Alpha-Core Breakup in the Strong Decay of \({}_{\Lambda\Lambda}^{6}\mathrm{He}\) to a Deeply Bound \(H\) Dibaryon

Abstract

We investigate the effect of $\alpha$-core breakup on the strong conversion of \({}^{6}_{\Lambda\Lambda}\mathrm{He}\) into a deeply bound \(H\) dibaryon. In addition to the coherent \(H+{}^{4}\mathrm{He}\) channel, we evaluate the open final states \(H+p+{}^{3}\mathrm{H}\), \(H+n+{}^{3}\mathrm{He}\), and \(H+d+d\) using a translationally invariant Gaussian cluster description, including spin-isospin recoupling and full nonrelativistic three-body phase-space integrations. The breakup widths are normalized to Gal's intact-\(\alpha\) result. At \(B_{\Lambda\Lambda}^{H}=176~\mathrm{MeV}\), corresponding to \(m_H\simeq2055~\mathrm{MeV}\), the summed breakup width exceeds the intact-\(\alpha\) width by a factor \(R_{\mathrm{br}}=2.49\times10^{3}\). The resulting inclusive width and lifetime are \(\Gamma_{\mathrm{inc}}=3.87\times10^{-4}~\mathrm{eV}\) and \(\tau_{\mathrm{inc}}=1.70\times10^{-12}~\mathrm{s}\), respectively, compared with \(\tau_{\alpha}=4.25\times10^{-9}~\mathrm{s}\) for the intact-\(\alpha\) channel alone. The mass-dependent calculation shows that the inclusive lifetime crosses the characteristic hypernuclear weak-decay timescale near \(m_H\simeq2020~\mathrm{MeV}\) and increases rapidly as the \(H\) mass decreases. In the representative dark-matter-motivated interval \(1865\leq m_H\leq1885~\mathrm{MeV}\), we obtain \(6.59\times10^{-4}\lesssim\tau_{\mathrm{inc}}\lesssim 6.80\times10^{-3}~\mathrm{s}\), far exceeding the weak-decay timescale. Thus, although core breakup can dominate the inclusive strong width near \(m_H\simeq2055~\mathrm{MeV}\), weakly decaying double-\(\Lambda\) hypernuclei remain compatible, within the present framework, with a deeply bound \(uuddss\) state in the mass range relevant to sexaquark dark matter.