(Pseudo) Scalar mesons in a self-consistent NJL model

In this study, we investigate the mass spectra of pi and sigma mesons at finite chemical potential using the self-consistent NJL model and the Fierz-transformed interaction Lagrangian. The model introduces an arbitrary parameter alpha to reflect the weights of the Fierz-transformed interaction channels. We show that, when alpha exceeds a certain threshold value, the chiral phase transition transforms from a first-order one to a smooth crossover, which is evident from the behaviors of the chiral condensates and meson masses. Additionally, at a high chemical potential, the smaller the value of alpha, the higher the masses of the pi and sigma mesons. Moreover, the Mott and dissociation chemical potentials increase with the increase in alpha. Thus, the meson mass emerges as a valuable experimental observable for determining the value of alpha and investigating the properties of the chiral phase transition in dense QCD matter.