Charge-symmetry violation in pion scattering from three-body nuclei

Abstract

We discuss the experimental and theoretical status of charge-symmetry violation (CSV) in the elastic scattering of ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ on ${}^{3}\mathrm{H}$ and ${}^{3}\mathrm{He}.$ Analysis of the experimental data for the ratios ${r}_{1},$ ${r}_{2},$ and R at ${T}_{\ensuremath{\pi}}=142,$ 180, 220, and 256 MeV provides evidence for the presence of CSV. We describe pion scattering from the three-nucleon system in terms of single- and double-scattering amplitudes. External and internal Coulomb interactions as well as the ${\ensuremath{\Delta}}_{33}$-mass splitting are taken into account as sources of CSV. Reasonable agreement between our theoretical calculations and the experimental data is obtained for ${T}_{\ensuremath{\pi}}=180,$ 220, and 256 MeV. For these energies, it is found that the ${\ensuremath{\Delta}}_{33}$-mass splitting and the internal Coulomb interaction are the most important contributions for CSV in the three-nucleon system. The CSV effects are rather sensitive to the choice of pion-nuclear scattering mechanisms, but at the same time, our theoretical predictions are much less sensitive to the choice of the nuclear wave function. It is found, however, that data for ${r}_{2}$ and R at ${T}_{\ensuremath{\pi}}=142\mathrm{MeV}$ do not agree with the predictions of our model, which may indicate that there are additional mechanisms for CSV which are important only at lower energies.