l - th / 9 30 10 02 v 1 4 J an 1 99 3 The Momentum Dependence of the ρ − ω Mixing Amplitude in a Hadronic Model

The Momentum Dependence of the ρ − ω Mixing Amplitude in a Hadronic Model. 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 ¯ 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 N N ω and the N N ρ 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. The existence of a nonzero mixing matrix element between the isovector ρ meson and the isoscalar ω meson is by now firmly established [1,2,3]. In addition to the observed (small) branching ratio for the G-parity forbidden decay of the ω meson into two pions, the understanding of the pion form factor at the ω-meson point (q 2 = m 2 ω) necessitates the coherent interplay of two distinct amplitudes; a dominant, G-parity allowed contribution (γ → ρ → 2π) interfering with a small (γ → ω → ρ → 2π) amplitude arising from ρ − ω mixing [1,3]. It has long been recognized that a ρ − ω mixing amplitude would give rise to charge symmetry violation (CSV) in the nucleon-nucleon (NN) force [2,4,5]. The ρ − ω contribution to the NN interaction is constructed by employing NN−meson vertices constrained by empirical two-nucleon data. The ρ − ω mixing amplitude, on the other hand, is obtained from a measurement of the pion form factor at the on-shell ω-meson point [1,3,6]. In one boson exchange (OBE) models of the NN force, nucleons interact via the exchange of several mesons possessing different Lorentz and isospin transformation properties [7,8]. In this paper we are concerned with the mixing between the isoscalar ω meson and the neutral 1