Inclusive distributions for sequential decay processes

The multiplicity and inclusive distributions for the sequential decay of a massive state into massless particles are studied, with particular emphasis on polynomial matrix elements. Integral equations for these distributions are derived and discussed, and a Monte Carlo event generator is also described. In many of the models for which the average multiplicity grows linearly with mass, the inclusive spectra are similar to those obtained with a constant matrix element. However, there is also a large class of models in which the momentum spectrum flattens out after falling several decades. The large fluxes, the increase of associated multiplicities, and the large violations of scaling observed in large-transverse-momentum reactions would all receive natural explanations in cluster models with this kind of decay matrix element. The same mechanism gives a satisfactory phenomenology of the small-transverse-momentum events