Scaling Violations beyond the Leading Order

Abstract

This second part of lectures concerns the explicit construction of a method¹’²⁾ which generalizes beyond leading order the simple probabilistic interpretation of leading scaling violations. The results obtained in this language allow to predict the evolution with the variation of external invariants not only of “space-like” processes, where the off-shell partons starting the hard interaction have space-like four momenta, like in the case of deep inelastic scattering or Drell-Yan, but also of “time-like” processes, like the one-particle inclusive e⁺e⁻ annihilation, where the partons acting in the fragmentation functions have “time-like” off-shell invariant masses. Alternative methods exist, the operator product expansion in the first case³⁾ and the cut-vertices formalism in the second one⁴⁾, for computing equivalent quantities, i.e. the evolution of the moments of struc­ture/fragmentation functions, where, however, one cannot establish a probabilistic picture.