Weak magnetic field corrections to light vector or axial mesons mixings and vector meson dominance

Abstract

Weak magnetic-field-induced corrections to effective coupling constants describing light vector meson mixing and vector meson dominance (VMD) are derived. The magnetic field must be weak with respect to an effective quark mass M* such that: or . On that basis, a flavor SU(2) quark–quark interaction due to a non-perturbative one gluon exchange is considered. By means of methods usually applied to the Nambu—Jona-Lasinio and global color models, the equations for leading light vector/axial meson coupling to a background electromagnetic field are derived. The corresponding effective coupling constants are resolved in structureless mesons and long-wavelength limits. Some of the resulting coupling constants are redefined, so as to become magnetic-field-induced corrections to vector or axial meson couplings. Due to the approximated chiral symmetry of the model, light axial meson mixing induced by the magnetic field is also obtained. Numerical estimates are presented for the coupling constants and some of the corresponding momentum-dependent form factors. The contributions of the induced VMD and vector meson mixing couplings for the low-momentum pion electromagnetic form factor and for the (off-shell) charge symmetry violation potential at the constituent quark level are estimated. The relative overall weak magnetic-field-induced anisotropic corrections are of the order of , where n = 2 or n = 1, respectively.