Isospin-Violating Meson-Nucleon Vertices as an Alternate Mechanism of Charge-Symmetry Breaking

Abstract

We compute isospin-violating meson-nucleon coupling constants and their consequent charge-symmetry-breaking nucleon-nucleon potentials. The couplings result from evaluating matrix elements of quark currents between nucleon states in a nonrelativistic constituent quark model; the isospin violations arise from the difference in the up and down constituent quark masses. We find, in particular, that isospin violation in the omega-meson--nucleon vertex dominates the class IV CSB potential obtained from these considerations. We evaluate the resulting spin-singlet--triplet mixing angles, the quantities germane to the difference of neutron and proton analyzing powers measured in elastic $\vec{n}-\vec{p}$ scattering, and find them commensurate to those computed originally using the on-shell value of the $ρ$-$ω$ mixing amplitude. The use of the on-shell $ρ$-$ω$ mixing amplitude at $q^2=0$ has been called into question; rather, the amplitude is zero in a wide class of models. Our model possesses no contribution from $ρ$-$ω$ mixing at $q^2=0$, and we find that omega-meson exchange suffices to explain the measured $n-p$ analyzing power difference~at~183 MeV.