Locating the QCD critical endpoint through finite-size scaling

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, $119\text{MeV}\le T_c\le 162\text{MeV}$, $252\text{MeV}\le {\mu }_c\le 258\text{MeV}$, of the phase diagram.

4 pages, 3 figures

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