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

Abstract

A non-perturbative one gluon exchange quark-antiquark interaction is considered to compute flavor dependent U(3) Nambu-Jona-Lasinio (NJL)-type interaction of the form $G_{ij,\Gamma }(\bar{\psi }{\lambda }_i\Gamma \psi )(\bar{\psi }{\lambda }_j\Gamma \psi )$ for $i,j=\mathrm{0...8}$ and $\Gamma =I,i{\gamma }_5$ from one loop polarization process with non degenerate u-d-s quark effective masses. The resulting NJL-type coupling constants in all channels are resolved in the long-wavelength limit and 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 of $(M_{f_2}^{\ast }-M_{f_1}^{\ast }{)}^n/(M_{f_2}^{\ast }+M_{f_1}^{\ast }{)}^n$, for $n=1,2$, where $M_{f_i}^{\ast }$ are the effective masses of quarks $f_1,f_2=u,d$ and $s$. The scalar channel coupling constants $G_{ij,s}$ can be considerably smaller than 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 non-degeneracy. The effect of these coupling constants is also verified for some of the light scalar mesons masses, usually described by quark-antiquark states, and for some observables of the pseudoscalar mesons.

18 pages, revised, improved and extended version, accepted for publication

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Cited by in corpus (10)

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• Strangeness content of the pion in the U(3) Nambu-Jona-Lasinio model
• Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants
• Spontaneous symmetry breakings in the singlet scalar Yukawa model within the auxiliary field method
• U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses
• Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field
• Heavy-meson chiral Lagrangians, effective flavored couplings, SU(4) flavor breaking and their consequences
• $U_A(1)$ symmetry breaking quark interactions from vacuum polarization
• Charged pions asymmetry from the decay of light neutral axial mesons due to interference
• Symmetry breaking effects in pion couplings to constituent quark currents