Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Gabor Somogyi, Zoltan Trocsanyi

TL;DR

The paper develops a comprehensive subtraction scheme for NNLO QCD jet cross sections in $e^+e^-$ annihilation, focusing on regularizing the real-virtual contribution. It constructs local, four-dimensional counterterms that accurately reproduce singly-unresolved limits (collinear and soft) with full color and azimuthal correlations, and provides explicit phase-space mappings and kernels for both collinear and soft sectors, plus their integrated counterparts. By combining these RV counterterms with the previously established doubly-real and the remaining doubly-virtual pieces, the method yields finite, infrared-safe predictions for jet observables, as validated by numerical checks on thrust and the $C$-parameter. The approach is designed to be general for any number of massless final-state partons and paves the way for robust NNLO phenomenology in jet processes.

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 second part we deal with the regularization of the real-virtual contribution to the NNLO correction.

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

TL;DR

The paper develops a comprehensive subtraction scheme for NNLO QCD jet cross sections in annihilation, focusing on regularizing the real-virtual contribution. It constructs local, four-dimensional counterterms that accurately reproduce singly-unresolved limits (collinear and soft) with full color and azimuthal correlations, and provides explicit phase-space mappings and kernels for both collinear and soft sectors, plus their integrated counterparts. By combining these RV counterterms with the previously established doubly-real and the remaining doubly-virtual pieces, the method yields finite, infrared-safe predictions for jet observables, as validated by numerical checks on thrust and the -parameter. The approach is designed to be general for any number of massless final-state partons and paves the way for robust NNLO phenomenology in jet processes.

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 second part we deal with the regularization of the real-virtual contribution to the NNLO correction.

Paper Structure

This paper contains 25 sections, 111 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Notation
  3. Matrix elements
  4. Dimensional regularization, one-loop amplitudes and renormalization
  5. Remark on regularization-scheme dependence
  6. Cross sections
  7. Counterterms for the real-virtual cross section
  8. Factorization in the collinear and soft limits
  9. Collinear limit
  10. Soft limit
  11. Matching the collinear and soft limits
  12. Counterterms
  13. Collinear counterterms
  14. Soft-type counterterms
  15. Counterterms for the integrated approximate cross section
  16. ...and 10 more sections

Figures (1)

  • Figure 1: Graphical representation of the squared matrix element and the subtraction terms.