Since the discovery in 1952 of the first strange fragment in emulsion chamber experiments, much effort has been put into our knowledge of the nuclear chart to the SU(3) sector. Worldwide, the study of the interactions among nucleons and hyperons has been a priority in the research plan of many experimental facilities. After more than sixty years of Λ-hypernuclear studies, some attention has been placed in the production of ΛΛ-hypernuclei and more recently, proposals have been made to study Ξ-hypernuclear spectroscopy. Our main objective is to calculate the weak decay rate for ΛΛ-hypernuclei, including all the intermediate baryonic channels allowed by the strong interaction. In this contribution we focus on the analysis of the decay induced by two-body transitions starting with a ΛΛ pair. We present the weak and strong coupling constants required to perform such calculations using a mesonexchange model, built upon the exchange of mesons belonging to the ground state of pseudoscalar and vector octets. The tree-level values for the baryon-baryon-meson coupling constants are derived using SU(3) symmetry for pseudoscalar mesons and the Hidden Local Symmetry for vector mesons.

We study the non-mesonic weak decay of the doubly-strange hypernucleus 6 ΛΛ 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 Λ hyperons which induces novel weak transitions, whereby ΛΛ, ΞN and ΣΣ 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 ΛΛ → Y N decay rate studied in this work, ΓΛn + Γ Σ 0 n + Γ Σ − 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 ΓΛn/(Γ Σ 0 n + Γ Σ − p ), gets inverted when the mixing to ΞN states is incorporated in the initial correlated ΛΛ wave function. This sensitivity can be used experimentally to learn about the strong interaction in the strangeness −2 sector.

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