Statistical Model for Electron-Positron Annihilation into Hadrons

Abstract

A statistical model for the production of multibody hadronic states by $e^{+}{e}^{-}$ annihilation is discussed. We associate the secondary hadron momentum distributions for colliding-beam processes with the exponentially failling transverse-momentum distributions in hadron-hadron collisions. The consequence of this picture is that at high energies hadron multiplicity rises linearly with c.m. energy, unlike the $\ln s$ behavior for the multiplicity of secondaries in hadron-hadron collisions. If the total annihilation cross section is assumed to have a power falloff $\sim s^{-m}$, the $n$-pion cross sections follow a Poisson distribution with the most probable multiplicity $n_{\pi }=\frac{s^{\frac{1}{2}}}{〈E_{\pi }〉}+3-m$ and $〈E_{\pi }〉\sim 375$ MeV. An alternative statistical model based on jets is also briefly discussed. The storage rings now being constructed or envisaged should easily distinguish between the various possibilities.