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

Abstract

Two model-independent results on the momentum-dependence of $\rho$-$\omega$ 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 ${\rho }^0$, ${\omega }^0$ mesons such that, with the $\rho \omega$ element of the propagator defined by ${\Delta }_{\mu \nu }^{\rho \omega }(q^2)=(g_{\mu \nu }-q_{\mu }{q}_{\nu }/q^2)$$\theta (q^2)/(q^2-m_{\rho }^2)(q^2-m_{\omega }^2)$, $\theta (q^2)$ 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.

Comments: 14 pages, uses REVTEX Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also available via anonymous ftp at ftp://adelphi.adelaide.edu.au/pub/theory/ADP-95-35.T189.ps