$\rho$ condensation and physical parameters

Abstract

Recently we showed how a non-local Nambu-Jona-Lasinio model comes out from QCD in the low-energy limit. In this way, it is possible to fix all the free parameters of the model with physical ones. We use this approach to derive a local limit to the Nambu-Jona-Lasinio model with the parameters those obtained from QCD in order to fix the physical parameters of $\rho$ condensation. $\rho$ condensation is a consequence of the highly non-trivial behavior of the QCD vacuum in presence a very strong magnetic field giving rising to superconductive behavior in quark matter. Determination of the proper parameters for this state can be an important helpful guide to identify it experimentally.