Gluon-Gluon Antenna Functions from Higgs Boson Decay

TL;DR

This work shows that gluon-gluon antenna functions, which encode infrared singularities in QCD at NNLO, can be systematically derived from Higgs boson decay in an effective theory where the Higgs couples to gluons. By analyzing H→partons at NLO and NNLO and matching the infrared structure to Catani’s factorization, the authors extract and verify the NLO and NNLO gluon-gluon antenna functions from physical matrix elements. The results demonstrate explicit pole cancellations between real-emission and virtual contributions and align with known NNLO Higgs decay rates, establishing a process-based route to universal antenna subtraction terms. The approach, extended from prior work on quark-based antennae, provides a unified framework to derive all QCD antenna functions and paves the way for NNLO subtraction in production and scattering kinematics.

Abstract

Antenna functions describe the infrared singular behaviour of colour-ordered QCD matrix elements due to the emission of unresolved partons inside an antenna formed by two hard partons. In this paper, we show that antenna functions for hard gluon-gluon pairs can be systematically derived from the effective Lagrangian describing Higgs boson decay into gluons, and compute the the infrared structure of the colour-ordered Higgs boson decay matrix elements at NLO and NNLO.

Figures (2)

• Figure 1: Colour flow contained in tree level decay $H\to g g$. Double (single) lines denote adjoint (fundamental) colour indices.
• Figure 2: Colour flow contained in the colour ordered amplitude $M_{g g g g}^0 (p_1,p_i,p_j,p_k)$ contributing to the tree level decay $H \to g g gg$.