Emile Meoto
A Monte Carlo construction is presented for the three-body mesonic decay phase space of the hypertriton. This is accomplished using the Raubold-Lynch sequential two-body decay algorithm. The method factorises this three-body decay into successive two-body decays through a virtual intermediate subsystem, whose invariant mass is sampled over the full kinematically allowed region. Exact relativistic two-body kinematics and Lorentz transformations are employed to construct complete four-momenta for all decay products. The construction is applied to both charged- and neutral-pion decay channels, yielding events that reproduce the Lorentz-invariant three-body phase-space measure. The resulting momentum spectra, pairwise momentum correlations, opening-angle distributions, and Dalitz plots furnish a complete kinematic characterisation of both decay modes. The neutral-pion channel exhibits a larger available three-body energy and correspondingly broader kinematic limits. The unweighted events generated provide a kinematic baseline that can subsequently be weighted event by event with a weak-decay matrix element, for computing decay rates and other observables. For the neutral-pion channel, where no experimental data currently exists, the Lorentz-invariant phase-space constitutes a useful baseline for predictions.