On the origin of negative binomial multiplicity distributions in proton-nucleus collisions

Abstract

We investigate multiplicity distributions in ultrarelativistic proton-nucleus collisions in a string model approach. We try to disentangle the different sources of multiplicity fluctuations: nuclear structure, the parton structure of nucleons and the fragmentation of colour strings. We show that the multiplicity distribution can be written as a continuous superposition ∫ dN W(N) P(N;n) of poissonian distributions P with variable mean values N, the weight factor W(N) representing nuclear and nucleonic structure, whereas the poisson distribution P reflects fluctuations due to string fragmentation. By using the string model VENUS, we show that W(N) can be well approximated by a gamma distribution G(k, N;N) , leading to a negative binomial distribution N(k, N;n) for the multiplicity distribution, with the same parameters as for G ! This has interesting consequences: for small 〈 n〈 (small rapidity window) the fragmentation fluctuations dominate; for large 〈 n〉 they are negligible!