KNO scaling function of modified negative binomial distribution

Abstract

We investigate the KNO scaling function of the modified negative binomial distribution (MNBD), because this MNBD can explain the oscillating behaviors of the cumulant moment observed in $e^+e^-$ annihilations and in hadronic collisions. By using a straightforward method and the Poisson transform we derive the KNO scaling function from the MNBD. The KNO form of experimental data in $e^{+}e^{-}$ collisions and hadronic collisions are analyzed by the KNO scaling function of the MNBD and that of the negative binomial distribution (NBD). The KNO scaling function of the MNBD describes the data as well as that of the NBD.