Negative binomial distribution and multiplicities in proton collisions

Abstract

The production of particles in proton collision experiments provides fundamental information about the mechanisms of conversion of the initial energy of protons into a given number of secondary particles by measuring their Multiplicity Distribution in strong nuclear interactions. In this context, the Negative Binomial Model has been extensively used in theoretical studies and in parameterization of experimental information, making it important, therefore, to know the hypotheses involved in the elaboration of the model, in order to provide adequate application and interpretation of results. Thus, we make a discussion of the Negative Binomial Model based on the performance of a classical random experiment, which leads and assists in obtaining the analytical expression of the Probability Function. We also express the Probability Function in terms of the Gamma Function, the multiplicity variable and the mean multiplicity adopting a mathematical procedure not found in the specific literature. Implications of the application of the model in the study of Multiplicity Distributions in collisions between protons are discussed.

DOI:https://doi.org/10.56238/interdiinovationscrese-050