Abstract
Particle production in proton collision experiments provides fundamental information on the mechanisms of initial energy conversion of protons in a 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 parameterization of experimental information, making it important to know the hypotheses involved in the elaboration of the model, in order to provide adequate application and interpretation of results. We thus conduct a discussion of the Negative Binomial Model based on the realization of a classic random experiment, which leads and assists in obtaining the analytical expression of the Probability Function. We also express the said Function of Probability in terms of the Gamma Function, the multiplicity variable and the average multiplicity adopting a mathematical procedure not found in the specific literature. Implications of the application of the model in the study of Multiplicities Distributions in collisions between protons are discussed.
Keywords:
Multiplicity distributions; Negative Binomial distritibution; Multiparticle production; Proton collisions
