Lifetime of the hypertriton

Abstract

Conflicting values of the hypertriton lifetime $\tau({}_\Lambda^3\mathrm{H})$ were derived in relativistic heavy ion (RHI) collision experiments over the last decade. A very recent ALICE Collaboration measurement is the only experiment where the reported $\tau({}_\Lambda^3\mathrm{H})$ comes sufficiently close to the free-$\Lambda$ lifetime $\tau_\Lambda$,as expected naively for a very weakly bound $\Lambda$ in ${}_\Lambda^3\mathrm{H}$. We revisited theoretically this ${}_\Lambda^3\mathrm{H}$ lifetime puzzle, using ${}_\Lambda^3\mathrm{H}$ and ${}^3\mathrm{He}$ wave functions computed within the abinitio no-core shell model employing interactions derived from chiral effective field theory to calculate the two-body decay rate $\Gamma({}_\Lambda^3\mathrm{H}\to{}^3\mathrm{He}+\pi^-)$. We found significant but opposing contributions arising from $\Sigma NN$ admixtures in ${}_\Lambda^3\mathrm{H}$ and from $\pi^- -{}^3\mathrm{He}$ final-state interaction. To derive $\tau({}_\Lambda^3\mathrm{H})$, we evaluated the inclusive $\pi^-$ decay rate $\Gamma_{\pi^-}({}_\Lambda^3\mathrm{H})$ by using the measured branching ratio $\Gamma({}_\Lambda^3\mathrm{H}\to{}^3\mathrm{He}+\pi^-)/\Gamma_{\pi^-}({}_\Lambda^3\mathrm{H})$ and added the $\pi^0$ contributions through the $\Delta I = \frac{1}{2}$ rule. The resulting $\tau({}_\Lambda^3\mathrm{H})$ varies strongly with the rather poorly known $\Lambda$ separation energy $E_{\mathrm{sep}}({}_\Lambda^3\mathrm{H})$ and it is thus possible to associate each one of the distinct RHI $\tau({}_\Lambda^3\mathrm{H})$ measurements with its own underlying value of $E_{\mathrm{sep}}({}_\Lambda^3\mathrm{H})$.