Two model-independent results for the momentum dependence of ϱ-ω mixing
Abstract 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 q 2 = 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 ϱ 0 , ω 0 mesons such that, with the ϱω element of the propagator defined by Δ μν ϱω (q 2 ) = (g μν − q μ q ν q 2 )θ(q 2 ) (q 2 − m ϱ 2 )(q 2 − m ω 2 ) , θ(q 2 ) 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.