Local finiteness for real-virtual corrections to electroweak production in partonic collisions

TL;DR

This work develops a local subtraction framework to render real-virtual NNLO QCD corrections for hadroproduction of colorless electroweak final states IR-finite at the integrand level in both loop momentum and final-state phase space. By decomposing the one-loop qqbar amplitude into loop-polarization and non-polarization parts and leveraging universal IR kernels derived from single-Higgs production, the authors construct nested counterterms that factorize IR singularities locally. The method extends to qqbar and qg channels at order $\alpha_s^2$, with explicit handling of fermion-loop, leading-color, subleading-color, and loop-polarization contributions, supported by Ward-identity arguments and cross-section-level factorization. The resulting IR-finite real-virtual cross sections pave the way toward fully numerical NNLO calculations for hadron-collider processes involving colorless final states, and the framework is validated through detailed infrared checks and cross-channel consistency. This approach offers a path to compute NNLO cross sections by combining real, virtual, and double-real pieces within a common, local integrand, facilitating precise collider phenomenology.

Abstract

We present a local subtraction scheme that enables the combined integration of loop momenta and the final-state parton phase space in real-virtual NNLO QCD corrections to cross sections for hadroproduction of electroweak and other colorless states. All initial- and final-state infrared singularities are subtracted at the integrand level in momentum space, yielding a locally finite integral ready for numerical integration in four dimensions. The subtraction terms are all based on the well-understood process of single-Higgs production. The core of our subtraction scheme relies on achieving local factorization in all infrared limits of real and virtual momenta. This necessitates systematic modifications of the original Feynman integrand for loop amplitudes, enabling gauge symmetry cancellations before performing integrations. Our approach provides an essential step toward NNLO cross-section calculations for hadron collider processes, where both loop and phase-space integrations are carried out numerically.

Figures (1)

• Figure 1: Diagrams that give rise to either loop polarizations (the first two columns) or power singularities (the third column) as $p_3 \parallel p_1$ (the first row) or $p_3 \parallel p_2$ (the second row).