$\sigma$ meson exchange effect on nonmesonic hypernuclear weak decay observables

Abstract

We analyze the influence of $\sigma$ meson exchange on the main nonmesonic hypernuclear weak decay observables: the total rate, ${\Gamma }_{NM}$, the neutron-to-proton branching ratio, ${\Gamma }_{n/p}$, and the proton asymmetry parameter, $a_{\Lambda }$. The $\sigma$ meson exchange is added to the standard strangeness-changing weak $\Lambda N\to NN$ transition potential, which includes the exchange of the complete pseudoscalar and vector mesons octet ($\pi$, $\eta$, $K$, $\rho$, $\omega$, $K^{\ast }$). Using a shell model formalism, the $\sigma$ meson weak coupling constants are adjusted to reproduce the recent ${\Gamma }_{NM}$ and ${\Gamma }_{n/p}$ experimental data for ${}_{\Lambda }^{5}He$. Numerical results for the remaining observables of ${}_{\Lambda }^{5}He$ and all the observables of ${}_{\Lambda }^{12}C$ decays are presented. They clearly show that the addition of the $\sigma$ meson, in spite of improving some observables values, is not enough to reproduce simultaneously all the measurements, and the puzzle posed by the experimental data remains unexplained.

Comments: 4 pages, 1 figure. Submitted for publication in Phys. Rev