Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L

TL;DR

This paper computes four-loop contributions to non-singlet structure functions in deep-inelastic scattering, revealing significant n_f^2 terms, confirming previous anomalous dimension results, and predicting higher-order effects using advanced computational methods.

Contribution

It provides the first detailed calculation of four-loop n_f^2 and n_f^3 contributions to structure functions, confirming and extending previous theoretical predictions.

Findings

n_f^2 contributions are numerically larger than n_f^3

Results agree with threshold and high-energy resummation predictions

Confirms earlier four-loop anomalous dimension calculations

Abstract

We have calculated the n_f^2 and n_f^3 contributions to the flavour non-singlet structure functions F_2 and F_L in inclusive deep-inelastic scattering at the fourth order in the strong coupling alpha_s. The coefficient functions have been obtained by computing a very large number of Mellin-N moments using the method of differential equations, and then determining the analytic forms in N and Bjorken-x from these. Our new n_f^2 terms are numerically much larger than the n_f^3 leading large-nf parts which were already known; they agree with predictions of the threshold and high-energy resummations. Furthermore our calculation confirms the earlier determination of the four-loop n_f^2 part of the corresponding anomalous dimension. Via the no-pi^2 conjecture/theorem for Euclidean physical quantities, we predict the z4 n_f^3 part of the fifth-order anomalous dimension for the evolution of non-singlet quark distributions.