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.
Highlights
Neutrinos and eventually the light axial mesons can be considered to probe the axial content of the nucleon, or their corresponding constituent quarks, and of other hadrons
A similar question to the one raised above arises: how can a topologically conserved quantity, involving the constituent quark vector current, be related to the nonconservation of the vector current that is due to the nondegenerate quark masses? to the axial current coupling to the vector meson, the axial meson profile and coupling might “select” a topologically preserved component of the vector current
In the presence of another particle, or in a finite density medium, the conservation of momentum can be satisfied and this anomalous mixing can contribute because vector and axial mesons propagate in orthogonal directions
Summary
Neutrinos and eventually the light axial mesons can be considered to probe the axial content of the nucleon, or their corresponding constituent quarks, and of other hadrons. Several nucleon properties are described directly, and mostly, in terms of constituent quarks that carry masses and charges of hadrons and they are directly responsible for the nucleon’s couplings to mesons and other particles This association might somewhat manifest in baryon form factors. Light vector meson (rho and omega) anomalous couplings to the constituent quark axial current will be derived in the vacuum and under a constant weak magnetic field by considering the same framework used in [16,54,59–61]. These anomalous couplings can be considered as corrections to the rho/omega (A1=f1) form factors that correspond to a very small axial (vector) component. In the last section there is a summary and final remarks
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