Abstract
It is generally assumed that in order to preserve Bose symmetry in the left- (or right-chiral) current it is necessary to equally distribute the chiral anomaly between the vectorial and the axial Ward identities, requiring the use of counterterms to restore consistency. In this work, we show how to calculate the quantum breaking of the left- and right-chiral currents in a way that allows to preserve Bose symmetry independently of the chiral anomaly, using the implicit regularization method.
Highlights
Almost half a century after the seminal papers [1,2], reporting the existence of theories with anomalous breaking of symmetries, it remains to present date still a challenge to deal explicitly with these quantum breakings in a perturbative field theoretical approach, as the latter requires the use of an invariant regularization and renormalization program.The necessity to have the gauge symmetries of the Standard Model implemented to all loop orders led to the advent of dimensional regularization (DR) [3,4], which has been since one of the most widely used regularizations, as it respects unitarity and causality to all orders
DR is, burdened by the technical complexity associated in dealing with dimension specific objects, such as the LeviCivita tensor and the γ5 matrix [5,6,7], which can be present in theories with anomalous breakings
After a resumée of the Implicit Regularization (IReg) in the chapter, we present in Sect. 3 the quantities to be evaluated in 2-d and 4-d, proceed to calculate them in Sects. 4.1 and 4.2, and we study their anomalous breakings in the light of Bose symmetry
Summary
Almost half a century after the seminal papers [1,2], reporting the existence of theories with anomalous breaking of symmetries, it remains to present date still a challenge to deal explicitly with these quantum breakings in a perturbative field theoretical approach, as the latter requires the use of an invariant regularization and renormalization program. It should be emphasized that the choice of the WI to be satisfied (or not) can be made without breaking momentum routing invariance of an amplitude [15, 18] In this contribution we use IReg as a tool to identify and resolve the source of conflict in the implementation of Bose symmetry in the left–right (chiral) sector of gauge currents, which reportedly [26] constrains the values of the anomaly in the related vector-axial representation. The anticommutator evaluates, in the cases considered in the present contribution, all chirality mixing amplitudes to zero, prior to the use of a regularization By avoiding this relation and using IReg combined with the symmetrization of the trace, one obtains full consistency of the Bose symmetry and the values that the anomaly can take in the equivalent left–right and vector-axial representations.
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