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

Abstract

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

Comments: v1: 17 pages, 2 figures, 3 tables; v2: slightly edited, Table 3 corrected, submitted for publication; v3: slightly edited in response to referee's comments, 19 pages, 2 figures, 3 tables, PLB published version