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ADIABATIC CHEMICAL FREEZE-OUT AND WIDE RESONANCE
MODIFICATION IN A THERMAL MEDIA
K.A. Bugaev 1† , D.R. Oliinychenko 2 , E.G. Nikonov 3 , A.S. Sorin 2 and G.M. Zinovjev 1
(1) Bogolyubov Institute for Theoretical Physics, Metrologichna str. 14 B , Kiev 03680, Ukraine
(2) Bogoliubov Laboratory of Theoretical Physics, JINR, Joliot-Curie str. 6, Dubna, Russia
(3) Laboratory for Information Technologies, JINR, Joliot-Curie str. 6, 141980 Dubna, Russia
† E-mail: Bugaev@th.physik.uni-frankfurt.de
The hadron resonance gas model [1] is a reliable theoretical tool to extract information
about the chemical freeze-out (FO) stage of the relativistic heavy ion collisions. However,
the question about the reliable chemical FO criterion has a long history [1, 2]. Very
recently this question was thoroughly investigated again [2], using the most sophisticated
version of the hadron resonance gas model. Similarly to [1] it was found that none of
the formerly suggested chemical FO criteria is robust, if the realistic particle table with
the hadron masses up to 2.6 GeV is used. However, in [2] the criterion of the adiabatic
chemical FO was suggested. In [2] it was also shown that despite an essential difference
with the model of [1] the same conclusion on the constant entropy per particle at chemical
FO is reproduced by the chemical FO parameters found in [1]. Thus, it turns out that
the criterion of the constant entropy per particle at chemical FO is, indeed, the reliable
one.
Despite the long history of this question there was no a single try to understand what
is the physical reason behind any of the chemical FO criterion. Therefore we developed
a simple model equation of state which not only well describes the chemical FO thermodynamic
parameters and reproduces the constant value of the entropy per particle at
the chemical FO, but which allows us to elucidate the real mass spectra of mesons and
baryons that generate such a criterion. Our analysis demonstrates that the real mass
spectrum of hadrons is very much different from the Hagedorn mass spectrum which is
traditionally expected to emerge already for hadrons with masses above 1.2 GeV [3]. We
argue that the real mass spectrum of hadrons is not an exponential, but a power-like
and the reason for such a behavior is in the existence of many wide resonances. The
main point is that that the presence of thermal media essentially modifies the resonance
mass distribution in case of large width and leads to the resonance sharpening near the
threshold. The related effect of wide resonance enhancement compared to their treatment
as stable particles with the average resonance mass is also discussed. Both effects are
demonstrated in Fig. 2. Based on these findings we suggest that the quark-gluon bags
maybe observed at the NICA energies as the narrow resonances with mass between 2.5
and 4 GeV which are absent in the tables of elementary particle properties.
Contacting the non-relativistic Boltzmann distribution in resonance energy φ(m,T) ≃
[ mT
2π 2 ]3
2
exp [ − m T
]
with the cut Gaussian distribution Θ
(
m−M
Th
k
) ]
exp
[− (m k−m) 2
over
the resonance mass m one can easily see that the maximum of the resulting mass distribution
is located at m = ˜m k ≡ m k − σ2 k
T
for k-th resonance. In addition, the resonance
degeneracy factor g k is changed to an effective value ˜g k = g k exp[
σ 2
k
2T 2 ]. Here m k denotes
the mean mass of the resonance k-th in a vacuum, while its Gaussian width in a vacuum is
σ k (note that thetrue width of such a resonance is Γ k = Qσ k with Q ≡ 2 √ 2 ln2 ≈ 2.355).
32
2σ 2 k