The four-dimensional helicity scheme and dimensional reconstruction

Abstract

The four-dimensional helicity regularization scheme is often used in one-loop QCD computations. It was recently argued in Ref. [1] that this scheme is inconsistent beyond the one-loop order in perturbation theory. In this paper, we clarify the reason for this inconsistency by studying the perturbative expansion of the vector current correlator in one-flavor QED through three-loop order. We develop a simple, practical way to fix the four-dimensional helicity scheme using the idea of dimensional reconstruction, and demonstrate its application in several illustrative examples.

7 pages

References in corpus (7)

• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO
• Electroweak gauge boson production at hadron colliders through O(alpha_s^2)
• Full one-loop amplitudes from tree amplitudes
• NNLO corrections to event shapes in $e^{+}{e}^{-}$ annihilation
• Using Dimensional Reduction for Hadronic Collisions
• Regularization Schemes and Higher Order Corrections

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