Subtraction terms for one-loop amplitudes with one unresolved parton

TL;DR

This work provides a complete set of subtraction terms for one-loop amplitudes with one unresolved parton in NNLO calculations for $e^+e^-$ annihilation to 2 and 3 jets, including analytic integration over the unresolved phase space. It develops a dipole-based subtraction framework, decomposes amplitudes into primitive parts, and derives explicit integrated results for single- and mixed-loop unresolved configurations across all relevant color sectors. The results are formulated to be compatible with multiple dimensional-regularization schemes and are essential for canceling infrared divergences before Monte Carlo integration, enabling NNLO predictions for jet processes in electron-positron annihilation. The paper thus advances the practical implementation of NNLO Monte Carlo programs for $e^+e^-\to$ jets by providing the required subtraction terms and their integrated forms.

Abstract

Fully differential next-to-next-to-leading order calculations require a method to cancel infrared singularities. In a previous publication, I discussed the general setup for the subtraction method at NNLO. In this paper I give all subtraction terms for electron-positron annihilation associated with one-loop amplitudes with one unresolved parton. These subtraction terms are integrated within dimensional regularization over the unresolved one-particle phase space. The results can be used with all variants of dimensional regularization (conventional dimensional regularization, the 't Hooft-Veltman scheme and the four-dimensional scheme).