Bound state in the vector channel of the extended Nambu--Jona-Lasinio model at fixed f_\pi

TL;DR

This paper demonstrates the existence of a bound state in the vector channel of the extended Nambu--Jona-Lasinio model at fixed f_pi, analyzing how the bound state properties depend on the coupling G_2 and quark mass.

Contribution

It reveals the conditions under which a vector bound state exists in the ENJL model at fixed f_pi, including the critical coupling values and mass behavior.

Findings

Bound state exists for any quark mass if G_2 ≥ 0.6/(8 f_pi^2)

Bound state becomes massless at G_2 = 1/(8 f_pi^2)

Model can fit rho meson mass with other observables

Abstract

We show that, as a consequence of fixing f_\pi = 93 MeV: (1) a bound state pole in the J^P = 1^- scattering amplitude of the ENJL model exists for arbitrarily weak (positive) vector coupling G_2 so long as the constituent quark mass is sufficiently large; (2) there is a bound state for any quark mass when G_2 \geq 0.6/(8 f_\pi^2); (3) this bound state becomes massless at G_2 = 1/(8 f_\pi^2) and a tachyon for G_2 exceeding it. We show by way of an example that the model has no trouble fitting the \rho meson mass simultaneously with other observables.