Inverse mass ordering of light scalar mesons in the Nambu Jona-Lasinio model

TL;DR

This paper investigates the inverse mass ordering of light scalar mesons within the three-flavor NJL model, demonstrating that a new flavor symmetry breaking mechanism can reproduce observed spectra and quark mass degeneracy.

Contribution

It introduces and tests a new mechanism for scalar meson mass ordering in the NJL model, aligning theoretical predictions with experimental observations.

Findings

NJL model reproduces inverse mass ordering with a new symmetry breaking term.

Degeneracy of strange and light quark masses achieved when inverse ordering is reproduced.

Scalar diquark masses support the consistency of quark mass degeneracy.

Abstract

The masses of the low-lying scalar mesons are investigated in the three-flavor Nambu Jona-Lasinio (NJL) model by treating the scalar mesons as composite objects of a quark and an antiquark. It is known that a simple $\bar qq$ picture fails to reproduce so-called inverse mass ordering for the scalar mesons. Recently a new mechanism to reproduce the observed mass spectrum of the scalar mesons was proposed in a linear sigma model by introducing flavor symmetry breaking induced by the U(1) axial anomaly. Motivated by this proposal, we examine whether this new mechanism works also in the NJL model. By calculating the scalar meson masses, we find that the NJL model reproduces the observed mass ordering with sufficient strength of the new term. With this mechanism, it turns out that the constituent strange quark mass gets degenerate to that of the up and down quark if the inverse mass ordering is reproduced. We also discuss the scalar diquark masses to check the consistency of the degeneracy of the constituent quark masses with the light baryon masses.