π-mesonic decay of the hypertriton

The π-mesonic decay of the hypertriton is calculated based on a hypertriton wave function and 3N scattering states, which are rigorous solutions of three-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The total π-mesonic decay rate is found to be 101% of the free Λ decay rate, which is close to the experimental data. Together with the nonmesonic decay the total lifetime of _Λ³H is predicted to be 2.56 × 10^-10 sec which is 3% smaller than for the free Λ particle. The differential decay rate is evaluated as a function of the pion momentum. The decay into the N+d+π channel is stronger than in the 3N+π channel in contrast to the situation for the nonmesonic decay. The ratio for the decay rate into ³He + π^- to the decay rate into all channels including π^- is found to be 0.379, which is close to the experimental value. We visualize the decay into the dominant channel p+d+π^- in a Dalitz plot. Finally we compare the polarization of the outgoing proton in free unpolarized Λ decay to the polarization of ³He in unpolarized _Λ³H decay and we compare the closely related asymmetry of π^- emitted parallel and antiparallel with respect to the spin direction for a polarized Λ to the corresponding asymmetry for a polarized _Λ³H.