ISOSPIN-BREAKING VACUUM-TO-π0, η PSEUDOSCALAR MATRIX ELEMENTS AT NEXT-TO-LEADING ORDER IN THE CHIRAL EXPANSION

Abstract

We employ chiral perturbation theory (ChPT) to evaluate the complete set of pseudoscalar matrix elements, <0|Pf|π0,η>, with Pf any of the flavor-diagonal pseudoscalar currents (f=u,d,s) to [Formula: see text], and to next-to-leading order in the chiral expansion. These matrix elements represent the basic input to a QCD sum rule analysis of isospin breaking in the πNN couplings using the three-point function method. We also discuss how one could use the results to construct a one-parameter family of interpolating fields for the π0, all of whose members have zero vacuum-to-η matrix element, and explain how this could in principle be used to provide nontrivial tests of the reliability of the assumptions underlying the use of three-point function method. It is shown that the isospin-breaking mixing parameters required for this construction receive significant corrections beyond leading order in the chiral expansion.