The real radiation antenna functions for $S\rightarrow Q\bar{Q}gg$ at NNLO QCD

TL;DR

The study extends NNLO QCD antenna subtraction to processes with massive final states by deriving and integrating the four-parton antennae for $S \\to Q\\bar{Q} gg$. The authors obtain analytic expressions for the integrated antenna functions \\mathcal{A}^0_4$ and \\tilde{\\mathcal{A}}^0_4$ in $D=4-2\\epsilon$ dimensions, expressed in harmonic polylogarithms of the mass-parameter variable $y$ and organized through 15 master integrals $T_1$–$T_{15}$ solved via differential equations. They validate the infrared structure through a detailed analysis of single-unresolved and double-soft limits and provide the master-integral machinery needed for other massive final-state NNLO applications. These results furnish the essential building blocks for the real-radiation piece of the NNLO cross section $d\\sigma_{NNLO}$ for $S \\to Q\\bar{Q} gg$, with the remaining real-virtual contribution to be addressed in a follow-up work. Overall, the work advances precise heavy-quark production predictions by delivering analytic, IR-safe subtraction terms and their integrated counterterms within the antenna framework.

Abstract

We analyze, in the antenna subtraction framework, the real radiation antenna functions for processes involving the production of a pair of heavy quarks and two gluons by an uncolored initial state at NNLO QCD. We provide explicit expressions for these functions and discuss their infrared singular behaviour. Our main results are the corresponding integrated antenna functions which are computed analytically. They are expressed in terms of harmonic polylogarithms.