(Pseudo) Scalar mesons in a self-consistent NJL model* *X.W. is supported by the Start-up Funding of Jiangsu University(4111190010) and the Natural Science Foundation of China (12147103)

Abstract

In this study, we investigate the mass spectra of π and σ mesons at finite chemical potential using the self-consistent NJL model and the Fierz-transformed interaction Lagrangian. The model introduces an arbitrary parameter α to reflect the weights of the Fierz-transformed interaction channels. We show that, when α 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 α, the higher the masses of the π and σ mesons. Moreover, the Mott and dissociation chemical potentials increase with the increase in α. Thus, the meson mass emerges as a valuable experimental observable for determining the value of α and investigating the properties of the chiral phase transition in dense QCD matter.