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inclusive charged particle distributions have been studied for a long time to derive the general properties of hadronic interactions at high energies .
a large body of the experimental data on charge particle production spectra in baryon - baryon , gamma - baryon and gamma - gamma collisions has been accumulated during last forty years . however , the underlying dynamics of hadron production in high energy particle interactions is still not fully understood .
recently , a new unified approach to describe the particle production spectra shape was proposed  @xcite .
it was suggested to approximate the charged particle spectra as function of the particle s transverse momentum by a sum of an exponential ( boltzmann - like ) and a power law statistical distributions : @xmath0 where @xmath1 with m equal to the produced hadron mass .
@xmath2 are the free parameters to be determined by fit to the data . the detailed arguments for this particular choice are given in  @xcite .
for the charged hadron spectra a mass of hadrons is assumed to be equal to the pion mass .
therefore , the hadroproduction process in baryon - baryon high energy interactions could be decomposed into at least two distinct parts .
these parts are characterized by two different sources of produced hadrons . the first one is associated with the baryon valence quarks and a quark - gluon cloud coupled to the valence quarks .
those partons preexist long time before the interaction and could be considered as being a thermalized statistical ensemble . when a coherence of these partonic systems is destroyed via strong interaction between the two colliding baryons these partons
hadronize into particles released from the collision .
the hadrons from this source are distributed presumably according to the boltzmann - like exponential statistical distribution in transverse plane w.r.t . the interaction axis .
the second source of hadrons is directly related to the virtual partons exchanged between two colliding partonic systems . in qcd
this mechanism is described by the bfkl pomeron exchange .
the radiated partons from this pomeron have presumably a typical for the pqcd power - law spectrum .
schematically figure  [ fig ] shows these two sources of particles produced in high energy baryonic collisions .
this explanation is qualitative , however .      in this paper
an attempt to study hadroproduction in heavy - ion collisions according to the introduced model is taken . in these collisions , due to a large number of colliding partons , extremely high energy densities , comparing to those in @xmath3-collisions , can be obtained .
the experimental data measured in auau collisions at @xmath4 gev / n by phenix  @xcite and pbpb collisions at @xmath5 tev / n by alice  @xcite are considered here . since the centre - of - mass energies per nucleon in these experiments are varied by a factor @xmath6 , a unified approach considering the energy density is suggested .
the energy density in heavy ion interactions is known to depend not only on the centre - of - mass energy , but also on the centrality of the collision .
hence , while the energy densities that can be reached at rhic  @xcite and at lhc  @xcite differ significantly , the energy density in central collisions at rhic might be of the same order as that in peripheral collisions at lhc .    therefore , we use a simple parameterization  @xcite for the initial energy density which is motivated by several model calculations .
@xmath7 where @xmath8gev/@xmath9 , @xmath10 , @xmath11 and @xmath12 gev  @xcite . here
the second factor is responsible for the incident energy dependence , @xmath13 is the c.m .
collision energy , and the third one shows the dependence on the number of binary parton - parton collisions @xmath14 which is related to the centrality of the collision .    according to the introduced model , the exponential term stands for the radiation of thermalized particles with distributions similar to boltzmann - like thermodynamics .
fitting the introduced formula ( eq .  [ eq : exppl ] ) to the measured experimental data allows to extract only the boltzmann - like statistical distribution from the whole statistical ensemble of produced hadrons .
this exponential distribution is characterized by a parameter @xmath15 analogous to the temperature in classical thermodynamics , which value is obtained from the fit .
therefore , it is interesting to study , how this temperature @xmath15 vary with the energy density obtained in the collision .
figure  [ tee ] shows this temperature @xmath15 as function of energy density .
as it was expected , the energy density obtained in central collisions at rhic is similar to those in peripherial collisions at lhc , therefore a smooth transition between these two experiments is observed .
one can notice the interesting behavior of the temperature as function of energy density ( @xmath16 ) , which is in a good agreement with the stefan - boltzmann law .
another observation on the temperature of the final state particles is that for high energy densities @xmath15 reaches a certain limit .
this can be explained from qgp theory that considers the phase transition temperature @xmath17 from qgp to hadrons : the system cools until it reaches the critical temperature , thus , the temperature of the final state should be always below @xmath17 . indeed , for high values of @xmath18 one can notice , that the oberved critical temperature is @xmath19 mev , that is similar to previous theoretical observations  @xcite .    in conclusion ,
the experimental results on charged hadron production in heavy - ion collisions obtained in the phenix and alice experiments have been analyzed in the framework of the new approach .
this approach allows to extract a part of the whole statistical ensemble of produced hadrons , those described by the boltzmann - like statistical distribution only .
this exponential distribution is characterized by a parameter @xmath15 analogous to the temperature in classical thermodynamics .
it is found that the parameter @xmath15 depends universally on the collision energy density rather than on the collision energy .
finally , the observed behavior of @xmath15 is formally similar to the stefan - boltzmann law well known in classic thermodynamics .    99 a.  a.  bylinkin and a.  a.  rostovtsev , `` systematic studies of hadron production spectra in collider experiments . '' arxiv:1008.0332 [ hep - ph ] a.  a.  bylinkin and a.  a.  rostovtsev , `` anomalous behavior of pion production in high energy particle collisions . ''
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the shapes of invariant differential cross section for charged particle production as function of transverse momentum measured in heavy - ion collisions are analyzed . 
 the data measured at rhic and lhc are treated as function of energy density according to a recent theoretical approach . 
 the boltzmann - like statistical distribution is extracted from the whole statistical ensemble of produced hadrons using the introduced model . 
 variation of the temperature , characterizing this exponential distribution , is studied as function of energy density .