Mass dependence of pseudocritical temperature in mean field approximation

We implement the Dyson-Schwinger equation approach to study the mass dependence of pseudocritical temperature of QCD crossover at zero chemical potential. For the quark-gluon vertex, we take simply the rainbow approximation, while for the gluon propagator, we make use of various dressing functions. We analyze the scaling behavior with these different gluon models and obtain the critical exponent consistent with the mean field value for 3D O(4) universality class, which means the rainbow truncation will lead to the mean field result, regardless of the gluon dressing model. The size of critical region is up to m(0) <= 1-2 MeV in this mean field approximation, which sets naturally an upper bound of the critical region since the fluctuations beyond mean field usually diminish the critical region. The pseudocritical temperature corresponds to the maximum value of the chiral susceptibility, and for the chiral susceptibility of a certain percentage of its maximum value, the corresponding temperature might be mass independent. We analyze this percentage and studied the pion mass range in which the corresponding temperature remain constant. The results show that this percentage and the pion mass range depend on the details of interaction kernel, which differs in gluon models.