Abstract
We investigate the regularization-scheme dependent treatment of $\gamma_{5}$ in the framework of dimensional regularization, mainly focusing on the four-dimensional helicity scheme (FDH). Evaluating distinctive examples, we find that for one-loop calculations, the recently proposed four-dimensional formulation (FDF) of the FDH scheme constitutes a viable and efficient alternative compared to more traditional approaches. In addition, we extend the considerations to the two-loop level and compute the pseudo-scalar form factors of quarks and gluons in FDH. We provide the necessary operator renormalization and discuss at a practical level how the complexity of intermediate calculational steps can be reduced in an efficient way.
Highlights
The success of quantum-field theoretical predictions over the past decades was enabled, among other things, by the applicability of dimensional regularization as the method provides a mathematically consistent tool to handle ultraviolet (UV) and infrared (IR) divergences in the multi-loop regime
Evaluating distinctive examples, we find that for one-loop calculations, the recently proposed four-dimensional formulation (FDF) of the four-dimensional helicity scheme (FDH) scheme constitutes a viable and efficient alternative compared to more traditional approaches
From the very moment of the introduction of dimensional regularization in Ref. [1], special attention had to be paid to the treatment of γ5 since the object is closely related to concepts that are only valid in integer dimensions
Summary
The success of quantum-field theoretical predictions over the past decades was enabled, among other things, by the applicability of dimensional regularization as the method provides a mathematically consistent tool to handle ultraviolet (UV) and infrared (IR) divergences in the multi-loop regime. In a series of publications [2,3,4,5,6,7,8,9,10,11,12,13,14,15] that cover a time span of more than 40 years, different approaches have been developed in order to find consistent rules for the treatment of γ5 in the dimensional framework Irrespective of this effort, in the overwhelming majority of computations that have been performed so far, the original γ5 definition of Ref.
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