Multiplicity distributions in e+e- annihilation into hadrons and pure birth branching processes

TL;DR

This paper presents a recursive solution for pure birth branching processes and demonstrates that multiplicity distributions in e+e- annihilation into hadrons up to 189 GeV are well modeled by a modified negative binomial distribution, explained by simple pure birth processes.

Contribution

It introduces a recursive solution using Koenigs function and Schroder equation for pure birth processes and applies it to describe hadron multiplicity distributions in e+e- annihilation.

Findings

Multiplicity distributions fit by modified negative binomial distribution up to 189 GeV

Pure birth branching process explains the distributions without multiple simultaneous production

Energy dependence of the evolution parameter analyzed

Abstract

Recursive solution for a general homogeneous in time pure birth branching process with simultaneous production of any number of particles and with continuous evolution parameter is given. Calculational algorithm based on the use of Koenigs function and functional Schroder equation is described. It is shown that multiplicity distributions in e+e- annihilation into hadrons for c.m. energies up to 189 GeV are well described by the modified negative binomial distribution, explained by simple pure birth branching process without multiple simultaneous particle production. The energy dependence of the evolution parameter is also discussed.