γ5 in the four-dimensional helicity scheme

Abstract

We investigate the regularization-scheme dependent treatment of γ 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 pseudoscalar 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.

Dimensional schemes for cross sections at NNLO

“…In addition, the regular four-dimensional photon results in terms ∝ g µν [4] which in turn give rise to integrals with a strictly four-dimensional loop momentum k 2 [4] in the numerator. 5 This requires a careful implementation of an algebra with d s -, d-, and four-dimensional objects in the one-loop amplitude [48,49]. Regarding the double-real contributions the situation is even worse.…”

May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

“…a cutoff scale, in order to separate different IR regions. 21 Such separation of the phase space introduces instabilities in the numerical evaluation of cross sections and differential distributions [158][159][160][161], and some care has to be taken in order to obtain stable and reliable results. Furthermore, the knowledge of logarithmic and power-correction terms in the cutoff plays a relevant role in the identification of universal structures, in the development of regularisation prescriptions and in resummation programs [146][147][148][149][150][151][152][153][154][155]162].…”

“…In dimensional schemes the problems are well-known (see e.g. the review [232]), and recent references have focused on comparing different γ 5 -prescriptions up to the two-loop level [21] and on determining gauge invariance-restoring counterterms for the Breitenlohner/Maison/'t Hooft/Veltman prescription of γ 5 [233]. Quite surprisingly, non-dimensional schemes are not exempted of issues in the presence of γ 5 [84,85].…”

“…Alternative studies that have a four-dimensional representation of the d-dimensional space-time have been studied, at one-loop level, in Ref [18],. displaying interesting features in formal[19,20] and in phenomenological applications[21,22] 3. A similar approach that does not alter the space-time dimension is considered in Sect.…”

Supercurrent anomaly and gauge invariance in the N=1 supersymmetric Yang-Mills theory

“…Indeed that is what we verify by applying a minimal prescription based on the symmetrization of the trace over the γ matrices involving γ 5 . This prescription does not make use of the property fγ 5 ; γ μ g ¼ 0, since the vanishing of such anticommutator inside divergent integrals is the origin of ambiguities [25] even when applied in the physical dimension [60,74]. Thus, for the traces involving four and six Dirac matrices and one γ 5 , we use…”