Lifetime of the hypertriton

Abstract

Conflicting values of the hypertriton lifetime $τ({}_Λ^3\mathrm{H})$ 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 $τ({}_Λ^3\mathrm{H})$ comes sufficiently close to the free-$Λ$ lifetime $τ_Λ$,as expected naively for a very weakly bound $Λ$ in ${}_Λ^3\mathrm{H}$. We revisited theoretically this ${}_Λ^3\mathrm{H}$ lifetime puzzle, using ${}_Λ^3\mathrm{H}$ 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 $Γ({}_Λ^3\mathrm{H}\to{}^3\mathrm{He}+π^-)$. We found significant but opposing contributions arising from $ΣNN$ admixtures in ${}_Λ^3\mathrm{H}$ and from $π^- -{}^3\mathrm{He}$ final-state interaction. To derive $τ({}_Λ^3\mathrm{H})$, we evaluated the inclusive $π^-$ decay rate $Γ_{π^-}({}_Λ^3\mathrm{H})$ by using the measured branching ratio $Γ({}_Λ^3\mathrm{H}\to{}^3\mathrm{He}+π^-)/Γ_{π^-}({}_Λ^3\mathrm{H})$ and added the $π^0$ contributions through the $ΔI = \frac{1}{2}$ rule. The resulting $τ({}_Λ^3\mathrm{H})$ varies strongly with the rather poorly known $Λ$ separation energy $E_{\mathrm{sep}}({}_Λ^3\mathrm{H})$ and it is thus possible to associate each one of the distinct RHI $τ({}_Λ^3\mathrm{H})$ measurements with its own underlying value of $E_{\mathrm{sep}}({}_Λ^3\mathrm{H})$.