First results for three-loop deep-inelastic structure functions in QCD

TL;DR

This work advances NNLO QCD in deep-inelastic scattering by computing the fermionic nf part of the three-loop non-singlet structure functions using a Mellin-moment strategy. It details the eight core technical challenges and the computational framework for reducing thousands of Feynman integrals to master integrals, employing harmonic sums and harmonic polylogarithms up to weight 6. The authors present explicit results for the fermionic three-loop anomalous dimension $ abla^{(2)}_{ns}(N)$ and the corresponding splitting function $P^{(2)}_{ns}(x)$, with cross-checks against independent calculations. They also extract threshold-resummation coefficients $B_2$ and $D_2^{DIS}$, finding $D_2^{DIS}=0$ in MSbar and underscoring implications for NNLL accuracy in DIS predictions.

Abstract

As a first step towards the complete calculation of deep-inelastic scattering at third order of massless perturbative QCD, we have computed the fermionic (nf) contributions to the flavour non-singlet structure functions in unpolarized electromagnetic scattering. We briefly discuss the approach chosen for this calculation, the problems we encountered and the status of the project. We show the results for the corresponding anomalous dimension in both Mellin-N and Bjorken-x. Together with the nf part of A_3, our calculation facilitates the complete determination of the threshold-resummation coefficients B_2 and D_2^DIS. The latter quantity vanishes in the MSbar scheme.