The $\pi$-mesonic decay of the hypertriton is calculated based on a hypertriton wave function and 3$N$ scattering states, which are rigorous solutions of three-body Faddeev equations using realistic $\mathrm{NN}$ and hyperon-nucleon interactions. The total $\pi$-mesonic decay rate is found to be 101% of the free $\Lambda$ decay rate, which is close to the experimental data. Together with the nonmesonic decay the total lifetime of ${}_{\Lambda }^3$H is predicted to be 2.56 $\times$ 10${}^{-10}$ sec which is 3% smaller than for the free $\Lambda$ particle. The differential decay rate is evaluated as a function of the pion momentum. The decay into the $N+d+\pi$ channel is stronger than in the $3N+\pi$ channel in contrast to the situation for the nonmesonic decay. The ratio for the decay rate into ${}^3$He + ${\pi }^{-}$ to the decay rate into all channels including ${\pi }^{-}$ is found to be 0.379, which is close to the experimental value. We visualize the decay into the dominant channel $p+d+{\pi }^{-}$ in a Dalitz plot. Finally we compare the polarization of the outgoing proton in free unpolarized $\Lambda$ decay to the polarization of ${}^3$He in unpolarized ${}_{\Lambda }^3$H decay and we compare the closely related asymmetry of ${\pi }^{-}$ emitted parallel and antiparallel with respect to the spin direction for a polarized $\Lambda$ to the corresponding asymmetry for a polarized ${}_{\Lambda }^3$H.

• Received 29 October 1997

DOI:https://doi.org/10.1103/PhysRevC.57.1595