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thermodynamic models have long been employed to estimate the temperatures reached in the relativistic heavy - ion collisions  @xcite .
particularly the hadron - resonance gas ( hrg ) model has been quite successful in describing the hadron multiplicities data in relativistic nucleus - nucleus collisions  @xcite , possibly with additional introduction of parameters to regulate deviations from full chemical equilibrium  @xcite .    in its simplest version
the hrg is described as a gas of non - interacting hadrons and resonances . in a more realistic hrg model one
has to take into account the attractive and repulsive interactions between hadrons . in this work
we study the influence of short - range repulsive interactions between hadrons on thermal fits to hadron yield data .
the repulsive interactions between hadrons are modeled via eigenvolume ( ev ) correction of the van der waals type @xcite . for a multi - component case
there is more than a single way to model the eigevolume corrections . in our analysis
we use two different formulations : the `` diagonal '' eigenvolume hrg model from  @xcite , and the `` crossterms '' ev model introduced in @xcite  ( see ref .
@xcite for technical details ) .
the `` diagonal '' model is simpler but it is not consistent with the 2nd order virial expansion of the equation of state of hard spheres .
the `` crossterms '' model , on the other hand , while technically more involved , is consistent with that expansion .    in our analysis
we include the established strange and non - strange hadrons listed in the particle data tables  @xcite , along with their decay branching ratios .
this includes mesons up to @xmath0 and ( anti)baryons up to @xmath1 .
the finite width of the resonances is taken into account by adding the additional integration over their breit - wigner shapes .
the feed - down from strong and electromagnetic decays of the unstable resonances to the total hadron yields is included in the standard way . the full chemical equilibrium assumed in this work , i.e. we do not consider here possible under- or over - saturation of the light and/or strange quarks which improves the data description but also introduces additional parameters  ( see , e.g. , ref .
first a bag - model inspired parametrization with the hadron eigenvolume proportional to its mass through a bag - like constant is employed , i.e. @xmath3 such eigenvolume parametrization had been obtained for the heavy hagedorn resonances , and was used to describe their thermodynamics  @xcite , their effect on particle yield ratios  @xcite , and compared to lattice qcd  @xcite .
the ev - hrg model fits are using the hadron yield data of the na49 collaboration , which include @xmath4 yields of charged pions , charged kaons , @xmath5 , @xmath6 , @xmath7 , @xmath8 , and , if available , @xmath9 , @xmath10 , measured in most central pb+pb collisions at @xmath11 , and @xmath12  gev  @xcite .
additionally , the data on the total number of participants , @xmath13 , is identified with total net baryon number and is included in the fit .
-@xmath2 plane where the `` crossterms '' eigenvolume hrg model with bag - like constant @xmath14 fixed to reproduce the hard - core radius of @xmath15  fm yields a better fit to the na49 data as compared to the point - particle hrg model .
the solid lines show the isentropic curves for the eigenvolume model , which go through the global @xmath16 minima .
( b ) collision energy dependence of entropy per baryon at global minima of thermal fits to na49 data . , title="fig:",scaledwidth=49.0% ] -@xmath2 plane where the `` crossterms '' eigenvolume hrg model with bag - like constant @xmath14 fixed to reproduce the hard - core radius of @xmath15  fm yields a better fit to the na49 data as compared to the point - particle hrg model .
the solid lines show the isentropic curves for the eigenvolume model , which go through the global @xmath16 minima .
( b ) collision energy dependence of entropy per baryon at global minima of thermal fits to na49 data . ,
title="fig:",scaledwidth=49.0% ]    for illustration purposes we consider here only the `` crossterms '' model and we fix the @xmath14 to reproduce the hard - core proton radius of @xmath15  fm .
a much more detailed study regarding fits with mass - proportional eigenvolumes can be found in  @xcite .
figure @xmath17a depicts the regions in the @xmath18-@xmath2 plane where the fit quality of na49 data in the ev model is better than in the non - interacting hrg .
the location of the fit minima within non - interacting hrg are shown by diamonds , and are consistent with the systematics established in numerous previous studies . at all
five na49 energies wide regions of improved @xmath16 values are observed at high temperatures and chemical potentials . at given bombarding energy , for a given set of radii ,
the ev hrg model fits do not just yield a single @xmath19 pair , but a whole range of @xmath19 pairs , each with similarly good fit quality .
these pairs form a valley in the @xmath19 plane along a line of nearly constant entropy per baryon , @xmath20 .
we also show the energy dependence of values of @xmath20 ( fig .
@xmath17b ) . the @xmath20 , extracted at different energies , is a robust observable : it is almost independent of the details of the modeling of the ev interactions and of the specific @xmath19 values obtained .
we also consider parameterization where all mesons are assumed to be point - like and where all baryons have a fixed hard - core radius @xmath21  fm .
as demonstrated in @xcite this parameterization yields a good description of lattice data on the pressure at least up to @xmath22  mev .
it was also shown in  @xcite that it leads to an irregular @xmath16 profile of thermal fit to alice hadron yield data with wide double minimum structure in the 155 - 210  mev temperature range . here
we investigate how inclusion of light nuclei influences the fit .
for that we consider the 0 - 10% centrality alice data which has a rich amount of data regarding yields of light nuclei .
the actual data used for fitting includes midrapidity yields of charged pions , charged kaons , and ( anti)protons  @xcite , ( anti)@xmath5 and ( anti)@xmath9  @xcite , ( anti)@xmath7 and @xmath23  @xcite , @xmath8  @xcite , ( anti)deuterons and ( anti)@xmath24he  @xcite , and ( anti)@xmath25h  @xcite .
the addition of light nuclei requires additional assumptions regarding their eigenvolumes .
first we consider only addition of ( anti)deuterons and compare two cases : ( 1 ) deuteron has same eigenvolume as baryons , i.e. @xmath26  fm ; ( 2 ) deuteron has a twice larger eigenvolume compared to baryons , i.e. @xmath27  fm .
the results of the calculations of @xmath16 temperature profile are depicted in fig .
[ fig : deuteron]a . note that @xmath2 is also fitted at each @xmath18 and found to be consistent with zero within fit errors .     of fit
to alice data on hadron + light nuclei yields in 0 - 10% most central pb+pb collisions at 2.76  tev within eigenvolume hrg model with point - like mesons , baryons with hard - core radius of 0.3  fm , and different assumptions for eigenvolumes of light nuclei . in ( a )
only ( anti)deuterons are added to fit with @xmath28  fm ( dashed line ) and @xmath29  fm ( solid line ) . in ( b ) light nuclei up to @xmath25h are added with @xmath30  fm  ( dashed ) , and @xmath31  ( solid ) , where @xmath32 is mass number . , title="fig:",scaledwidth=49.0% ]   of fit to alice data on hadron + light nuclei yields in 0 - 10% most central pb+pb collisions at 2.76  tev within eigenvolume hrg model with point - like mesons , baryons with hard - core radius of 0.3  fm , and different assumptions for eigenvolumes of light nuclei . in
( a ) only ( anti)deuterons are added to fit with @xmath28  fm ( dashed line ) and @xmath29  fm ( solid line ) . in ( b )
light nuclei up to @xmath25h are added with @xmath30  fm  ( dashed ) , and @xmath31  ( solid ) , where @xmath32 is mass number .
, title="fig:",scaledwidth=49.0% ]    if deuterons are assumed to have same eigenvolume as protons then the @xmath16 profile has a regular structure with a minimum at @xmath33  mev .
thus , even though inclusion of light nuclei may be questionable in general , it would seem that inclusion of deuterons into thermal fit would stabilise them with regards to the modeling of eigenvolume corrections .
this conclusion , however , is illusory .
changing deuteron eigenvolume to a physically more motivated value equal to twice that of proton one gets a very different @xmath16 profile : a two - minimum structure in a wide 155 - 210  mev temperature range , with improved fit quality at global minimum .
this change is attributed to a larger suppression of ( anti)deuteron yield at higher temperatures due to larger eigenvolume .
it is remarkable that fit can be so sensitive to the properties of only single particle species .
similarly , the inclusion of yields of @xmath24he and @xmath25h does not help to stabilise the fit , as seen in fig .
[ fig : deuteron]b .
this is so despite the remarkably large number of degrees of freedom @xmath34 .
we therefore conclude that introduction of light nuclei into thermal fits leads to a further destabilisation of the fit as it requires non - trivial assumptions regarding their eigenvolumes .
it is shown that thermal fits are very sensitive to the details of the modeling of the eigenvolume interactions . at given collision energy , the ev hrg model fits do not just yield a single @xmath19 pair , but a whole range of @xmath19 pairs , each with similarly good fit quality .
the entropy per baryon , on the other hand , appears to be a robust observable : its extracted value depends weakly on the modeling of hadron eigenvolumes .
finally , we explore the effect of including light nuclei into thermal fits and , somewhat surprisingly , find that results are even more sensitive to the assumptions regarding their eigenvolume parameters .
9 stoecker h , ogloblin a a and greiner w 1981 _ z. phys . _ a * 303 * 259
we analyze the sensitivity of thermal fits to heavy - ion hadron yield data of alice and na49 collaborations to the systematic uncertainties in the hadron resonance gas ( hrg ) model related to the modeling of the eigenvolume interactions . 
 we find a surprisingly large sensitivity in extraction of chemical freeze - out parameters to the assumptions regarding eigenvolumes of different hadrons . 
 we additionally study the effect of including yields of light nuclei into the thermal fits to lhc data and find even larger sensitivity to the modeling of their eigenvolumes . 
 the inclusion of light nuclei yields , thus , may lead to further destabilization of thermal fits . 
 our results show that modeling of eigenvolume interactions plays a crucial role in thermodynamics of hrg and that conclusions based on a non - interacting hrg are not unique .