Effects of $\mathrm{\Lambda }\mathrm{\Lambda }\text{−}\mathrm{\Xi }N$ mixing in the decay of $S=-2$ hypernuclei

The nonmesonic weak decay of the doubly strange hypernucleus ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}{}^6\mathrm{He}$ is studied within a model that considers the exchange of pseudoscalar and vector mesons. Special attention is paid to quantifying the strong interaction effects, focusing on the interaction among the two $\mathrm{\Lambda }$ hyperons that induces novel weak transitions, whereby $\mathrm{\Lambda }\mathrm{\Lambda }$, $\mathrm{\Xi }N$, and $\mathrm{\Sigma }\mathrm{\Sigma }$ states decay into a hyperon-nucleon pair. The initial strangeness $-2$ wave function is obtained from the solution of a $G$-matrix equation with the input of realistic strong baryon-baryon potentials, while the final hyperon-nucleon wave functions are derived analogously from a microscopic $T$-matrix calculation. The new $\mathrm{\Lambda }\mathrm{\Lambda }\to YN$ decay rate studied in this work, ${\mathrm{\Gamma }}_{\mathrm{\Lambda }n}+{\mathrm{\Gamma }}_{{\mathrm{\Sigma }}^{0}n}+{\mathrm{\Gamma }}_{{\mathrm{\Sigma }}^{-}p}$, represents 3–4% of the total one-baryon-induced nonmesonic decay and is remarkably affected by strong interaction effects. In particular, the relative importance of the partial decay rates encoded in the ratio ${\mathrm{\Gamma }}_{\mathrm{\Lambda }n}/({\mathrm{\Gamma }}_{{\mathrm{\Sigma }}^{0}n}+{\mathrm{\Gamma }}_{{\mathrm{\Sigma }}^{-}p})$ gets inverted when the mixing to $\mathrm{\Xi }N$ states is incorporated in the initial correlated $\mathrm{\Lambda }\mathrm{\Lambda }$ wave function. This sensitivity can be used experimentally to learn about the strong interaction in the strangeness $-2$ sector.

Figure 1

Diagrammatric representation of a $B_1{B}_2\to B_1^{\prime }{B}_2^{\prime }$ transition within a one-meson-exchange model. The cross represents an insertion of a weak vertex.

Figure 2

Different components of the relative $\mathrm{\Lambda }\mathrm{\Lambda }$ radial wave function corresponding to the ${}^{1}S_0$ channel and for a value of the relative momentum of 100 MeV.

Figure 3

Pole model diagrams contributing to the weak PC baryon-baryon-meson amplitudes. The label S denotes a strong BBM vertex.