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

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 $langle a_1^circ|H_{em}|f_1rangle$ 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.