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

TL;DR

This paper investigates the absence of pi^2 terms in physical anomalous dimensions in DIS, providing evidence up to fifth order and predicting new contributions based on a conjecture about zeta values.

Contribution

It offers strong support for the conjecture that even zeta values are absent in Euclidean physical quantities and uses this to predict unknown higher-order contributions.

Findings

Supports the conjecture up to fifth order in alpha_s.

Predicts new zeta_4 and zeta_6 contributions to anomalous dimensions.

Provides evidence from diagram computations for the absence of pi^2 terms.

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.