$U_A(1)$ symmetry breaking quark interactions from vacuum polarization

TL;DR

This paper derives sixth order quark interactions from vacuum polarization effects that break $U_A(1)$ symmetry, extending previous models and providing phenomenological insights into meson interactions and mixing parameters.

Contribution

It introduces new sixth order quark effective interactions from one-loop background field calculations that extend earlier fourth order models and include $U_A(1)$ symmetry breaking effects.

Findings

Derived sixth order quark interactions breaking $U_A(1)$ symmetry.

Compared meson interaction predictions with phenomenological data.

Calculated meson-mixing parameters consistent with existing results.

Abstract

By considering the one loop background field method for a quark-antiquark interaction, mediated by one (non perturbative) gluon exchange, sixth order quark effective interactions are derived and investigated in the limit of zero momentum transfer for large quark and/or gluon effective masses. They extend fourth order quark interactions worked out in previous works of the author. These interactions break $U_A(1)$ symmetry and may be either momentum independent or dependent. Part of these interactions vanish in the limit of massless quarks, and several other -- involving vector and/or axial quark currents -- survive. In the local limit of the resulting interactions, some phenomenological implications are presented, which correspond to corrections to the Nambu-Jona-Lasinio model. By means of the auxiliary field method, the local interactions give rise to three meson interactions whose values are compared to phenomenological values found in the literature. Contributions for meson-mixing parameters are calculated and compared to available results.