Chemical potential response of pseudoscalar meson masses in the Nambu--Jona-Lasinio model

TL;DR

This study investigates how the masses of pseudoscalar mesons like pions and kaons respond to changes in chemical potential within the NJL model, considering different vector coupling scenarios and their dependence on quark mass differences.

Contribution

It provides a detailed analysis of the chemical potential response of meson masses in the NJL model, including effects of vector coupling and quark mass differences, which is novel.

Findings

dm/dμ for pions differs significantly from that for kaons.

The response depends strongly on the mass difference between quarks.

Including vector coupling g_V alters the response behavior.

Abstract

Using the Nambu--Jona-Lasinio (NJL) model we study chemical potential response of the pion and kaon masses as a function of temperature and chemical potential, i.e., dm/d\mu (T, \mu). First, we obtain the responses assuming the vector-axial vector coupling is zero (g_V=0). Then, we include a non-zero g_V and study the effects of g_V on the responses. We find that the behavior of dm/d\mu for the pion is quite different from that for the kaon. It means that dm/d\mu is much dependent on the mass difference between the two quarks, i.e., the u and s quarks (or even between the u and d quarks). Our results may give a clue to future studies of dm/d\mu on the lattice.