Abstract
Considering the 3d Ising universality class of the QCD critical endpoint we use a universal effective action for the description of the baryon-number density fluctuations around the critical region. Calculating the baryon-number multiplicity moments and determining their scaling with system's size we show that the critical region is very narrow in the direction of the baryon chemical potential $\mu$ and wide in the temperature direction $T$ for $T > T_c$. In this context, published experimental results on local proton density-fluctuation measurements obtained by intermittency analysis in transverse momentum space in NA49 central A+A collisions at $\sqrt{s_{NN}}=17.2$ GeV (A=C,Si,Pb), restrict significantly the location $(\mu_c,T_c)$ of the QCD critical endpoint. The main constraint is provided by the freeze-out chemical potential of the Si+Si system, which shows non-conventional baryon density fluctuations, restricting $(\mu_c,T_c)$ within a narrow domain, $119~\textrm{MeV} \leq T_c \leq 162~\textrm{MeV}$, $252~\textrm{MeV} \leq \mu_c \leq 258~\textrm{MeV}$, of the phase diagram.
Highlights
The search for the QCD critical endpoint (CEP), remnant of the chiral symmetry breaking, at a finite baryon density and high temperature, is the main task in contemporary relativistic ion collision experiments [1,2]
We will assume that CEP belongs to the 3D Ising universality class, a hypothesis which is strongly supported by several theoretical works [11,12,13,14,15]
We demonstrate that the Ising-QCD partition function reproduces consistently the finite-size scaling behavior expected for the 3D Ising universality class
Summary
The search for the QCD critical endpoint (CEP), remnant of the chiral symmetry breaking, at a finite baryon density and high temperature, is the main task in contemporary relativistic ion collision experiments [1,2]. We will make an effort to estimate the QCD CEP location employing an appropriate effective action for the thermodynamic description of the baryonic fluid around the critical region. To this end, we will assume that CEP belongs to the 3D Ising universality class, a hypothesis which is strongly supported by several theoretical works [11,12,13,14,15].
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