  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.
