Hypernuclear constraints on the existence and lifetime of a deeply bound $H$ dibaryon

We study to what extent the unique observation of $\mathrm{\Lambda }\mathrm{\Lambda }$ hypernuclei by their weak decay into known $\mathrm{\Lambda }$ hypernuclei, with lifetimes of order 10${}^{-10}$ s, rules out the existence of a deeply bound doubly-strange ($\mathcal{S}$=$-$2) $H$ dibaryon. Treating ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6\mathrm{H}\mathrm{e}$ (the Nagara emulsion event) in a realistic $\mathrm{\Lambda }-\mathrm{\Lambda }-{}^4$He three-body model, we find that the ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6\mathrm{H}\mathrm{e}\to H+{}^4\mathrm{H}\mathrm{e}$ strong-interaction lifetime increases beyond 10${}^{-10}$ s for $m_H<m_{\mathrm{\Lambda }}+m_n$, about 176 MeV below the $\mathrm{\Lambda }\mathrm{\Lambda }$ threshold, so that such a deeply bound $H$ is not in conflict with hypernuclear data. Constrained by $\mathrm{\Lambda }$ hypernuclear $\mathrm{\Delta }\mathcal{S}$=1 nonmesonic weak-interaction decay rates, we follow EFT methods to evaluate the $\mathrm{\Delta }\mathcal{S}$=2 $H\to nn$ weak-decay lifetime of $H$ in the mass range $2m_n\lesssim m_H<m_{\mathrm{\Lambda }}+m_n$. The resulting $H$ lifetime is of order 10${}^5$ s, many orders of magnitude shorter than required to qualify for a dark-matter candidate.