Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations

TL;DR

This paper proposes a regulator-independent way to define the finite part of IR-divergent scattering amplitudes in N=4 SYM, using wedge functions, and demonstrates its validity across different regularizations and loop orders.

Contribution

It introduces a prescription for unambiguous, regulator-independent finite amplitudes in N=4 SYM by factoring IR divergences with wedge functions, applicable to various regularizations.

Findings

Wedge functions defined via form factors for dimensional and Higgs regularizations.

Demonstrated regulator independence of the finite amplitude at two loops.

Linked wedge functions to dual conformal Ward identities.

Abstract

The IR-divergent scattering amplitudes of N=4 supersymmetric Yang-Mills theory can be regulated in a variety of ways, including dimensional regularization and massive (or Higgs) regularization. The IR-finite part of an amplitude in different regularizations generally differs by an additive constant at each loop order, due to the ambiguity in separating finite and divergent contributions. We give a prescription for defining an unambiguous, regulator-independent finite part of the amplitude by factoring off a product of IR-divergent "wedge" functions. For the cases of dimensional regularization and the common-mass Higgs regulator, we define the wedge function in terms of a form factor, and demonstrate the regularization independence of the n-point amplitude through two loops. We also deduce the form of the wedge function for the more general differential-mass Higgs regulator, although we lack an explicit operator definition in this case. Finally, using extended dual conformal symmetry, we demonstrate the link between the differential-mass wedge function and the anomalous dual conformal Ward identity for the finite part of the scattering amplitude.