Two Model-Independent Results for the Momentum Dependence of Rho-Omega Mixing

الأصل · EN

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 Δρωμν(q²)= (gμν-qμqν/q²)θ(q²)/(q²-m²ρ)(q²- m²ω), 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.