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In this work corrections to the usual flavor SU(2) Nambu-Jona-Lasiniocoupling due to a weak external magnetic field are calculated by consideringquark polarization in a (dressed) gluon exchange mechanism for quarkinteractions. The quark field is splitted into two components, one thatcondenses and another one that is a background field for interacting quarks,being the former integrated out. The resulting determinant is expanded forrelatively large quark mass and small magnetic field, $(eB_0/{M^*}^2)<1$ byresolving magnetic field dependent low energy quark effective interactions.Besides the corrections for the NJL and vector NJL effective couplings,different $B_0-$dependent effective couplings that break isospin and chiralsymmetry emerge.

SU(2) low energy quark effective couplings in weak external magnetic field