Monte Carlo phase space evaluation

Abstract

A new, efficient method of generating Monte Carlo phase space integrals for multi-particle systems is derived. By using the analytically exact integrals for zero-mass particles as a comparison function, we generate the integrals for massive particles with an extremely high efficiency. We thus can generate unit weight events, simulating actual experimental data. The events are generated in two distinct steps. First, effective masses, conserving energy and momentum are generated. Next, the effective masses are allowed to sequentially “decay” via two-body models, and the decay products are then given an angular distribution, in their own center-of-mass system. The resulting two momenta are then Lorentz transformed into the appropriate laboratory system. Our method is contrasted to traditional methods of generating similar events, where the “dice” are thrown “flat” in effective mass, and comparisons of efficiency are made. For large numbers of particles and very high energies, the improvement is enormous. In addition, new methods of generating distribution functions are introduced.