A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions

TL;DR

The paper addresses the challenge of NNLO jet cross sections by introducing a comprehensive subtraction scheme for doubly-real emissions in e+e- annihilation. It constructs a hierarchy of counterterms (A2, A1, A12) with exact phase-space factorization and dedicated momentum mappings to render the doubly-real contribution finite in four dimensions, with plans to treat remaining NNLO pieces in companion work. The framework is explicit, process-independent, and capable of handling full color and azimuthal correlations, and numerical tests confirm integrability for three-jet observables. This work provides a foundational, scalable approach for NNLO calculations and sets the stage for matching to parton showers and higher-order extensions.

Abstract

We present a subtraction scheme for computing jet cross sections in electron-positron annihilation at next-to-next-to-leading order accuracy in perturbative QCD. In this first part we deal with the regularization of the doubly-real contribution to the NNLO correction.

Figures (17)

• Figure 1: Graphical representation of the singly-collinear momentum mapping and the implied factorization of the phase space.
• Figure 2: Graphical representation of the singly-soft momentum mapping and the implied factorization of the phase space.
• Figure 3: Graphical representation of the soft limit of collinear and soft-type mappings.
• Figure 4: Graphical representation of the triply-collinear momentum mapping and the implied factorization of the phase space.
• Figure 5: Graphical representation of the doubly-collinear momentum mapping and the implied factorization of the phase space.