Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field

TL;DR

This paper derives unusual axial current couplings of constituent quarks to light vector mesons in vacuum and weak magnetic fields, revealing anisotropic interactions and form factors suppressed compared to minimal couplings.

Contribution

It introduces novel axial and vector meson couplings mediated by nonperturbative gluon exchange, including anisotropic effects and meson mixing under magnetic fields.

Findings

Couplings are suppressed by approximately 1/M*^2 compared to minimal coupling.

Anisotropic and polarization-dependent interactions are identified.

Meson mixing occurs at non-zero magnetic fields, affecting meson interactions.

Abstract

Unusual constituent quark axial current couplings to light vector mesons, $\rho$ and $\omega$, are derived in the vacuum and under weak magnetic field by considering a quark-antiquark interaction mediated by a non perturbative gluon exchange. Similarly, light axial mesons are found to couple anomalously with the constituent quark vector current. These interactions are of the type of the Wess-Zumino-Witten terms, being strongly anisotropic and dependent on the vector (or axial) meson polarization. They also provide axial (vector) form factors for the vector (axial) mesons and are quite small, suppressed nearly by $1/{M^*}^2$ with respect to the vector mesons minimal coupling to the quark vector current. Some three leg meson vertices are also presented: $\pi-\rho-A_1$ and $V_1V_2 A$ (where $V_1,V_2$ are vector mesons and $A$ an axial meson). A vector and axial-vector mesons mixing is identified at non zero magnetic field which however can contribute only in the presence of a third particle or in a medium. Numerical results are presented for different effective gluon propagators.