$q^2$-Dependence of Meson Mixing in Few-Body Charge Symmetry Breaking: $\pi^o-\eta$ Mixing to One Loop in Chiral Perturbation Theory

摘要

It is pointed out that the meson mixing matrix elements usually consideredresponsible for the bulk of the observed few-body charge symmetry breaking arenaturally $q^2$-dependent in QCD. For $\pi^o-\eta$ mixing, using the usualrepresentation of the pseudoscalar fields, the leading $q^2$ dependence can beexplicitly calculated using chiral perturbation theory to one loop, the resultbeing a significant decrease in the magnitude of the matrix element in goingfrom timelike to spacelike values of $q^2$. Since it is the latter range of$q^2$ which is relevant to NN scattering and the few-body bound state, thisresult calls into serious question the standard treatment of few-body chargesymmetry breaking contributions associated with $\pi^o-\eta$ and $\rho -\omega$mixing.