Hot QCD at finite isospin density: confronting SU(3) Nambu-Jona-Lasinio model with recent lattice data

Extending our recently published $SU(2)$ results for zero temperature we now compute the QCD equation of state for finite isospin density within the three flavor Nambu-Jona-Lasinio model in the mean field approximation, motivated by the recently obtained Lattice QCD results for both zero and finite temperatures. Like our previous study, here also we have considered both the commonly used Traditional cutoff Regularization Scheme and the Medium Separation Scheme. Our results are compared with recent high-precision lattice simulations as well as previously obtained results in two-flavor Nambu-Jona-Lasinio model. The agreement between the lattice results and the predictions from three-flavor NJL model is very good for low values of $\mu_I$ (for both zero and finite temperatures). For larger values of $\mu_I$, the agreement between lattice data and the two-flavor NJL predictions is surprisingly good and better than with the three-flavor predictions.