Chiral QCD phase in equilibrium with Hadron Gas and the location of the critical point

We develop a description of the equation of state of QCD matter with restored chiral symmetry, which is in thermal and chemical equilibrium with the hadronic phase. The hadron gas is described with self-consistent volume corrections. The chiral phase is composed of a group of few quark condensates, each of which corresponds to a family of hadrons with specific quark content. Between the two phases and along the chemical freeze-out curve we apply not only the conservation of quantum numbers, carried by quarks, but the more restrictive requirement of conservation of particle numbers per family. For hadronic radius connected with the repulsive interaction, $r_0$, equal for all hadrons, we find that the pion system is responsible for the shift of the transition from higher order (crossover) to first order. We calculate the position of the critical point as function of $r_0$. We present full results for a specific choice of $r_0$.