One-loop QCD corrections to gluon-gluon scattering at NNLO

TL;DR

This work provides analytic O($\alpha_s^4$) virtual QCD corrections to gluon-gluon scattering arising from the self-interference of the one-loop amplitude, renormalised in the $\overline{MS}$ scheme and computed in conventional dimensional regularisation. It presents the infrared pole structure using Catani's formalism and extracts a finite remainder expressed in logarithms, completing the one-loop, 2→2 matrix elements needed for NNLO jet predictions at hadron colliders. The results, together with prior results for quark-quark and quark-gluon subprocesses, furnish the full set of NNLO virtual corrections for 2→2 parton scattering and are essential for constructing NNLO jet cross sections when combined with real-emission contributions. The methodology relies on color-space formalism, QGRAF generation, IBP reduction to master integrals (one-loop bubble and box in $D=6-2\epsilon$), and careful treatment of ultraviolet renormalisation and infrared factorisation. The work paves the way for systematic NNLO calculations of hadronic jet processes and informs the development of three-loop splitting functions and NNLO jet programs.

Abstract

We present the O(alphas^4) virtual QCD corrections to gluon-gluon scattering due to the self-interference of the one-loop amplitude. We give analytic expressions renormalised in the MSbar scheme and work in conventional dimensional regularisation. We write the structure of the infrared divergences from direct Feynman diagram evaluation in terms of the Catani formalism for infrared divergences. Formulae for the finite remainder are given in terms of logarithms that are real in the physical region. These results, together with those previously obtained for quark-quark and quark-gluon scattering complete the one-loop matrix elements for 2 to 2 processes needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders.