Weighted power counting and chiral dimensional regularization

TL;DR

This paper introduces a modified dimensional-regularization method tailored for chiral and parity-violating quantum field theories, simplifying proofs of renormalizability and consistency across all orders.

Contribution

It proposes a new regularization technique that maintains physical components of fields, uses evanescent higher-derivative terms, and employs weighted power counting for efficient renormalization control.

Findings

Ensures consistency of chiral dimensional regularization to all orders.

Simplifies proofs of renormalizability and the Adler-Bardeen theorem.

Applicable to wider classes of models with complex computations.

Abstract

We define a modified dimensional-regularization technique that overcomes several difficulties of the ordinary technique, and is specially designed to work efficiently in chiral and parity violating quantum field theories, in arbitrary dimensions greater than 2. When the dimension of spacetime is continued to complex values, spinors, vectors and tensors keep the components they have in the physical dimension, therefore the $\gamma $ matrices are the standard ones. Propagators are regularized with the help of evanescent higher-derivative kinetic terms, which are of the Majorana type in the case of chiral fermions. If the new terms are organized in a clever way, weighted power counting provides an efficient control on the renormalization of the theory, and allows us to show that the resulting chiral dimensional regularization is consistent to all orders. The new technique considerably simplifies the proofs of properties that hold to all orders, and makes them suitable to be generalized to wider classes of models. Typical examples are the renormalizability of chiral gauge theories and the Adler-Bardeen theorem. The difficulty of explicit computations, on the other hand, may increase.