Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond

TL;DR

The authors derive universal infrared-factorization formulae for tree-level QCD amplitudes applicable at any perturbative order and compute the universal soft and/or collinear factors at O(αS^2). They introduce a general triple-collinear kinematic framework and derive spin-dependent splitting functions, including azimuthal correlations, and they formulate soft currents for single and double soft emissions, as well as soft–collinear limits with color coherence. The results unify soft and collinear factorization, provide explicit O(αS^2) ingredients for NNLO jet calculations, and have potential implications for parton showers and resummation beyond current accuracy.

Abstract

We study the infrared behaviour of tree-level QCD amplitudes and we derive infrared-factorization formulae that are valid at any perturbative order. We explicitly compute all the universal infrared factors that control the singularities in the various soft and/or collinear limits at O(as^2).

Figures (11)

• Figure 1: Dominant diagrams for the multiple collinear limit at ${\cal O}(\alpha_{\mathrm{S}}^{m-1})$ in a physical gauge.
• Figure 2: An interference diagram for the triple collinear limit $a\rightarrow a_1a_2a_3$.
• Figure 3: The diagram for the collinear decay $q\rightarrow {\bar{q}^\prime}_1q^\prime_2q_3$.
• Figure 4: The diagrams for the collinear decay $q\rightarrow {\bar{q}}_1q_2q_3$.
• Figure 5: The diagrams for the collinear decay $q\rightarrow g_1g_2q_3$.