  An effective model with pions and constituent quarks in the presence of a
weak external background electromagnetic field is derived by starting from a
dressed one gluon exchange quark-quark interaction.By applying the auxiliary
field and background field methods, the structureless pion limit is considered
to extract effective pion and constituent quark couplings in the presence of a
weak magnetic field. The leading terms of a large quark and gluon masses
expansion are obtained by resolving effective coupling constants which turn out
to depend on a weak magnetic field. Two pion field definitions are considered
for that. Several relations between the effective coupling constants and
parameters can be derived exactly or in the limit of very large quark mass at
zero and weak constant magnetic field. Among these ratios, the Gell Mann Oakes
Renner and the quark level Goldberger Treiman relations are obtained. In
addition to that, in the pion sector, the leading terms of Chiral Perturbation
Theory coupled to the electromagnetic field is recovered. Some numerical
estimates are provided for the effective coupling constants and parameters.
