Analytic results for decays of color singlets to $gg$ and $q \bar q$ final states at NNLO QCD with the nested soft-collinear subtraction scheme

TL;DR

The work delivers compact analytic NNLO QCD formulas for color-singlet decays to gg and qqbar final states, using the nested soft-collinear subtraction scheme to achieve fully differential, local, and analytic results. It develops and applies an iterative subtraction framework to separate double-real, real-virtual, and double-virtual contributions for Higgs decays to gg and bb, including comprehensive treatment of soft and collinear singularities and sector decompositions. The authors validate their formulas against independent analytic and numerical results, achieving per-mille level agreement, and provide jet-rate cross-checks that reinforce reliability. By furnishing explicit building blocks and phase-space constructions, the paper advances the application of the nested soft-collinear subtraction scheme to arbitrary NNLO QCD calculations at colliders.

Abstract

We present compact analytic formulas that describe the decay of colorless particles to both $q \bar q$ and $gg$ final states through next-to-next-to-leading order in perturbative QCD in the context of the nested soft-collinear subtraction scheme. In addition to their relevance for the description of decays like $V \to q \bar q'$, $V= Z,W$, $H \to b \bar b$ and $H \to gg$, these results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at colliders within the nested soft-collinear subtraction scheme.

Figures (2)

• Figure 1: Diagrams for $H \to b\bar{b}b\bar{b}$ decay. The gluon emission off the bubble in $Hb \bar{b}$ vertex describes diagrams where the gluon is emitted from one of the outgoing quark lines.
• Figure 2: Interference contributions for the triple collinear limit $1||3||4$.