Quark-bag model with low-energy pion interactions. I. Theory

A standard method for restoring chiral symmetry in the bag model is to introduce an explicit external pion field. Questions of the consistency and compatibility of this method with the assumptions of the static-cavity approximation of the bag model are discussed. An approximate version of the model is justified. It is argued that consistency requires treating pion-induced quark-pair creation and annihilation at the bag surface as a zeroth-order process in pion-coupling perturbation theory. An approximation treating these pairs as an inward extension of the pion field is discussed. The resulting model gives an improved value of $g_A$.