Speaker
Description
The three-body mesonic decays of the hypertriton are studied through Dalitz plots of their Lorentz-invariant phase space. Events are generated with the Raubold--Lynch algorithm. It factorises each decay into two successive two-body decays through a virtual nucleon--deuteron subsystem, whose invariant mass is sampled over its full kinematic range. Exact relativistic kinematics, isotropic angular sampling and Lorentz boosts give complete four-momenta for every event. An accept/reject step then produces unweighted samples distributed according to the phase-space measure. The available energies in the three-body decays are calculated from the recent $\Lambda$ separation energy in the MAMI A1 experiment. Dalitz plots are constructed in the frame-independent invariant-mass-squared variables. In both channels, events populate the kinematically allowed region uniformly, which confirms that flat relativistic three-body phase space is reproduced. The neutral-pion channel occupies a larger Dalitz region, consistent with its larger available energy. This approach allows for a separation between kinematics and dynamics. Any departure from uniformity in future calculations or measurements can be attributed directly to the weak-decay matrix element and to final-state interactions. For the neutral-pion channel, where no experimental data exist, these results provide a first kinematic reference.