KNO scaling 30 years later

KNO scaling, i.e. the collapse of multiplicity distributions P_n onto a universal scaling curve manifests when P_n is expressed as the distribution of the standardized multiplicity (n-c)/lambda with c and lambda being location and scale parameters governed by leading particle effects and the growth of average multiplicity. At very high energies, strong violation of KNO scaling behavior is observed (p-pbar) and expected to occur (e+e-). This challenges one to introduce novel, physically well motivated and preferably simple scaling rules obeyed by high-energy data. One possibility what I find useful and which satisfies the above requirements is the repetition of the original scaling prescription (shifting and rescaling) in Mellin space, that is, for the multiplicity moments' rank. This scaling principle is discussed here, illustrating its capabilities both on model predictions and on real data.