Flavor-dependent U(3) Nambu-Jona-Lasinio coupling constant

A nonperturbative one-gluon exchange quark-antiquark interaction is considered to compute flavordependent U(3) Nambu-Jona-Lasinio-type (NJL-type) interactions of the form G(ij,Gamma)((psi) over bar lambda i Gamma(psi))((psi) over bar lambda i Gamma(psi))for i, j = 0.8 and Gamma = I; i gamma(5) 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 f(1), f(2) = 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.

Automated summary

In this study, the flavor-dependent NJL-type interactions with one-gluon exchange quark-antiquark interaction were considered, leading to resolved coupling constants in all channels in the long-wavelength limit. The effect of flavor-dependent coupling constants on the masses of pions, kaons, and light scalar mesons was found to be significant compared to the effect of non-degeneracy of u, d, and s quark masses.