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

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

1996-06-27

arxiv.org/abs/nucl-th/9606054v1

Phys.Lett. B385 (1996) 25-32

Physics

Nuclear Physics

Nuclear Theory

14 pages. To appear in Phys. Lett. B

Scientific paper

10.1016/0370-2693(96)00896-9

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 $\langle a_1^\circ|H_{em}|f_1\rangle$ 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.

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