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

TL;DR

This paper develops a method to construct two-loop amplitude integrands for photoproduction in QCD that preserve Ward identities and are finite locally, facilitating numerical integration and future extensions to jet processes.

Contribution

It introduces explicit ultraviolet counterterms that maintain Ward identities, enabling locally finite two-loop integrands for photoproduction in QCD.

Findings

Constructed locally finite two-loop amplitude integrands.

Ensured Ward identity preservation at the integrand level.

Laid groundwork for extending to processes with final-state jets.

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.