Applications of a cluster decomposition of many-dimensional phase space to high-energy collisions

Abstract

A high-dimensional phase space is reduced in an approximate way to a much smaller dimensional phase space, by singling out a “cluster” of a smaller number of particles (e.g. two or three). We derive the invariant mass distribution of the cluster, and, for fixed invariant mass, its c.m.s. energy distribution. The basis of the method is a two-cluster decomposition of the original phase space into the cluster of interest and the remainder. Simple, explicit formulas are given for all particles massless, and for one particle with mass and the others massless. A recipe is stated for the application of these easily calculable distributions to practical situations where the masses of particles must be taken into account. Numerical examples illustrating the validity of the approximations and applications to high-energy elementary particle collisions are given.