CoLoRFulNNLO for hadron collisions: integrating the iterated single unresolved subtraction terms

TL;DR

The work delivers analytic, ε-expanded results for the integrated iterated single unresolved subtraction terms within CoLoRFulNNLO for color-singlet hadron collisions, exploiting exact phase-space convolutions from momentum mappings. By casting integrated counterterms as parametric integrals and evaluating them in terms of generalized polylogarithms, the authors obtain coefficient functions that, when convolved with PDFs, form the I12 insertion operator acting on the Born cross section. The methodology handles endpoint singularities via careful subtractions and sector decomposition, and the results are organized into explicit IFIF, SS, and IFS components with a concrete Higgs-HEFT example to illustrate the I12 structure. The framework lays the groundwork for robust NNLO predictions in hadron-initiated color-singlet processes and is readily extensible to more complex final states with jets. The explicit pole content and the all-orders ε-structure provide a solid basis for cross-checking IR cancellation and for efficient numerical implementation.

Abstract

We present the analytic integration of the iterated single unresolved subtraction terms in the extension of the CoLoRFulNNLO subtraction scheme to color-singlet production in hadron collisions. We exploit the fact that, in this scheme, subtraction terms are defined through momentum mappings which lead to exact phase space convolutions for real emissions. This allows us to write the integrated subtraction terms as parametric integrals, which can be evaluated using standard tools. Finally, we show that the integrated iterated single unresolved approximate cross section can be written as a convolution of the Born cross section with an appropriately defined insertion operator.

Figures (2)

• Figure 1: Sample diagram for the purely gluonic double real emission subprocess for Higgs production in the HEFT approximation.
• Figure :