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Catani's generalization of collinear factorization breaking

Leandro Cieri, Prasanna K. Dhani, Germán Rodrigo

Abstract

We consider the most general form of soft and collinear factorization for hard-scattering amplitudes to all orders in perturbative Quantum Chromodynamics. Specifically, we present the generalization of collinear factorization to configurations with several collinear directions, where the most singular behaviour is encoded by generalized collinear splitting amplitudes that manifestly embed the breaking of strict collinear factorization in space-like collinear configurations. We also extend the analysis to the simultaneous soft-collinear factorization with multiple collinear directions where naïve multiplicative factorization does not hold. As an illustrative example of factorization breaking, we present explicit results at the one-loop level in the soft-collinear limit.

Catani's generalization of collinear factorization breaking

Abstract

We consider the most general form of soft and collinear factorization for hard-scattering amplitudes to all orders in perturbative Quantum Chromodynamics. Specifically, we present the generalization of collinear factorization to configurations with several collinear directions, where the most singular behaviour is encoded by generalized collinear splitting amplitudes that manifestly embed the breaking of strict collinear factorization in space-like collinear configurations. We also extend the analysis to the simultaneous soft-collinear factorization with multiple collinear directions where naïve multiplicative factorization does not hold. As an illustrative example of factorization breaking, we present explicit results at the one-loop level in the soft-collinear limit.
Paper Structure (8 sections, 31 equations, 5 figures)

This paper contains 8 sections, 31 equations, 5 figures.

Table of Contents

  1. Introduction
  2. QCD Factorization in IR limits
  3. Soft factorization
  4. Collinear factorization
  5. Soft-collinear factorization
  6. Generalized collinear and soft-collinear factorization
  7. Conclusion
  8. Additional details

Figures (5)

  • Figure 1: Footage of original handwritten blackboard discussion by Stefano Catani, September 2023, Sesto Fiorentino, Firenze, Italy.
  • Figure 2: TL collinear factorization with two collinear directions.
  • Figure 3: SL collinear factorization with two collinear directions.
  • Figure 4: TL soft-collinear factorization. The soft current effectively interacts with the collinear parent partons.
  • Figure 5: SL soft-collinear factorization. The generalized splitting amplitude embeds the soft interactions.