Fluctuating temperature and baryon chemical potential in heavy-ion collisions and the position of the critical end point in the effective QCD phase diagram

We use the linear sigma model with quarks to locate the critical end point in the effective QCD phase diagram accounting for fluctuations in the temperature and quark chemical potential. For this purpose, we use the nonequilibrium formalism provided by the superstatistics framework. We compute the effective potential in the high- and low-temperature approximations up to sixth order and include the contribution of ring diagrams to account for plasma screening effects. We fix the model parameters from relations between the thermal sigma and pion masses imposing a first-order phase transition at zero temperature and a finite critical value for the baryon chemical potential that we take of the order of the nucleon mass. We find that the critical end point displacement due to fluctuations in the temperature and/or quark chemical potential is almost negligible.