Managing γ 5 in Dimensional Regularization II: the Trace with more γ 5’s

Abstract

In the present paper we evaluate the anomaly for the abelian axial current in a non abelian chiral gauge theory, by using dimensional regularization. This amount to formulate a procedure for managing traces with more than one γ 5 .The suggested procedure obeys Lorentz covariance and cyclicity, at variance with previous approaches (e.g. the celebrated 't Hooft and Veltman's where Lorentz is violated)The result of the present paper is a further step forward in the program initiated by a previous work on the traces involving a single γ 5 . The final goal is an unconstrained definition of γ 5 in dimensional regularization. Here, in the evaluation of the anomaly, we profit of the axial current conservation equation, when radiative corrections are neglected. This kind of tool is not always exploited in field theories with γ 5 , e.g. in the use of dimensional regularization of infrared and collinear divergences..

γ5 in the four-dimensional helicity scheme

“…II C, the evaluation of the Lorentz algebra using an anticommuting γ can therefore not be used to obtain the quark form factor related to Lagrangian (3.1) in a massless framework. 13 However, in Sec. IV B we consider Eq.…”

“…in Refs. [4,5] and [12,13,15] by modifying the trace operation in such a way that the result in Eq. (2.19) is recovered.…”

“…(2.5) and distinguish the evanescent coupling α e which is related to ϵ-scalar-fermion interactions from the gauge (2018) coupling α s . 12 The two-loop calculations are performed by using a (quasi) d s -dimensional Lorentz algebra as given in Eq. (2.6).…”

“…The right diagram is proportional to the evanescent coupling α e and only contributes in the FDH scheme. 12 For the definition of α e we refer to Ref. [24].…”

“…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 γ 5 in the dimensional framework. Irrespective of this effort, in the overwhelming majority of computations that have been performed so far, the original γ 5 definition of Ref.…”