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

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 Schrödinger 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.