Conflicting values of the hypertriton ($_��^{3}$H) lifetime were extracted in recent relativistic heavy-ion collision experiments. The ALICE Collaboration's reported $_��^{3}$H lifetime $��(_��^{3}$H) is compatible within measurement uncertainties with the free $��$ lifetime $��_��$, as naively expected for a loosely bound $��$ hyperon in $_��^{3}$H, whereas STAR's reported range of $��(_��^{3}$H) values is considerably shorter: $��_{\rm STAR}(_��^{3}$H)$\sim$(0.4-0.7)$��_��$. This $_��^{3}$H lifetime puzzle is revisited theoretically using $_��^{3}$H three-body wavefunctions generated in a chiral effective field theory approach to calculate the decay rate $��(_��^{3}$H$\,\to ^3$He$\,+��^-$). Significant but opposing contributions arise from $��NN$ admixtures in $_��^{3}$H and from $��^-$-$^3$He final-state interaction. Evaluating the inclusive $��^-$ decay rate $��_{��^-}(_��^{3}$H) via a branching ratio $��(_��^{3}$H$\,\to ^{3}$He+$��^-)/��_{��^-}(_��^{3}$H) determined in helium bubble-chamber experiments, and adding $��_{��^0}(_��^{3}$H) through the $��I=\frac{1}{2}$ rule, we derive $��(_��^{3}$H) assuming several different values of the $��$ separation energy $B_��(_��^{3}$H). It is concluded that each of ALICE and STAR reported $��(_��^{3}$H) intervals implies its own constraint on $B_��(_��^{3}$H): $B_��\lesssim 0.1$ MeV for ALICE, $B_��\gtrsim 0.2$ MeV for STAR.

14 pages, 3 tables, 1 figure. v1 -- before submission for publication. v2 -- minor editorial revisions, as submitted for publication. v3 -- slight editorial revision, few references deleted and few added. v4 -- PLB 811 (2020) 135916 published version