Multiplicity distributions in high-energy hadron-nucleus collisions. I. Formalism

The problem of multiparticle production in hadron-nucleus collisions is formulated in a way consistent with the Gribov-Glauber theory for inelastic cross section on the one hand, while being the generalization of a particle production model for pp collisions on the other hand. The latter is the geometrical branching model that satisfactorily describes geometrical scaling and Koba-Nielsen-Olesen scaling. The formalism allows the incident hadron to be broken by the first collision. Dependences on the impact parameter b and the multiplicity of gray particles $N_g$ are carefully taken into account. The average multiplicity as a function of the number of inelastic collisions, whether holding b,$N_g$ fixed, or integrated, is derived, and is shown to agree with the data with a universal slope parameter β. General formulas for the multiplicity distributions are obtained for produced particles as well as for shower particles. A universal property of particle production in hN and hA collisions based on effective interactions among many partons is discussed. The geometrical branching model is then further developed to make possible the determination of β to be 0.5.