$\Delta I=1$ axial-vector mixing and charge symmetry breaking

Abstract

Phenomenological Lagrangians that exhibit (broken) chiral symmetry as well as isospin violation suggest short-range charge symmetry breaking (CSB) nucleon-nucleon potentials with a \mbox{\boldmath \sigma}_1 \!\cdot\!\mbox{\boldmath \sigma}_2 structure. This structure could be realized by the mixing of axial-vector ($1^{+}$) mesons in a single-meson exchange picture. The Coleman-Glashow scheme for $\Delta I_z=1$ charge symmetry breaking applied to meson and baryon $SU(2)$ mass splittings suggests a universal scale. This scale can be extended to $\Delta I=1$ nonstrange CSB transitions $⟨a_1^{\circ }|H_{em}|f_1⟩$ of size $-0.005$ GeV${}^2$. The resulting nucleon-nucleon axial-vector meson exchange CSB potential then predicts $\Delta I=1$ effects which are small.

Comments: 14 pages. To appear in Phys. Lett. B