Off-shell behavior of the π-η mixing amplitude

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Abstract
We extend a recent calculation of the momentum dependence of the ρ-ω mixing amplitude to the pseudoscalar sector. The π-η 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 π-η amplitude is, however, practically identical to the one recently predicted for ρ-ω 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 π-η mixing amplitude predicted from chiral perturbation theory. Alternatively, one can use chiral-perturbation-theory results to set stringent limits on the value of the NNη coupling constant.
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