Understanding Radiatively Induced Lorentz-CPT Violation in Differential Regularization

TL;DR

This paper examines the ambiguity in calculating the radiatively induced Chern-Simons term using differential regularization, highlighting the role of renormalization scales and discussing ways to resolve the ambiguity.

Contribution

It introduces a detailed analysis of the perturbative ambiguity in differential regularization for Lorentz-CPT violation and compares it with other schemes, proposing methods to eliminate the ambiguity.

Findings

The ambiguity is characterized by an indefinite ratio of renormalization scales.

The results align with those from other regularization schemes.

Ambiguity can be resolved by physical requirements or fundamental principles.

Abstract

We have investigated the perturbative ambiguity of the radiatively induced Chern-Simons term in differential regularization. The result obtained in this method contains all those obtained in other regularization schemes and the ambiguity is explicitly characterized by an indefinite ratio of two renormalization scales. It is argued that the ambiguity can only be eliminated by either imposing a physical requirement or resorting to a more fundamental principle. Some calculation techniques in coordinate space are developed in the appendices.