Kuˇcera
34 ,61 , C. Kuhn , P.G. Kuijer , L. Kumar , S. Kundu , P. Kurashvili ,A. Kurepin , A.B. Kurepin , A. Kuryakin , S. Kushpil , J. Kvapil , M.J. Kweon , J.Y. Kwon ,Y. Kwon , S.L. La Pointe , P. La Rocca , Y.S. Lai , A. Lakrathok , M. Lamanna , R. Langoy ,K. Lapidus , A. Lardeux , P. Larionov , E. Laudi , R. Lavicka , T. Lazareva , R. Lea , L. Leardini ,J. Lee , S. Lee , S. Lehner , J. Lehrbach , R.C. Lemmon , I. León Monzón , E.D. Lesser ,M. Lettrich , P. Lévai , X. Li , X.L. Li , J. Lien , R. Lietava , B. Lim , V. Lindenstruth ,A. Lindner , C. Lippmann , M.A. Lisa , A. Liu , J. Liu , S. Liu , W.J. Llope , I.M. Lofnes ,V. Loginov , C. Loizides , P. Loncar , J.A. Lopez , X. Lopez , E. López Torres , J.R. Luhder ,M. Lunardon , G. Luparello , Y.G. Ma , A. Maevskaya , M. Mager , S.M. Mahmood , T. Mahmoud ,A. Maire , R.D. Majka
146 ,i , M. Malaev , Q.W. Malik , L. Malinina
75 ,iv , D. Mal’Kevich , P. Malzacher ,G. Mandaglio
32 ,56 , V. Manko , F. Manso , V. Manzari , Y. Mao , M. Marchisone , J. Mareš ,G.V. Margagliotti , A. Margotti , A. Marín , C. Markert , M. Marquard , N.A. Martin ,P. Martinengo , J.L. Martinez , M.I. Martínez , G. Martínez García , S. Masciocchi , M. Masera ,A. Masoni , L. Massacrier , E. Masson , A. Mastroserio
53 ,138 , A.M. Mathis , O. Matonoha ,P.F.T. Matuoka , A. Matyja , C. Mayer , F. Mazzaschi , M. Mazzilli , M.A. Mazzoni , A.F. Mechler ,F. Meddi , Y. Melikyan
62 ,93 , A. Menchaca-Rocha , C. Mengke , E. Meninno
29 ,114 , A.S. Menon ,M. Meres , S. Mhlanga , Y. Miake , L. Micheletti , L.C. Migliorin , D.L. Mihaylov ,K. Mikhaylov
75 ,92 , A.N. Mishra , D. Mi´skowiec , A. Modak , N. Mohammadi , A.P. Mohanty ,B. Mohanty , M. Mohisin Khan
16 ,v , Z. Moravcova , C. Mordasini , D.A. Moreira De Godoy ,L.A.P. Moreno , I. Morozov , A. Morsch , T. Mrnjavac , V. Muccifora , E. Mudnic , D. Mühlheim ,S. Muhuri , J.D. Mulligan , A. Mulliri
23 ,55 , M.G. Munhoz , R.H. Munzer , H. Murakami ,S. Murray , L. Musa , J. Musinsky , C.J. Myers , J.W. Myrcha , B. Naik , R. Nair , B.K. Nandi ,R. Nania
10 ,54 , E. Nappi , M.U. Naru , A.F. Nassirpour , C. Nattrass , R. Nayak , T.K. Nayak ,S. Nazarenko , A. Neagu , R.A. Negrao De Oliveira , L. Nellen , S.V. Nesbo , G. Neskovic ,D. Nesterov , L.T. Neumann , B.S. Nielsen , S. Nikolaev , S. Nikulin , V. Nikulin , F. Noferini
10 ,54 ,P. Nomokonov , J. Norman
79 ,127 , N. Novitzky , P. Nowakowski , A. Nyanin , J. Nystrand , M. Ogino ,A. Ohlson , J. Oleniacz , A.C. Oliveira Da Silva , M.H. Oliver , C. Oppedisano , A. Ortiz Velasquez ,T. Osako , A. Oskarsson , J. Otwinowski , K. Oyama , Y. Pachmayer , V. Pacik , S. Padhan ,D. Pagano , G. Pai´c , J. Pan , S. Panebianco , A.K. Pandey , P. Pareek
50 ,141 , J. Park ,J.E. Parkkila , S. Parmar , S.P. Pathak , B. Paul , J. Pazzini , H. Pei , T. Peitzmann , X. Peng ,L.G. Pereira , H. Pereira Da Costa , D. Peresunko , G.M. Perez , S. Perrin , Y. Pestov , V. Petráˇcek ,M. Petrovici , R.P. Pezzi , S. Piano , M. Pikna , P. Pillot , O. Pinazza
34 ,54 , L. Pinsky , C. Pinto ,S. Pisano
10 ,52 , D. Pistone , M. Płosko´n , M. Planinic , F. Pliquett , M.G. Poghosyan , B. Polichtchouk ,N. Poljak , A. Pop , S. Porteboeuf-Houssais , V. Pozdniakov , S.K. Prasad , R. Preghenella , F. Prino ,C.A. Pruneau , I. Pshenichnov , M. Puccio , J. Putschke , S. Qiu , L. Quaglia , R.E. Quishpe ,S. Ragoni , S. Raha , S. Rajput , J. Rak , A. Rakotozafindrabe , L. Ramello , F. Rami ,S.A.R. Ramirez , R. Raniwala , S. Raniwala , S.S. Räsänen , R. Rath , V. Ratza , I. Ravasenga ,K.F. Read
96 ,130 , A.R. Redelbach , K. Redlich
85 ,vi , A. Rehman , P. Reichelt , F. Reidt , X. Ren ,R. Renfordt , Z. Rescakova , K. Reygers , A. Riabov , V. Riabov , T. Richert
81 ,89 , M. Richter ,P. Riedler , W. Riegler , F. Riggi , C. Ristea , S.P. Rode , M. Rodríguez Cahuantzi , K. Røed , − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration R. Rogalev , E. Rogochaya , D. Rohr , D. Röhrich , P.F. Rojas , P.S. Rokita , F. Ronchetti ,A. Rosano , E.D. Rosas , K. Roslon , A. Rossi , A. Rotondi , A. Roy , P. Roy , O.V. Rueda ,R. Rui , B. Rumyantsev , A. Rustamov , E. Ryabinkin , Y. Ryabov , A. Rybicki , H. Rytkonen ,O.A.M. Saarimaki , R. Sadek , S. Sadhu , S. Sadovsky , K. Šafaˇrík , S.K. Saha , B. Sahoo ,P. Sahoo , R. Sahoo , S. Sahoo , P.K. Sahu , J. Saini , S. Sakai , S. Sambyal , V. Samsonov
93 ,98 ,D. Sarkar , N. Sarkar , P. Sarma , V.M. Sarti , M.H.P. Sas , E. Scapparone , J. Schambach ,H.S. Scheid , C. Schiaua , R. Schicker , A. Schmah , C. Schmidt , H.R. Schmidt , M.O. Schmidt ,M. Schmidt , N.V. Schmidt
68 ,96 , A.R. Schmier , J. Schukraft , Y. Schutz , K. Schwarz ,K. Schweda , G. Scioli , E. Scomparin , J.E. Seger , Y. Sekiguchi , D. Sekihata ,I. Selyuzhenkov
93 ,107 , S. Senyukov , D. Serebryakov , A. Sevcenco , A. Shabanov , A. Shabetai ,R. Shahoyan , W. Shaikh , A. Shangaraev , A. Sharma , A. Sharma , H. Sharma , M. Sharma ,N. Sharma , S. Sharma , O. Sheibani , K. Shigaki , M. Shimomura , S. Shirinkin , Q. Shou ,Y. Sibiriak , S. Siddhanta , T. Siemiarczuk , D. Silvermyr , G. Simatovic , G. Simonetti , B. Singh ,R. Singh , R. Singh , R. Singh , V.K. Singh , V. Singhal , T. Sinha , B. Sitar , M. Sitta ,T.B. Skaali , M. Slupecki , N. Smirnov , R.J.M. Snellings , C. Soncco , J. Song , A. Songmoolnak ,F. Soramel , S. Sorensen , I. Sputowska , J. Stachel , I. Stan , P.J. Steffanic , E. Stenlund ,S.F. Stiefelmaier , D. Stocco , M.M. Storetvedt , L.D. Stritto , A.A.P. Suaide , T. Sugitate , C. Suire ,M. Suleymanov , M. Suljic , R. Sultanov , M. Šumbera , V. Sumberia , S. Sumowidagdo , S. Swain ,A. Szabo , I. Szarka , U. Tabassam , S.F. Taghavi , G. Taillepied , J. Takahashi , G.J. Tambave ,S. Tang , M. Tarhini , M.G. Tarzila , A. Tauro , G. Tejeda Muñoz , A. Telesca , L. Terlizzi ,C. Terrevoli , D. Thakur , S. Thakur , D. Thomas , F. Thoresen , R. Tieulent , A. Tikhonov ,A.R. Timmins , A. Toia , N. Topilskaya , M. Toppi , F. Torales-Acosta , S.R. Torres , A. Trifiró
32 ,56 ,S. Tripathy
50 ,69 , T. Tripathy , S. Trogolo , G. Trombetta , L. Tropp , V. Trubnikov , W.H. Trzaska ,T.P. Trzcinski , B.A. Trzeciak
37 ,63 , A. Tumkin , R. Turrisi , T.S. Tveter , K. Ullaland , E.N. Umaka ,A. Uras , G.L. Usai , M. Vala , N. Valle , S. Vallero , N. van der Kolk , L.V.R. van Doremalen ,M. van Leeuwen , P. Vande Vyvre , D. Varga , Z. Varga , M. Varga-Kofarago , A. Vargas ,M. Vasileiou , A. Vasiliev , O. Vázquez Doce , V. Vechernin , E. Vercellin , S. Vergara Limón ,L. Vermunt , R. Vernet , R. Vértesi , M. Verweij , L. Vickovic , Z. Vilakazi , O. Villalobos Baillie ,G. Vino , A. Vinogradov , T. Virgili , V. Vislavicius , A. Vodopyanov , B. Volkel , M.A. Völkl ,K. Voloshin , S.A. Voloshin , G. Volpe , B. von Haller , I. Vorobyev , D. Voscek , J. Vrláková ,B. Wagner , M. Weber , S.G. Weber , A. Wegrzynek , S.C. Wenzel , J.P. Wessels , J. Wiechula ,J. Wikne , G. Wilk , J. Wilkinson , G.A. Willems , E. Willsher , B. Windelband , M. Winn ,W.E. Witt , J.R. Wright , Y. Wu , R. Xu , S. Yalcin , Y. Yamaguchi , K. Yamakawa , S. Yang ,S. Yano , Z. Yin , H. Yokoyama , I.-K. Yoo , J.H. Yoon , S. Yuan , A. Yuncu , V. Yurchenko ,V. Zaccolo , A. Zaman , C. Zampolli , H.J.C. Zanoli , N. Zardoshti , A. Zarochentsev , P. Závada ,N. Zaviyalov , H. Zbroszczyk , M. Zhalov , S. Zhang , X. Zhang , Z. Zhang , V. Zherebchevskii ,Y. Zhi , D. Zhou , Y. Zhou , Z. Zhou , J. Zhu , Y. Zhu , A. Zichichi
10 ,26 , G. Zinovjev , N. Zurlo , Affiliation notes i Deceased ii Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA),Bologna, Italy iii
Dipartimento DET del Politecnico di Torino, Turin, Italy iv M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia v Department of Applied Physics, Aligarh Muslim University, Aligarh, India vi Institute of Theoretical Physics, University of Wroclaw, Poland
Collaboration Institutes A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS),Kolkata, India Budker Institute for Nuclear Physics, Novosibirsk, Russia California Polytechnic State University, San Luis Obispo, California, United States Central China Normal University, Wuhan, China − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi’, Rome, Italy Chicago State University, Chicago, Illinois, United States China Institute of Atomic Energy, Beijing, China Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia COMSATS University Islamabad, Islamabad, Pakistan Creighton University, Omaha, Nebraska, United States Department of Physics, Aligarh Muslim University, Aligarh, India Department of Physics, Pusan National University, Pusan, Republic of Korea Department of Physics, Sejong University, Seoul, Republic of Korea Department of Physics, University of California, Berkeley, California, United States Department of Physics, University of Oslo, Oslo, Norway Department of Physics and Technology, University of Bergen, Bergen, Norway Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFNSezione di Torino, Alessandria, Italy Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy European Organization for Nuclear Research (CERN), Geneva, Switzerland Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split,Croatia Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, CzechRepublic Faculty of Science, P.J. Šafárik University, Košice, Slovakia Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt,Germany Fudan University, Shanghai, China Gangneung-Wonju National University, Gangneung, Republic of Korea Gauhati University, Department of Physics, Guwahati, India Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn,Germany Helsinki Institute of Physics (HIP), Helsinki, Finland High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico Hiroshima University, Hiroshima, Japan Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms, Germany Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania Indian Institute of Technology Bombay (IIT), Mumbai, India Indian Institute of Technology Indore, Indore, India Indonesian Institute of Sciences, Jakarta, Indonesia INFN, Laboratori Nazionali di Frascati, Frascati, Italy INFN, Sezione di Bari, Bari, Italy INFN, Sezione di Bologna, Bologna, Italy INFN, Sezione di Cagliari, Cagliari, Italy INFN, Sezione di Catania, Catania, Italy INFN, Sezione di Padova, Padova, Italy − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration INFN, Sezione di Roma, Rome, Italy INFN, Sezione di Torino, Turin, Italy INFN, Sezione di Trieste, Trieste, Italy Inha University, Incheon, Republic of Korea Institute for Nuclear Research, Academy of Sciences, Moscow, Russia Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic Institute of Space Science (ISS), Bucharest, Romania Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico iThemba LABS, National Research Foundation, Somerset West, South Africa Jeonbuk National University, Jeonju, Republic of Korea Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik undMathematik, Frankfurt, Germany Joint Institute for Nuclear Research (JINR), Dubna, Russia Korea Institute of Science and Technology Information, Daejeon, Republic of Korea KTO Karatay University, Konya, Turkey Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3,Grenoble, France Lawrence Berkeley National Laboratory, Berkeley, California, United States Lund University Department of Physics, Division of Particle Physics, Lund, Sweden Nagasaki Institute of Applied Science, Nagasaki, Japan Nara Women’s University (NWU), Nara, Japan National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens, Greece National Centre for Nuclear Research, Warsaw, Poland National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India National Nuclear Research Center, Baku, Azerbaijan National Research Centre Kurchatov Institute, Moscow, Russia Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark Nikhef, National institute for subatomic physics, Amsterdam, Netherlands NRC Kurchatov Institute IHEP, Protvino, Russia NRC «Kurchatov»Institute - ITEP, Moscow, Russia NRNU Moscow Engineering Physics Institute, Moscow, Russia Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom Nuclear Physics Institute of the Czech Academy of Sciences, ˇRež u Prahy, Czech Republic Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States Ohio State University, Columbus, Ohio, United States Petersburg Nuclear Physics Institute, Gatchina, Russia Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia
Physics Department, Panjab University, Chandigarh, India
Physics Department, University of Jammu, Jammu, India
Physics Department, University of Rajasthan, Jaipur, India
Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
Physik Department, Technische Universität München, Munich, Germany
Politecnico di Bari, Bari, Italy
Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für SchwerionenforschungGmbH, Darmstadt, Germany
Rudjer Boškovi´c Institute, Zagreb, Croatia
Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India − Pb collisions at √ s NN = 2.76 TeV ALICE Collaboration School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom
Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru
St. Petersburg State University, St. Petersburg, Russia
Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France
Suranaree University of Technology, Nakhon Ratchasima, Thailand
Technical University of Košice, Košice, Slovakia
The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland
The University of Texas at Austin, Austin, Texas, United States
Universidad Autónoma de Sinaloa, Culiacán, Mexico
Universidade de São Paulo (USP), São Paulo, Brazil
Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
Universidade Federal do ABC, Santo Andre, Brazil
University of Cape Town, Cape Town, South Africa
University of Houston, Houston, Texas, United States
University of Jyväskylä, Jyväskylä, Finland
University of Liverpool, Liverpool, United Kingdom
University of Science and Technology of China, Hefei, China
University of South-Eastern Norway, Tonsberg, Norway
University of Tennessee, Knoxville, Tennessee, United States
University of the Witwatersrand, Johannesburg, South Africa
University of Tokyo, Tokyo, Japan
University of Tsukuba, Tsukuba, Japan
Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France
Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France
Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire(DPhN), Saclay, France
Università degli Studi di Foggia, Foggia, Italy
Università degli Studi di Pavia, Pavia, Italy
Università di Brescia, Brescia, Italy
Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India
Warsaw University of Technology, Warsaw, Poland
Wayne State University, Detroit, Michigan, United States
Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany
Wigner Research Centre for Physics, Budapest, Hungary
Yale University, New Haven, Connecticut, United States