Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1995-06-28
Phys.Lett. B362 (1995) 11-16
Physics
Nuclear Physics
Nuclear Theory
14 pages, uses REVTEX Entire manuscript available as a ps file at http://www.physics.adelaide.edu.au/theory/home.html Also ava
Scientific paper
10.1016/0370-2693(95)01208-8
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^{\rho\omega}_{\mu\nu}(q^2)= (g_{\mu\nu}-q_\mu q_\nu /q^2)$$\theta (q^2)/(q^2-m^2_\rho )(q^2- m^2_\omega )$, $\theta (q^2)$ 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.
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