SCET approach to regularization-scheme dependence of QCD amplitudes

TL;DR

This paper analyzes how different regularization schemes in massless QCD affect scattering amplitudes, demonstrating scheme independence of certain functions and providing transition rules between schemes up to NNLO.

Contribution

It establishes the consistency of FDH and DRED schemes at NNLO and develops transition rules for amplitudes across various regularization schemes using SCET.

Findings

FDH and DRED are consistent up to NNLO with proper renormalization

Jet and soft functions in SCET are scheme independent

Transition rules between schemes are constructed up to NNLO

Abstract

We investigate the regularization-scheme dependence of scattering amplitudes in massless QCD and find that the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED) are consistent at least up to NNLO in the perturbative expansion if renormalization is done appropriately. Scheme dependence is shown to be deeply linked to the structure of UV and IR singularities. We use jet and soft functions defined in soft-collinear effective theory (SCET) to efficiently extract the relevant anomalous dimensions in the different schemes. This result allows us to construct transition rules for scattering amplitudes between different schemes (CDR, HV, FDH, DRED) up to NNLO in massless QCD. We also show by explicit calculation that the hard, soft and jet functions in SCET are regularization-scheme independent.