The Non-Mesonic Weak Decay of Double-Lambda Hypernuclei: A Microscopic Approach

TL;DR

This paper investigates the non-mesonic weak decay mechanisms of double-Lambda hypernuclei using a microscopic approach, including hyperon-induced channels, and predicts decay rates relevant for experimental studies and understanding hypernuclear physics.

Contribution

It introduces a comprehensive microscopic model for double-Lambda hypernuclei decay, incorporating hyperon-induced channels and meson exchange contributions, extending previous single-Lambda hypernuclei studies.

Findings

Decay rate for $ ext{ΛΛ} o ext{Λ} n$ is about 2.5% of free Λ decay rate.

Decay rate for $ ext{ΛΛ} o ext{Σ}^0 n$ and $ ext{ΛΛ} o ext{Σ}^- p$ is about 0.25% of free Λ decay rate.

Predictions highlight the importance of experimental measurements for hypernuclear physics and the possible existence of the H-dibaryon.

Abstract

The non--mesonic weak decay of double--$\Lambda$ hypernuclei is studied within a microscopic diagrammatic approach. Besides the nucleon--induced mechanism, $\Lambda N\to nN$, widely studied in single--$\Lambda$ hypernuclei, additional hyperon--induced mechanisms, $\Lambda \Lambda\to \Lambda n$, $\Lambda \Lambda\to \Sigma^0 n$ and $\Lambda \Lambda\to \Sigma^-p$, are accessible in double--$\Lambda$ hypernuclei and are investigated here. As in previous works on single--$\Lambda$ hypernuclei, we adopt a nuclear matter formalism extended to finite nuclei via the local density approximation and a one--meson exchange weak transition potential (including the ground state pseudoscalar and vector octets mesons) supplemented by correlated and uncorrelated two--pion--exchange contributions. The weak decay rates are evaluated for hypernuclei in the region of the experimentally accessible light hypernuclei $^{10}_{\Lambda\Lambda}$Be and $^{13}_{\Lambda\Lambda}$B. Our predictions are compared with a few previous evaluations. The rate for the $\Lambda \Lambda\to \Lambda n$ decay is dominated by $K$--, $K^*$-- and $\eta$--exchange and turns out to be about 2.5\% of the free $\Lambda$ decay rate, $\Gamma_{\Lambda}^{\rm free}$, while the total rate for the $\Lambda \Lambda\to \Sigma^0 n$ and $\Lambda \Lambda\to \Sigma^- p$ decays, dominated by $\pi$--exchange, amounts to about 0.25\% of $\Gamma_{\Lambda}^{\rm free}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the non--mesonic decay of strangeness $-2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$--dibaryon.