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

Abstract: We investigate the effect of $α$-core breakup on the strong conversion of ({}^{6}_{ΛΛ}\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-(α) result. At (B_{ΛΛ}^{H}=176~\mathrm{MeV}), corresponding to (m_H\simeq2055~\mathrm{MeV}), the summed breakup width exceeds the intact-(α) width by a factor (R_{\mathrm{br}}=2.49\times10^{3}). The resulting inclusive width and lifetime are (Γ{\mathrm{inc}}=3.87\times10^{-4}~\mathrm{eV}) and (τ{\mathrm{inc}}=1.70\times10^{-12}~\mathrm{s}), respectively, compared with (τα=4.25\times10^{-9}~\mathrm{s}) for the intact-(α) 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}\lesssimτ{\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-(Λ) hypernuclei remain compatible, within the present framework, with a deeply bound (uuddss) state in the mass range relevant to sexaquark dark matter.