Effects of $\Lambda \Lambda -\Xi N$ mixing in the decay of $S=-2$ hypernuclei

Abstract

We study the non-mesonic weak decay of the doubly-strange hypernucleus ${}_6^{\Lambda \Lambda }$He within a model which considers the exchange of pseudoscalar and vector mesons. Special attention is paid into quantifying the strong interaction effects, focussing on the interaction among the two {\Lambda} hyperons which induces novel weak transitions, whereby {\Lambda}{\Lambda}, {\Xi}N and {\Sigma}{\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 {\Lambda}{\Lambda} $\to$ Y N decay rate studied in this work, ${\Gamma }_{\Lambda n}+{\Gamma }_{{\Sigma }^{0}n}+{\Gamma }_{{\Sigma }^{-}p}$ , represents 3-4% of the total one-baryon induced non-mesonic decay and is remarkably affected by strong interaction effects. In particular, the relative importance of the partial decay rates, encoded in the ratio ${\Gamma }_{\Lambda n}/({\Gamma }_{{\Sigma }^{0}n}+{\Gamma }_{{\Sigma }^{-}p})$, gets inverted when the mixing to {\Xi}N states is incorporated in the initial correlated {\Lambda}{\Lambda} wave function. This sensitivity can be used experimentally to learn about the strong interaction in the strangeness -2 sector.