Abstract
We investigate QCD amplitudes with massive quarks computed in the four-dimensional helicity scheme (FDH) and dimensional reduction at NNLO and describe how they are related to the corresponding amplitudes computed in conventional dimensional regularization. To this end, the scheme dependence of the heavy quark and the velocity-dependent cusp anomalous dimensions is determined using soft-collinear effective theory. The results are checked against explicit computations of massive form factors in FDH at NNLO. Our results complete the description of the scheme dependence of QCD amplitudes at NNLO.
Highlights
In the presence of massive quarks there are additional structures in the IR singularities of QCD amplitudes [19]
We investigate QCD amplitudes with massive quarks computed in the fourdimensional helicity scheme (FDH) and dimensional reduction at NNLO and describe how they are related to the corresponding amplitudes computed in conventional dimensional regularization
The generalization of the scheme dependence at NNLO to QCD amplitudes including massive quarks is the main result of this paper
Summary
As has been shown in a series of papers [8, 12, 17, 18, 33], a consistent formulation of the dimensional reduction (dred) and the four-dimensional helicity (fdh) scheme in the framework of massless QCD requires the introduction of three vector spaces. For a detailed discussion and a precise definition of the schemes, of the related vector spaces and their algebraic relations we refer to ref. Arbitrary fdh quantities in general depend on Nǫ. They are in the following denoted by a bar. The perturbative expansion of fdh/dred quantities in terms of the UV renormalized couplings is in the following written as.
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