σ meson exchange effect on non-mesonic hypernuclear weak decay observables

Abstract

We analyze the influence of \ensuremath{\sigma} meson exchange on the main non-mesonic hypernuclear weak decay observables: Total rate ${\ensuremath{\Gamma}}_{\mathrm{NM}}$, neutron-to-proton branching ratio ${\ensuremath{\Gamma}}_{n/p}$, and proton asymmetry parameter ${a}_{\ensuremath{\Lambda}}$. The \ensuremath{\sigma} meson exchange is added to the standard strangeness-changing weak $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{NN}$ transition potential, which includes the exchange of the complete pseudoscalar and vector mesons octet ($\ensuremath{\pi},\ensuremath{\eta},K,\ensuremath{\rho},\ensuremath{\omega},{K}^{*}$). Using a shell model formalism, the \ensuremath{\sigma} meson weak coupling constants are adjusted to reproduce the recent ${\ensuremath{\Gamma}}_{\mathrm{NM}}$ and ${\ensuremath{\Gamma}}_{n/p}$ experimental data for ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$. Numerical results for the remaining observables of ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ and all the observables of ${}_{\ensuremath{\Lambda}}^{12}C$ decays are presented. They clearly show that the addition of the \ensuremath{\sigma} meson improves the agreement with the data. However, its effect it is not enough to reproduce well the ${a}_{\ensuremath{\Lambda}}$ values, which means that other improvements of the model must be explored to explain the puzzle posed by the experiments.