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Ward identity preserving local ultraviolet counterterms for photoproduction at two loops in QCD

Charalampos Anastasiou, Julia Karlen, Roshni Sahoo, George Sterman, Matilde Vicini

Abstract

We review the construction of locally finite two-loop amplitude integrands for photoproduction via quark annihilation, presented in arXiv:2509.07805. Building on established techniques for off-shell colorless production, we extend this local subtraction framework to handle transient singularities arising from real outgoing photons. These singularities manifest only at the integrand level, yielding finite contributions upon integration. In these proceedings, we provide the explicit construction of ultraviolet counterterms that satisfy necessary Ward identity cancellations, ensuring that the integrand is rendered integrable. This work provides a locally finite amplitude integrand that is ready for numerical integration in momentum space. Furthermore, it establishes the foundation for extending local subtraction frameworks to processes involving final-state jets.

Ward identity preserving local ultraviolet counterterms for photoproduction at two loops in QCD

Abstract

We review the construction of locally finite two-loop amplitude integrands for photoproduction via quark annihilation, presented in arXiv:2509.07805. Building on established techniques for off-shell colorless production, we extend this local subtraction framework to handle transient singularities arising from real outgoing photons. These singularities manifest only at the integrand level, yielding finite contributions upon integration. In these proceedings, we provide the explicit construction of ultraviolet counterterms that satisfy necessary Ward identity cancellations, ensuring that the integrand is rendered integrable. This work provides a locally finite amplitude integrand that is ready for numerical integration in momentum space. Furthermore, it establishes the foundation for extending local subtraction frameworks to processes involving final-state jets.
Paper Structure (8 sections, 22 equations, 1 figure)

This paper contains 8 sections, 22 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Transient Infrared Singularities
  3. Nested self-energy corrections
  4. Nested triangle subgraphs
  5. Ultraviolet Singularities
  6. Nested self-energy corrections
  7. Nested triangle subgraphs
  8. Outlook & Conclusion

Figures (1)

  • Figure 1: Two-loop diagrams with one-loop corrections to real photon vertices.