CoLoRFulNNLO for hadron collisions: regularizing initial-state double real emissions

Abstract

We present the extension of the completely local subtraction scheme CoLoRFulNNLO to color-singlet production in hadron collisions. We provide explicit momentum mappings and the complete set of double-real counterterms required for this class of processes. The counterterms are systematically derived from the known infrared limit formulae of QCD matrix elements, and particular care has been taken to ensure their analytic integrability. The resulting construction involves a relatively small number of counter-events, preserving the locality and efficiency of the scheme. All formulae have been implemented within the publicly available NNLOCAL Monte Carlo program, and we explicitly validate all IR limits using arbitrary-precision computer algebra and present representative results. The counterterms presented here constitute a self-contained subset applicable to general hadronic processes within the CoLoRFulNNLO approach.

Figures (8)

• Figure 1: The splitting configuration for $(ir)\to i+r$ final-state splitting. The arrows in the figure denote momentum and flavor flow. The precise flavor mapping for the ${\cal C}_{ir}^{FF(0,0)}$ counterterm is given in the table.
• Figure 2: The splitting configuration for $a\to (ar)+r$ initial-state splitting. The arrows in the figure denote momentum and flavor flow. The precise flavor mapping for the ${\cal C}_{ar}^{IF(0,0)}$ counterterm is given in the table.
• Figure 3: The splitting configuration for $a\to (ars)+r+s$ initial-state triple collinear splitting. The arrows in the figure denote momentum and flavor flow. The precise flavor mapping for the ${\cal C}_{ars}^{IFF(0,0)}$ counterterm is given in the table.
• Figure 4: The behavior of ratios of subtraction terms and the squared matrix element in double unresolved limits. Here $|{\cal M}|^2$ denotes the tree-level squared matrix element for the $g(p_1) + g(p_2) \to H(p_3) + g(p_4) + g(p_5)$ subprocess, while ${\cal A}^{(0)}={\cal A}^{(0)}_1+{\cal A}^{(0)}_2-{\cal A}_{12}$ is the sum of all subtraction terms.
• Figure 5: The behavior of ratios of subtraction terms and the squared matrix element in the double unresolved collinear-soft limit. $|{\cal M}|^2$ and ${\cal A}^{(0)}$ are the same as in fig. \ref{['fig:A2lim']}.