Two model-independent results for the momentum dependence of ϱ-ω mixing

Two model-independent results on the momentum-dependence of ϱ-ω mixing are described. First, an explicit choice of interpolating fields for the vector mesons is displayed for which both the mixing in the propagator and the isospin-breaking at the nucleon-vector meson vertices (and hence also the one-vector-meson-exchange contribution to NN charge symmetry breaking) vanish identically at q2 = 0. Second, it is shown, using the constraints of unitarity and analyticity on the spectral function of the vector meson propagator, that there is no possible choice of interpolating fields for the ϱ0, ω0 mesons such that, with the ϱω element of the propagator defined by Δμνϱω(q2) = (gμν − qμqνq2)θ(q2)(q2 − mϱ2)(q2 − mω2), θ(q2) is independent of momentum. It follows that the standard treatment of charge symmetry breaking in few-body systems cannot be interpreted as arising from any realizable effective meson-baryon Lagrangian and must, therefore, be considered purely phenomenological in content.