  Weak magnetic field induced corrections to effective coupling constants
describing light vector mesons mixings and vector meson dominance (VMD) are
derived. The magnetic field must be weak with respect to an effective quark
mass $M^*$ such that: $eB_0/{M^*}^2< 1$ or $eB_0/{M^*}^2<<1$.For that, a flavor
SU(2) quark-quark interaction due to non perturbative one gluon exchange is
considered. By means of methods usually applied to the Nambu Jona Lasinio (NJL)
and Global Color Models (GCM), leading light vector/axial mesons couplings to a
background electromagnetic field are derived. The corresponding effective
coupling constants are resolved in the structureless mesons and longwavelength
limits. Some of the resulting coupling constants are redefined such as to
become magnetic field induced corrections to vector or axial mesons couplings.
Due to the approximated chiral symmetry of the model, light axial mesons
mixings induced by the magnetic field are also obtained. Some numerical
estimates are presented for the coupling constants and for some of the
corresponding momentum dependent vertices. The contributions of the induced VMD
and vector mesons 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 $(eB_0/{M^*}^2)^n$,
where $n=2$ or $n=1$ respectively.

High Energy Physics - Phenomenology;Nuclear Theory