Two-loop off-shell QCD amplitudes in FDR

Ben Page,Roberto Pittau

doi:10.1007/jhep11(2015)183

Abstract

We link the FDR treatment of ultraviolet (UV) divergences to dimensional regularization up to two loops in QCD. This allows us to derive the one-loop and two-loop coupling constant and quark mass shifts necessary to translate infrared finite quantities computed in FDR to the MSbar renormalization scheme. As a by-product of our analysis, we solve a problem analogous to the breakdown of unitarity in the Four Dimensional Helicity (FDH) method beyond one loop. A fix to FDH is then presented that preserves the renormalizability properties of QCD without introducing evanescent quantities.

Highlights

But produces a finite and regulator free answer when acting on divergent integrands.3 In this way no CTs need to be incorporated into L: they are traded for a change in the definition of the loop integration
As the FDR UV subtraction is consistently encoded in the definition of a four-dimensional and finite loop integration, the FDR approach to QFT does not require the introduction of counterterms in the Lagrangian
An order-by-order renormalization is avoided: the lth perturbative order is computed by only looking at l-loop Feynman diagrams

Summary

Introduction

But produces a finite and regulator free answer when acting on divergent integrands. In this way no CTs need to be incorporated into L: they are traded for a change in the definition of the loop integration. But produces a finite and regulator free answer when acting on divergent integrands.. But produces a finite and regulator free answer when acting on divergent integrands.3 In this way no CTs need to be incorporated into L: they are traded for a change in the definition of the loop integration. FDR directly generates renormalized amplitudes since it is independent of any UV cutoff. We introduce them in the context of this paper only because we want to work out the correspondence of FDR with a canonical renormalization approach based on counterterms. When studying eq (1.1) one needs to reconcile the value ns = n dictated by DReg in (1.1a) with ns = 4 used in (1.1b) This has to be done without spoiling the renormalizability of QCD.

Objectives

Results

Conclusion