Off-shell behavior of the pi - eta mixing amplitude.

Abstract

We extend a recent calculation of the momentum dependence of the \ensuremath{\rho}-\ensuremath{\omega} mixing amplitude to the pseudoscalar sector. The \ensuremath{\pi}-\ensuremath{\eta} mixing amplitude is calculated in a hadronic model where the mixing is driven by the neutron-proton mass difference. Closed-form analytic expressions are presented in terms of a few nucleon-meson parameters. The observed momentum dependence of the mixing amplitude is strong enough as to question earlier calculations of charge-symmetry-breaking observables based on the on-shell assumption. The momentum dependence of the \ensuremath{\pi}-\ensuremath{\eta} amplitude is, however, practically identical to the one recently predicted for \ensuremath{\rho}-\ensuremath{\omega} mixing. Hence, in this model, the ratio of pseudoscalar-to-vector mixing amplitudes is, to a good approximation, a constant solely determined from nucleon-meson coupling constants. Furthermore, by selecting these parameters in accordance with charge-symmetry-conserving (CSC) data and SU(3)-flavor symmetry, we reproduce the momentum dependence of the \ensuremath{\pi}-\ensuremath{\eta} mixing amplitude predicted from chiral perturbation theory. Alternatively, one can use chiral-perturbation-theory results to set stringent limits on the value of the NN\ensuremath{\eta} coupling constant.