The Four Dimensional Helicity Scheme Beyond One Loop

TL;DR

The work addresses the mismatch between the Four Dimensional Helicity (FDH) scheme and a physically consistent regularization by embedding FDH within a renormalizable Dimensional Reduction framework and introducing the ${\widehat{{\rm DR}}}$ scheme. It derives the ultraviolet and infrared counterterms needed to map FDH amplitudes to renormalized HV amplitudes through two loops, showing that evanescent contributions are controlled by universal anomalous dimensions and jet/soft functions. By connecting FDH to DR and then to HV, the paper provides explicit transformation rules, including a concrete one-loop example, enabling practitioners to exploit FDH's helicity/unitarity advantages while delivering HV-compatible, renormalized results. This enables precise differential predictions in QCD and aligns FDH-based calculations with standard renormalization, running couplings, and PDF schemes. The approach has practical impact for higher-order QCD computations where unitarity techniques and helicity methods are powerful but must be connected to a renormalizable, scheme-consistent framework.

Abstract

I describe a procedure by which one can transform scattering amplitudes computed in the four dimensional helicity scheme into properly renormalized amplitudes in the 't Hooft-Veltman scheme. I describe a new renormalization program, based upon that of the dimensional reduction scheme and explain how to remove both finite and infrared-singular contributions of the evanescent degrees of freedom to the scattering amplitude.