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$ΔI=1$ axial-vector mixing and charge symmetry breaking

S. A. Coon·B. H. J. McKellar·V. G. J. Stoks
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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 $σ$}_1 \!\cdot\!\mbox{\boldmath $σ$}_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 $ΔI_{z}=1$ charge symmetry breaking applied to meson and baryon $SU(2)$ mass splittings suggests a universal scale. This scale can be extended to $ΔI=1$ nonstrange CSB transitions $\langle a_1^\circ|H_{em}|f_1\rangle$ of size $-0.005$ GeV$^2$. The resulting nucleon-nucleon axial-vector meson exchange CSB potential then predicts $ΔI=1$ effects which are small.

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S. A. Coon, B. H. J. McKellar, V. G. J. Stoks. 1996-06-27. $ΔI=1$ axial-vector mixing and charge symmetry breaking. https://doi.org/10.1016/0370-2693(96)00896-9

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