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Two-Loop Spacelike Splitting Amplitudes in Full-Color QCD

Federico Buccioni, Hanyu Fang, Kai Yan

Abstract

The study of QCD scattering amplitudes in the collinear regime provides crucial insight into the factorization properties of hadronic cross sections. In this paper, we present the first complete results for two-loop spacelike splitting amplitudes in full-color QCD, in all partonic channels and helicity configurations. We confirm the universality of a class of contributions already found in N=4 super Yang--Mills (sYM) theory, and identify previously unknown sources of collinear factorization-violating (CFV) effects. Consistent with recent observations in N=4 sYM, all CFV contributions cancel in color-summed squared amplitudes, implying the universality of single-parton collinear factorization for jet cross sections at third order in QCD.

Two-Loop Spacelike Splitting Amplitudes in Full-Color QCD

Abstract

The study of QCD scattering amplitudes in the collinear regime provides crucial insight into the factorization properties of hadronic cross sections. In this paper, we present the first complete results for two-loop spacelike splitting amplitudes in full-color QCD, in all partonic channels and helicity configurations. We confirm the universality of a class of contributions already found in N=4 super Yang--Mills (sYM) theory, and identify previously unknown sources of collinear factorization-violating (CFV) effects. Consistent with recent observations in N=4 sYM, all CFV contributions cancel in color-summed squared amplitudes, implying the universality of single-parton collinear factorization for jet cross sections at third order in QCD.

Paper Structure

This paper contains 12 sections, 60 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Discontinuities and factorization violation
  3. Spacelike splitting from full-color QCD amplitudes
  4. Spacelike to timelike crossing.
  5. Differential equations method.
  6. Two-loop generalized splitting amplitudes
  7. Cancellation of CFV terms at squared amplitude level
  8. Summary and Outlook
  9. The $g\to gg$ splitting
  10. The $q\to qg$ splitting
  11. The $g\to \bar{q}q$ splitting
  12. The $q\to gq$ splitting

Figures (3)

  • Figure 1: Analytic continuation of $\tau$$(\equiv \tau_{{\color{darkred}{\rm in}}})$ and $\tau_I$ from the spacelike to the timelike collinear regime; ${\color{darkred}{\rm in}}$ denotes an incoming particle and $I$ an outgoing spectator.
  • Figure 2: Kinematics of the $p_2\parallel p_3$ spacelike collinear splitting
  • Figure 3: Representative planar $(\mathrm{a}_{1,2})$ and non-planar $(\mathrm{b}_{1,2})$ diagrams contributing to the tripole $(\mathrm{a}_{1},\mathrm{b}_{1})$ and $\mathbf{C}_{gg}$$(\mathrm{a}_{2},\mathrm{b}_{2})$ operators present in Eq. \ref{['eq:roperator']} .