First Forcer results on deep-inelastic scattering and related quantities

TL;DR

This paper reports four-loop calculations of splitting and coefficient functions in deep-inelastic scattering using the Forcer program, providing new insights into the analytic structure and large-N behavior of these quantities.

Contribution

It presents the first four-loop results for splitting functions and coefficient functions in deep-inelastic scattering, including analytic N-dependence and cusp anomalous dimension contributions.

Findings

Computed lowest three moments for non-singlet functions

Determined N-dependence of nf^3 and nf^2 parts

Provided evidence for non-zero quartic group invariants in cusp anomalous dimension

Abstract

We present results on the fourth-order splitting functions and coefficient functions obtained using Forcer, a four-loop generalization of the Mincer program for the parametric reduction of self-energy integrals. We have computed the respective lowest three even-N and odd-N moments for the non-singlet splitting functions and the non-singlet coefficient functions in electromagnetic and nu+nu(bar) charged-current deep-inelastic scattering, and the N=2 and N=4 results for the corresponding flavour-singlet quantities. Enough moments have been obtained for an LLL-based determination of the analytic N-dependence of the nf^3 and nf^2 parts, respectively, of the singlet and non-singlet splitting functions. The large-N limit of the latter provides the complete nf^2 contributions to the four-loop cusp anomalous dimension. Our results also provide additional evidence of a non-vanishing contribution of quartic group invariants to the cusp anomalous dimension.