Revisiting the hypertriton lifetime puzzle

TL;DR

This paper investigates the conflicting measurements of the hypertriton lifetime from recent experiments, using a theoretical approach to understand the underlying decay mechanisms and constraints on its binding energy.

Contribution

The study provides a theoretical analysis of the hypertriton lifetime puzzle using chiral effective field theory and decay rate calculations, linking experimental results to hypernuclear binding energies.

Findings

ALICE and STAR experiments imply different constraints on the hypertriton's binding energy.

Theoretical decay rate calculations show opposing effects from $ ext{Sigma} NN$ admixtures and final-state interactions.

The hypertriton lifetime measurements correspond to distinct ranges of $ ext{Lambda}$ separation energy.

Abstract

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