Hadroproduction in heavy-ion collisions
HHadroproduction in heavy-ion collisions
A. A. Bylinkin, ∗ A. A. Rostovtsev, † and N. S. Chernyavskaya Institute for Theoretical and Experimental Physics, ITEP, Moscow, Russia
The shapes of invariant differential cross section for charged particle production as function oftransverse momentum measured in heavy-ion collisions are analyzed. The data measured at RHICand LHC are treated as function of energy density according to a recent theoretical approach. TheBoltzmann-like statistical distribution is extracted from the whole statistical ensemble of producedhadrons using the introduced model. Variation of the temperature, characterizing this exponentialdistribution, is studied as function of energy density.
I. INTRODUCTION
Inclusive charged particle distributions have been stud-ied for a long time to derive the general properties ofhadronic interactions at high energies. A large bodyof the experimental data on charge particle productionspectra in baryon-baryon, gamma-baryon and gamma-gamma collisions has been accumulated during last fortyyears. However, the underlying dynamics of hadron pro-duction in high energy particle interactions is still notfully understood.Recently, a new unified approach to describe the par-ticle production spectra shape was proposed [1]. It wassuggested to approximate the charged particle spectraas function of the particle’s transverse momentum by asum of an exponential (Boltzmann-like) and a power lawstatistical distributions: dσP T dP T = A e exp ( − E T kin /T e ) + A (1 + P T T · N ) N , (1)where E T kin = (cid:112) P T + M − M with M equal to the pro-duced hadron mass. A e , A, T e , T, N are the free param-eters to be determined by fit to the data. The detailedarguments for this particular choice are given in [1]. Forthe charged hadron spectra a mass of hadrons is assumedto be equal to the pion mass.Therefore, the hadroproduction process in baryon-baryon high energy interactions could be decomposedinto at least two distinct parts. These parts are char-acterized by two different sources of produced hadrons.The first one is associated with the baryon valence quarksand a quark-gluon cloud coupled to the valence quarks.Those partons preexist long time before the interactionand could be considered as being a thermalized statisticalensemble. When a coherence of these partonic systems isdestroyed via strong interaction between the two collidingbaryons these partons hadronize into particles releasedfrom the collision. The hadrons from this source aredistributed presumably according to the Boltzmann-likeexponential statistical distribution in transverse planew.r.t. the interaction axis. The second source of hadrons ∗ [email protected] † [email protected] is directly related to the virtual partons exchanged be-tween two colliding partonic systems. In QCD this mech-anism is described by the BFKL Pomeron exchange. Theradiated partons from this Pomeron have presumably atypical for the pQCD power-law spectrum. Schematicallyfigure 1 shows these two sources of particles produced inhigh energy baryonic collisions. This explanation is qual-itative, however. This simple model is naive, though it FIG. 1. Two different sources of hadroproduction: red ar-rows - particles produced by the preexisted partons, green -particles produced via the Pomeron exchange. allows to make a number of predictions which have beenchecked experimentally [3–5].In this paper an attempt to study hadroproduction inheavy-ion collisions according to the introduced model istaken. In these collisions, due to a large number of collid-ing partons, extremely high energy densities, comparingto those in pp -collisions, can be obtained. The experi-mental data measured in AuAu collisions at √ s = 200GeV/N by PHENIX [6] and PbPb collisions at √ s = 2 . ≈
14, a unified approach consider-ing the energy density is suggested. The energy densityin heavy ion interactions is known to depend not only onthe centre-of-mass energy, but also on the centrality ofthe collision. Hence, while the energy densities that canbe reached at RHIC [6] and at LHC [7] differ significantly,the energy density in central collisions at RHIC might beof the same order as that in peripheral collisions at LHC. a r X i v : . [ h e p - ph ] M a y Therefore, we use a simple parameterization [8] forthe initial energy density which is motivated by severalmodel calculations. ε = ε ( ss ) α/ N collβ , (2)where ε = 1GeV/fm , α ≈ . β ≈ . √ s =200 GeV [8]. Here the second factor is responsible forthe incident energy dependence, √ s is the c.m. collisionenergy, and the third one shows the dependence on thenumber of binary parton-parton collisions N coll which isrelated to the centrality of the collision. FIG. 2. Temperature of charged particles released in heavy-ion collisions as function of energy density.
According to the introduced model, the exponentialterm stands for the radiation of thermalized particleswith distributions similar to Boltzmann-like thermody-namics. Fitting the introduced formula (eq. 1) to themeasured experimental data allows to extract only the Boltzmann-like statistical distribution from the wholestatistical ensemble of produced hadrons. This expo-nential distribution is characterized by a parameter T e analogous to the temperature in classical thermodynam-ics, which value is obtained from the fit. Therefore, it isinteresting to study, how this temperature T e vary withthe energy density obtained in the collision.Figure 2 shows this temperature T e as function ofenergy density. As it was expected, the energy densityobtained in central collisions at RHIC is similar to thosein peripherial collisions at LHC, therefore a smooth tran-sition between these two experiments is observed. Onecan notice the interesting behavior of the temperatureas function of energy density ( T e ∝ ε / ), which is ina good agreement with the Stefan-Boltzmann law. An-other observation on the temperature of the final stateparticles is that for high energy densities T e reaches acertain limit. This can be explained from QGP theorythat considers the phase transition temperature T c fromQGP to hadrons: the system cools until it reaches thecritical temperature, thus, the temperature of the finalstate should be always below T c . Indeed, for high valuesof ε one can notice, that the oberved critical temperatureis T c ≈
200 MeV, that is similar to previous theoreticalobservations [9].In conclusion, the experimental results on chargedhadron production in heavy-ion collisions obtained in thePHENIX and ALICE experiments have been analyzed inthe framework of the new approach. This approach al-lows to extract a part of the whole statistical ensembleof produced hadrons, those described by the Boltzmann-like statistical distribution only. This exponential distri-bution is characterized by a parameter T e analogous tothe temperature in classical thermodynamics. It is foundthat the parameter T e depends universally on the colli-sion energy density rather than on the collision energy.Finally, the observed behavior of T e is formally similarto the Stefan-Boltzmann law well known in classic ther-modynamics. [1] A. A. Bylinkin and A. A. Rostovtsev, “Systematic stud-ies of hadron production spectra in collider experiments.”arXiv:1008.0332 [hep-ph][2] A. A. Bylinkin and A. A. Rostovtsev, “Anomalous behav-ior of pion production in high energy particle collisions.”Eur. Phys. J. C , 1961 (2012) arXiv:1112.5734 [hep-ph][3] A. A. Bylinkin and A. A. Rostovtsev, “Comparativeanalysis of pion, kaon and proton spectra produced atPHENIX.” arXiv:1203.2840 [hep-ph][4] A. A. Bylinkin and A. A. Rostovtsev, “An analysis ofcharged particles spectra in events with different chargedmultiplicity.” arXiv:1205.4432 [hep-ph][5] A. A. Bylinkin and A. A. Rostovtsev, “A variation of thecharged particle spectrum shape as function of rapidity inhigh energy pp collisions” arXiv:1205.6382 [hep-ph][6] S. S. Adler et al. [PHENIX Collaboration], “Identified charged particle spectra and yields in Au+Au collisions atS(NN)**1/2 = 200-GeV,” Phys. Rev. C (2004) 034909[nucl-ex/0307022].[7] B. Abelev et al. [ALICE Collaboration], “Centrality De-pendence of Charged Particle Production at Large Trans-verse Momentum in Pb–Pb Collisions at √ s NN = 2 . (2013) 52 [arXiv:1208.2711 [hep-ex]].[8] I. N. Mishustin and J. I. Kapusta, “Collective decel-eration of ultrarelativistic nuclei and creation of quarkgluon plasma,” Phys. Rev. Lett. (2002) 112501 [hep-ph/0110321].[9] R. Hagedorn, “Multiplicities, P(t) Distributions And TheExpected Hadron → Quark - Gluon Phase Transition,”Riv. Nuovo Cim.6N10