Four-loop splitting functions in QCD -- The gluon-gluon case --

TL;DR

This paper calculates the four-loop gluon-gluon splitting function in QCD, providing new moments and improved approximations that enhance precision for collider physics applications.

Contribution

It presents the first analytical computation of the N=<20 moments of P_{gg} at four loops, improving the accuracy of splitting functions used in QCD calculations.

Findings

Computed four-loop moments for P_{gg} for N<20

Constructed improved approximations for P_{gg}(x)

Found N^3LO contributions are about 1% at x >~ 10^{-4}

Abstract

We have computed the even-N moments N =< 20 of the gluon-gluon splitting function P_{gg} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop P_{gg}(x) that should be sufficient for a wide range of collider-physics applications. The N^3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1% or less at x >~ 10^{-4} at a standard reference scale with alpha_s = 0.2.