A General Approach To Photon Radiation Off Fermions

TL;DR

This work develops a general, process-independent dipole subtraction formalism for photon radiation off massive fermions, extending Catani–Seymour methods to arbitrary masses and helicities and to neutral partners. By constructing emitter–spectator dipoles and a corresponding mapping to reduced kinematics, it isolates IR and collinear singularities into analytically integrable terms while leaving a finite real-emission remainder for numerical integration. The method is demonstrated on representative photonic corrections to $\gamma\gamma\to t\bar t(\gamma)$, $e^-e^-\gamma\to e^-e^-\gamma(\gamma)$, and $\mu^+\mu^-\to \nu_e\bar{\nu}_e(\gamma)$, showing improved numerical stability and accuracy relative to phase-space slicing. The results support practical implementation with arbitrary masses and polarizations and lay groundwork for a full QCD generalization with heavy quarks. The approach provides a robust, scalable tool for precision EW calculations in collider phenomenology and beyond.

Abstract

Soft or collinear photon emission potentially poses numerical problems in the phase-space integration of radiative processes. In this paper, a general subtraction formalism is presented that removes such singularities from the integrand of the numerical integration and adds back the analytically integrated contributions that have been subtracted. The method is a generalization of the dipole formalism of Catani and Seymour, which was formulated for NLO QCD processes with massless unpolarized particles. The presented formalism allows for arbitrary mass and helicity configurations in processes with charged fermions and any other neutral particles. Particular attention is paid to the limit of small fermion masses, in which collinear singularities cause potentially large corrections. The actual application and the efficiency of the formalism are demonstrated by the discussion of photonic corrections to the processes γγ--> t \bar t (γ), e^- γ--> e^- γ(γ), and μ^+ μ^- --> ν_e \barν_e (γ).

Figures (2)

• Figure 1: Effective diagrams for the different emitter/spectator cases.
• Figure 2: Definition of kinematical variables for ${{\rm d}}\phi(p_i,p_j,k;P_{ij})$ in the CM frame of $P_{ij}$.