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

• Published in: Physical review. D 2021-05, Vol.103 (9), p.1, Article 094028
• Main Author: Braghin, Fabio L.
• Format: Article
• Language: English
• Subjects: Coupling; Flavor (particle physics); Gluons; Kaons; Mesons; Pions; Quarks
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.103.094028

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, iγ5 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.