Fabio L. Braghin

Phys. Rev. D

24/05/2021

Abstract

A nonperturbative one-gluon exchange quark-antiquark interaction is considered to compute flavor-dependent U(3) Nambu–Jona-Lasinio-type (NJL-type) interactions of the form Gij,Γ(¯ψλiΓψ)(¯ψλjΓψ) for i,j = 0 … 8 and Γ = I,i γ5 from the one-loop polarization process with nondegenerate u-d-s quark effective masses. The resulting NJL-type coupling constants in all channels are resolved in the long-wavelength limit and the numerical results are presented for different choices of an effective gluon propagator. Leading deviations with respect to a flavor symmetric coupling constant are found to be of the order (M∗f2−M∗f1)n/(M∗f2+M∗f1)n, for n = 1, 2, where M∗fi are the effective masses of quarks f1, f2 = u, d and s. The scalar channel coupling constants Gij, s can be considerably smaller than the pseudoscalar ones. The effect of the flavor-dependence of coupling constants for the masses of pions and kaons may be nearly of the same order of magnitude as the effect of the u, d, and s quark mass nondegeneracy. The effect of these coupling constants is also verified for some of the light scalar meson masses, usually described by quark-antiquark states, and for some observables of the pseudoscalar mesons.

10.1103/PhysRevD.103.094028