Koba-Nielsen-Olesen Scaling at Finite Energies

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Abstract
Since Slattery's analysis of the Serpukhov and National Accelerator Laboratory (NAL) multiplicity data shows Koba-Nielsen-Olesen (KNO) scaling behavior to remarkable accuracy, it is of interest to examine KNO scaling at finite energies. We discuss the fact that KNO's argument in favor of asymptotic scaling fails at any finite energy, and the corrections exceed the experimental limits at NAL energies. We show that energy conservation forbids exact moment scaling in any finite energy range, and we establish a sufficient condition for a distribution to obey scaling within the observed accuracy. We further point out that only the first two moments calculated by Slattery are independent. Finally, we produce a simple model showing how unitarity can generate the long-range correlations in the rapidity variable that KNO scaling implies.