Q2-dependence of meson mixing in few-body charge symmetry breaking. π0-η mixing to one loop in chiral perturbation theory

Abstract

It is pointed out that the meson mixing matrix elements usually considered responsible for the bulk of the observed few-body charge symmetry breaking are naturally q2-dependent in QCD. For π0-η mixing, using the usual representation of the pseudoscalar fields, the leading q2-dependence can be explicitly calculated using chiral perturbation theory to one loop, the result being a significant decrease in the magnitude of the matrix element in going from timelike to spacelike values of q2. Since it is the latter range of q2 which is relevant to NN scattering and the few-body bound state, this result calls into serious question the standard treatment of few-body charge symmetry breaking contributions associated with π0-η and ϱ-ω mixing.