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.
Highlights
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
This is a consequence of the fact that dot products of a ǫ-scalar field Awith the vectors n, nare vanishing, i.e. n · A = n · A = 0. It follows that soft ǫ-scalars cannot be emitted from the Wilson lines. This explains in a direct way the result [4] that the scheme dependence of general next-to-leading order (NLO) amplitudes is contained in the parton anomalous dimensions
With the results presented in this paper we complete the understanding of the scheme dependence of IR divergent NNLO virtual amplitudes with massless particles
Summary
Dimensional reduction has been shown to be mathematically consistent [36] and equivalent to dimensional regularization [6, 7] on the level of IR finite Green functions. In [12,13,14,15] it has been shown that in cdr the general structure of the anomalous dimension operator Γ, which controls the IR divergences of QCD scattering amplitudes, is exactly known up to two-loop level and only involves colour dipoles. In those papers it was conjectured, by using soft-collinear factorization constraints and symmetry arguments, that this simple structure is more general and it is valid to all orders in perturbation theory. External gluons are treated in the same way in hv and fdh and the metric tensors in polarization sums are the same in the two schemes
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