Derivative expansion of the effective action in Yang-Mills theory

The effective action model for mesons relies on the one-loop effective action in quantum chromodynamics in the presence of a constant background chromoelectric field in a fixed direction in group space. We extend this effective action so as to include those terms quadratic in the first derivate of the field, for both a chromoelectric and chromomagnetic background field. An instability arises in the chromoelectric case.