Role of the axial vectora1-meson exchange in hypernuclear nonmesonic weak decays

Abstract

In the meson-theoretical potential model for the study of the nonmesonic decay rates and asymmetries of hypernuclei, for the first time, the axial-vector ${a}_{1}$ meson (${J}^{\mathrm{PC}}={1}^{++},{m}_{{a}_{1}}=1230\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$) is introduced. The ${a}_{1}$ meson is the chiral partner of the \ensuremath{\rho} meson and has been treated in the meson-pair exchange framework as $\ensuremath{\rho}\ensuremath{\pi}/{a}_{1}$ and $\ensuremath{\sigma}\ensuremath{\pi}/{a}_{1}$. This is analogous to the treatment of \ensuremath{\rho} and \ensuremath{\sigma} exchange in our model. The ${a}_{1}$-meson exchange is found to give remarkable modifications of the parity-conserving decay potentials $({}^{1,3}S\ensuremath{\rightarrow}{}^{1,3}S$ and ${}^{3}{S}_{1}\ensuremath{\rightarrow}{}^{3}{D}_{1})$ at short range $r\ensuremath{\leqslant}1$ fm. As a result, the calculated intrinsic asymmetry parameter ${\ensuremath{\alpha}}_{\ensuremath{\Lambda}}$ for ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ becomes very small and positive in good agreement with the recent high-quality experimental data. The calculated small values of ${\ensuremath{\alpha}}_{\ensuremath{\Lambda}}$ are well compared with the data for ${}_{\ensuremath{\Lambda}}^{11}\mathrm{B}$ and ${}_{\ensuremath{\Lambda}}^{12}\mathrm{C}$ within error bars. The inclusion of the ${a}_{1}$ meson also improves the ${\ensuremath{\Gamma}}_{n}/{\ensuremath{\Gamma}}_{p}$ ratios and leads to a consistent explanation for the existing nonmesonic weak decay data of the light \ensuremath{\Lambda} hypernuclei $(A\ensuremath{\leqslant}12)$. The results calculated in the $\ensuremath{\pi}+2\ensuremath{\pi}/\ensuremath{\rho}+2\ensuremath{\pi}/\ensuremath{\sigma}+\ensuremath{\omega}+K+\ensuremath{\rho}\ensuremath{\pi}/{a}_{1}+\ensuremath{\sigma}\ensuremath{\pi}/{a}_{1}$ exchange interaction model are presented together with the estimates without ${a}_{1}$. Also, the derivation of the expression for the proton asymmetry is described in some detail to elucidate the calculation procedures and phase conventions.