Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions

Abstract

We study the higher-order corrections to structure functions in inclusive deep-inelastic scattering (DIS) in massless perturbative QCD, in the context of the conjectured absence of even-n values of the Riemann zeta-function zeta_n, i.e., of powers of pi^2, in Euclidean physical quantities. We provide substantial additional support for this conjecture by demonstrating that it holds, as far as it can be tested by the results of diagram computations, for the physical anomalous dimensions of structure functions at the fourth and fifth order in the strong coupling constant alpha_s. The conjecture is then employed to predict hitherto unknown zeta_4 and zeta_6 contributions to the anomalous dimensions for parton distributions and to the coefficient functions for the longitudinal structure function F_L.