Net baryon number probability distribution near the chiral phase transition

Abstract

We discuss properties of the net baryon number probability distribution near the chiral phase transition to explore the effect of critical fluctuations. Our studies are performed within Landau theory, where the coefficients of the polynomial potential are parametrized, so as to reproduce the mean-field (MF), the $Z(2)$ and $O(4)$ scaling behaviors of the cumulants of the net baryon number. We show, that in the critical region, the structure of the probability distribution changes, dependently on values of the critical exponents. In the MF approach, as well as in the $Z(2)$ universality class, the contribution of the singular part of the thermodynamic potential tends to broaden the distribution. By contrast, in the model with $O(4)$ scaling, the contribution of the singular part results in a narrower net baryon number probability distribution with a wide tail.