General Chiral-Symmetry Breaking andσTerms

We systematically investigate the properties of general chiral-symmetry breaking in a $\sigma$ model. We obtain not only the conventional results of nonlinear pion models, but also the effects of the symmetry breaking upon $\sigma$ terms. We show that the $\sigma$ terms depend upon the fraction of the pion mass coming from the chirally symmetric part of the model, as well as upon the representation of the symmetry-breaking part of the model.