Strong CP violation and chiral symmetry breaking in hot and dense quark matter

We investigate chiral symmetry breaking and strong CP violation effects in the phase diagram of strongly interacting matter. We demonstrate the effect of strong CP violating terms on the phase structure at finite temperature and densities in a 3-flavor Nambu-Jona-Lasinio (NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term. This is investigated using an explicit structure for the ground state in terms of quark-antiquark condensates for both in the scalar and the pseudoscalar channels. CP restoring transition with temperature at zero baryon density is found to be a second order transition at $\theta = \pi$ while the same at finite chemical potential and small temperature turns out to be a first order transition. Within the model, the tri-critical point turns out to be $(T_c,\mu_c)\simeq(273,94)$ MeV at $\theta = \pi$ for such a transition.