Constraining the position of the CEP through the speed of sound in the LSMq

We study the chiral phase transition within the linear sigma model with quarks from its thermodynamical potential considering quantum corrections up to ring diagrams in the high-temperature regime. Demanding a second order phase transition as expected in the chiral limit at low baryon chemical potential, that the curvature of the critical line matches the one obtained in lattice simulations and that the value of the speed of sound at high temperature and zero density has its measured value, we constrain the couplings and other free parameters of the model. We set restrictions to locate the position of the critical end point in the phase diagram from a fast drop-off of the critical line reminiscent from the behavior of the speed of sound near criticality. Our results set tight constrains in parameter space for the model to exhibit realistic features.