The ALICE detector will offer very good conditions to study the space-time characteristics of particle production in heavy-ion collisions at LHC from measurements of the correlation function of identical and non-identical particles at small relative velocities. The correlations - induced by Coulomb and nuclear final-state interactions - of non-identical particles appear to be directly sensitive to the space-time asymmetries of particle production allowing, in particular, a measurement of the mean relative delays in particle emission at time scales as small as few fm/c. The problem of Coulomb interaction of the correlated particles is particularly important in the case of the large effective volumes formed in ultra-relativistic heavy-ion reactions

Erazmus, B

Lednicky, R

Lyuboshitz, V L

Martin, L

Mikhailov, K

Pluta, J

Roy, C

Sinyukov, Yu M

Stavinsky, A V

Werner, K

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PARTICLE CORRELATIONS WITH HEAVY IONS AT LHCENERGIESB. ERAZMUS, L. MARTIN, C. ROY, K. WERNERSUBATECH(UMR, Universite, Ecole des Mines, IN2P3/CNRS)4, rue Alfred Kastler, La Chantrerie44070 Nantes, FranceE-mail: erazmus@subatech.in2p3.frR. LEDNICKYInstitute of Physics, Na Slovance 218040 Prague 8, Czech RepublicV. LYUBOSHITZJINR Dubna, P.O.Box 79,Moscow, RussiaK. MIKHAILOV, A. STAVINSKYITEP, B.Cheremushkinskaya 25,117259 Moscow, RussiaJ. PLUTAInstitute of Physics, Warsaw University of Technology,00-662 Warsaw, PolandYu. SINYUKOVInstitute for Theoretical Physics of National Acad. Sci.,Kiev 252143, Ukrainefor the ALICE COLLABORATIONThe ALICE detectorwill oer very good conditions to study the space-timecharac-teristics of particle production in heavy-ion collisions at LHC from measurementsof the correlation function of identical and non-identical particles at small relativevelocities. The correlations - induced by Coulomb and nuclear nal-state interac-tions - of non-identical particles appear to be directly sensitive to the space-timeasymmetries of particle production allowing, in particular, a measurement of themean relative delays in particle emission at time scales as small as few fm/c.Theproblem of Coulomb interaction of the correlated particles is particularly impor-tant in the case of the large eective volumes formed in ultra-relativistic heavy-ionreactions.11 IntroductionParticle correlations at high energies usually measure only a part of the space-time emission region since the sources, despite their fast longitudinal motion,emit the correlated particles with small relative velocities mainly at close space-time points.The features of emitting sources can be investigated in the frame of anapproach which includes the dynamics of the emission process as well as theeects of quantum statistics and nal state, Coulomb and strong interactions.It is important that particle correlations contain information about the dy-namical evolution of the emission process, such as proper time of decoupling(freeze-out) duration of particle emission and the presence of collective ows.This information is, in principle, closely related to the QGP formation1;2;32 SimulationsOur correlation analysis were performed using the string Model for Ultra-relativistic Hadronic Interactions VENUS (version 5.14)4;5. Based on thestring model, one rst determines connected regions of high energy density.These regions are referred to as quark matter (QM) droplets. For such regions,the initially produced hadrons serve only as a mean to produce the propeructuations in the energy density. Presently the model is not well suited forthe LHC energy region. However, it provides space-time and momentum spacecharacteristics of the freeze-out points of the emitted particles, which can beused as an approximation accounting for the basic features of the multiparticleproduction, including the fast longitudinal motion of the source as well as theresonance production.The events were generated without the phase of the particle rescatteringand droplet formation which normally leads to the increase of the space-timecharacteristics of particle emission. Instead, we introduce the scale factor whichallows to extend the production region or introduce the shifts in emission timesof various particle species in a controlled way.The generation of events using VENUS model is followed by the calculationof the correlation function for the selected pairs of identical and non-identicalparticles. In this way we can study the sensitivity of the ALICE detector toparticular correlation eects6.3 Experimental resolutionIn order to account for eects due to the experimental resolution we used aprogram based on parametrisation of the full detector simulation7. A realistic2Figure 1: Alice Detector.geometry of the ALICE central barrel has been taken into account (Fig. 1).This program does include contributions due to multiple scattering, measure-ment precision and detector alignment as well as uctuations in energy loss.Eects due to the track nding algorithms were not included since the track-ing eciency in ALICE is reather good and starts only to decrease at very lowtransverse momentum.The two-track resolution was not taken into account in the simulations.However, it is expected to have rather small eect on correlation functions oflike particles and practically no eect on unlike particle correlations at smallrelative velocities. The eect of the experimental resolution on the relativemomentum is summarized in Table 1.Table 1: The ALICE resolution: (Qi  Q`i), MeV/c. A cut Qinv< 0:05GeV=c has beenapplied.Particles QsideQoutQlongQinv++; + 0.3 3.8 0.7 1.2+K+; +K 0.4 4.0 1.1 1.8+p;  p 0.4 3.9 1.3 2.0K+K+;K+K 0.5 6.5 2.6 3.6K+p;K p 0.6 8.2 3.2 4.8pp 0.6 11.6 5.0 6.03Figure 2: The simulated correlation functions for two identical charged pions, kaons andprotons without and with the experimental resolution accounted for. The simulations weredone using VENUS model with the extended space-time freeze-out coordinates to set hri = 30fm and hti = 20 fm/c in the reaction c.m.s. (scale-factor = 5). For two pions the Gamowcorrectedcorrelation function is comparedwith that including the eect of quantumstatisticsonly.4 Correlation of identical particlesThe correlation function of identical particles is sensitive to the relative space-time distances between the emission points due to the eects of Bose-Einsteinor Fermi-Dirac statistics8;9and the strong and Coulomb nal state interac-tions10;11. The relative importance of these three factors will be dierentaccording to the particle species.In Fig. 2 we show the two-particle correlation functions for pions, kaonsand protons calculated taking into account the eects of quantum statisticsand both Coulomb and nuclear nal state interactions. In the case of largeeective sources, the correlations of two protons are, due to their relatively4v→1v→2v→k→*/µ=v→1-v→2ψcos(ψ)> 0v→1v→2v→k→*/µ=v→1-v→2ψcos(ψ)< 0Figure 3: We can determine which sort of particles was produced earlier and which laterby studying the correlation functions of two non-identical particles separately for the anglesless and greater than 90between the relative velocity k= (k= p1=  p2and  is thereduced mass of the two particles) and the total pair velocity v.small Bohr radius of 58 fm, stronger than those of pions and kaons. Thus, thecorrelations of protons appear to be a sensitive probe of the evolution of thecollision in the case of large emitting region.The correlation functions are only weakly aected by the experimentalresolution even in the case of large sizes expected at LHC energies.5 Correlations of non-identical particlesThe non-identical particle correlations can be used for the determination of thespace-time parameters of the emission process in a similar way as the identicalones using the sensitivity of the Coulomb and strong interaction eects tothe space and time intervals of particle emissions. On the other hand, thecorrelations of non-identical particles appear to be directly sensitive to thesequence of particle emission12. To study this sensitivity one should constructthe correlation functions R+(kv  0) and R (kv < 0) corresponding to thepositive and negative values of kv , respectively (Fig. 3). On the absenceof the space-time asymmetries, the ratio R+=R is equal unity. In Fig. 4 weillustrate the eect of the asymmetry in the case of the emission of K+K pairs. The structures (a deep or a peak) and their amplitude appearing in thisratio depend on the sign and the magnitude of the time delay introduced in5Figure 4: The distributions of the dierence of the K+and K emission times t =tK+  tK simulated by VENUS with the shifts hti =+10 and -5 fm/c introduced ad hoc,the corresponding correlation functions R+(v  k 0) and R (vk< 0) and their ratioscalculated forK+K pairs. The ratios distorted by the eect of experimental resolution arerepresented by open symbols.the calculations. The observation of a delay in the emission of K+and K canbe considered, in particular, as a strong indication of strangeness distillation.Fig. 5 demonstrates the scaling of the space-time asymmetry with theinverse Bohr radius for the like- and unlike-sign of K, p and Kp pairs withthe corresponding Bohr radii of 248.5, 225.5 and 83.6 fm, respectively. Thecorrelation functions for the K, p pairs were calculated using one simulatedevent only.Due to its very good resolution, the ALICE experiment will be sensitiveto the delays in the particle emission times of the order of a few fm/c even inthe frame of event-by-event analysis in the case of pairs involving pions.6Figure 5: The same ratios R+=R as in Fig. 4 calculated with hti = -10 fm/c for dierentpairs of non-identical particles, taking into account (open symbols) and neglecting (fullsymbols) the eect of experimental resolution.6 Coulomb corrections for interferometry analysisFor the large expanding hadron systems, expected at LHC energies, the usualGamow correction substantially deviates from the true Coulomb eects (seeFig. 2). A simple modication of the standard zero-distance correction hasbeen proposed13. This nite-size analytical Coulomb correction allows oneto extract the pure quantum statistics correlation function (e.g. in a hydro-dynamic model) of two identical charged pions or kaons in the case of rel-atively large eective emission volumes. This procedure can be useful for afast interferometry analysis and reasonable preliminary estimate of the modelparameters even at RHIC and LHC energies.70.811.21.41.61.820.811.21.41.61.820 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08Figure 6: The comparison of the Coulomb corrected two-pion correlation functions at SPSand LHC energies for pt=0.15 and 0.4 GeV/c, simulated with the hydrodynamical calcula-tions. The points near the unity correspond to the ratio of the reconstructed pure quantumstatistics correlation function to the nite-size corrected correlation function.0.811.21.41.61.820.811.21.41.61.820 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08 0.1Figure 7: The same as Fig. 6 for the two-kaon correlation functions at SPS and LHC energiesfor pt=0.15, 0.8 and 1.6 GeV/c.8In Figs. 6 and 7 we present the results of calculation of the pion and kaoncorrelation functions at SPS and LHC energies for various mean transversemomentum of the particles using the hydronynamic model14. The discrepancybetween the pure quantum statistics calculations and the nite-size correctionsappears to be signicant only for kaons at high transverse momentum.7 ConclusionsWe analyzed the ability of the ALICE detector for determination of the space-time characteristics of particle production in heavy-ion collisions at LHC.Correlation functions of various particle pairs can be measured and will beonly slightly distorted by the detector resolution eects.We demonstrated that non-identical particle correlations contain an infor-mation complementary to that provided by identical particles. In particular,the unlike particle correlations allow to determine the space-time asymmetriesin the particle emission process.The simulations of correlations of various particle pairs were performedusing the event generator VENUS adapted arbitrarily for LHC conditions andincluding the expected resolution of the ALICE detector. The results showthat the relative time delays of the order of a few fm/c can be measured.The two-particle Coulomb interaction gives an important contribution tocorrelations in the case of large sizes and lifetimes. An analytical correctionhas been proposed allowing to extract the pure quantum statistics correlationfunction and to rapidly estimate the parameters describing the emitting source.References1. S. Pratt, Phys. Rev. Lett. 53, 1219 (1984); Phys. Rev. D 33, 1314(1986); S. Pratt, T. Csorgo, J. Zimanyi, Phys. Rev. C 42, 2646 (1990).2. A.N. Makhlin, Yu.M. Sinyukov, Yad. Fiz. 46, 637 (1987); Z. Phys. C39, 69 (1988); Yu.M. Sinyukov, Nucl. Phys. A 498, 151c (1989).3. G. Bertsch, M. Gong, M. Tohyama, Phys. Rev. C 37, 1896 (1988).4. K. Werner, Phys. Rep. 232, 87 (1993).5. K. Werner and J. Aichelin, Phys. Rev. C 52, 1584 (1995).6. B.Erazmus, R.Lednicky, V.Lyuboshitz, L.Martin, K.Mikhailov, J.Pluta,Yu.Sinyukov, A.Stavinsky, K.Werner, ALICE Note, INT-95-43.7. ALICE Technical Proposal, CERN/LHCC 95-71, LHC/P3 (1995), Chap-ter 11.8. G. Goldhaber, Phys. Rev. 120, 300 (1960).9. M.I. Podgoretsky, Fiz. Elem. Chast. Atom. Yad. 20, 628 (1989) (Sov.J. Part. Nucl. 20, 266 (1989)).910. S.E. Koonin, Phys. Lett. B 70, 43 (1977).11. R. Lednicky, V.L. Lyuboshitz, Yad. Fiz. 35, 1316 (1982); Sov. J. Nucl.Phys. 35, 770 (1982); Proc. Int. Workshop on Particle Correlationsand Interferometry in Nuclear Collisions, CORINNE 90, Nantes, France,1990 (ed. D. Ardouin, World Scientic, 1990)p.42; JINR report P2-546-92 (1992) 1; Heavy Ion Physics 3, 93 (1996).12. R. Lednicky, V.L. Lyuboshitz, B. Erazmus, D. Nouais, Phys. Lett. B373, 30 (1996).13. Yu.M. Sinyukov, R. Lednicky, S.V. Akkelin, J. Pluta, B. Erazmus, Phys.Lett. B 432, 248 (1998).14. Yu.M. Sinyukov, Nucl. Phys. A 498, 151 (1989); S.V. Akkelin, Yu.M.Sinyukov, Phys. Lett. B 356, 525 (1995); Z. Phys. C 72, 501 (1996).10

Particle Correlations with Heavy Ions at LHC Energies

Particle Correlations with Heavy Ions at LHC Energies

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