Local Analytic Sector Subtraction at NNLO

TL;DR

The paper introduces a local analytic sector subtraction framework for infrared divergences in QCD at $NNLO$, built on a unitary sector partition of the real-radiation phase space and a flexible set of sector functions. By constructing minimal local counterterms from soft and collinear limits and mapping them to Born kinematics, the authors achieve analytic integration of unresolved radiation and exact pole cancellation with virtual contributions. The method is demonstrated via a proof-of-concept calculation for $e^+e^-\to q\bar q q'\bar q'$ in the $T_R C_F$ channel, showing precise agreement between analytic expectations and numerical results, including the correct scale dependence. The approach aims to generalize to more complex hadronic processes with massless final states, potentially extending to initial-state radiation and massive cases, offering a pathway toward efficient, fully differential NNLO predictions.

Abstract

We present a new method for the local subtraction of infrared divergences at next-to-next-to-leading order (NNLO) in QCD, for generic infrared-safe observables. Our method attempts to conjugate the minimal local counterterm structure arising from a sector partition of the radiation phase space with the simplifications following from analytic integration of the counterterms. In this first implementation, the method applies to final-state massless particles. We show how our method compactly organises infrared subtraction at NLO, we deduce in detail the general structure of the subtraction terms at NNLO, and we provide a proof of principle with a complete application to a simple process at NNLO.

Figures (1)

• Figure 1: Rescaled NNLO correction as a function of the renormalisation scale.