pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a five percent change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed. We investigate the chiral transition of two flavor QCD in the chiral limit (i.e. massless quarks). Assuming that effective restoration of axial vector symmetry takes place at temperatures above the critical temperature of chiral symmetry restoration the transition is expected to be a second order phase transition falling in the O(4)-universality class [1]. This motivates the application of effective models constructed in terms of order parameters to describe chiral transitions, see e.g. [1, 2] and references therein. Explicit symmetry breaking changes the second order transition to a smooth crossover. Here we study the chiral symmetry restoration with Dyson-Schwinger equations (DSE). In order to take into account the relevant degrees of freedom, i.e. the ones which retain long-range fluctuations in the vicinity of a second order phase transition, we need to employ a truncation of the quark-gluon vertex that includes mesonic fluctuations. Such a scheme has been proposed in [3]. At finite temperatures it leads to a renormalised quark DSE of the form