The Momentum Dependence of the $ρ-ω$ Mixing Amplitude in a Hadronic Model

Abstract

We calculate the momentum dependence of the $ρ-ω$ mixing amplitude in a purely hadronic model. The basic assumption of the model is that the mixing amplitude is generated by $N{\bar{N}}$ loops and thus driven entirely by the neutron-proton mass difference. The value of the amplitude at the $ω$-meson point is expressed in terms of only the $NNω$ and the $NNρ$ coupling constants. Using values for these couplings constrained by empirical two-nucleon data we obtain a value for the mixing amplitude in agreement with experiment. Extending these results to the spacelike region, we find a $ρ-ω$ contribution to the NN interaction that is strongly suppressed and opposite in sign relative to the conventional contribution obtained from using the constant on-shell value for the mixing amplitude.