Pion scattering, light resonances and chiral symmetry restoration at nonzero chiral imbalance and temperature

We calculate the pion scattering amplitude at nonzero temperature and nonzero $\mu_5$, the chemical potential associated to chiral imbalance in a locally $P$-breaking scenario. The amplitude is calculated up to next to leading order in Chiral Perturbation Theory and is unitarized with the Inverse Amplitude Method to generate the poles of the $f_0(500)$ and $\rho (770)$ resonances. Within the saturation approach, the thermal $f_0(500)$ pole allows to determine $T_c(\mu_5)$, the transition temperature for chiral symmetry restoration. Our results confirm the growing behaviour of $T_c(\mu_5)$ found in previous works and, through a fit to lattice results, we improve the uncertainty range of the low-energy constants associated to $\mu_5$ corrections in the chiral lagrangian. The results for the $\rho (770)$ pole are compatible with previous works regarding the dilepton yield in heavy-ion collisions.