On the Lorentz-breaking theory with higher derivatives in spinor sector

TL;DR

This paper investigates Lorentz-breaking gauge theories with higher derivatives in the spinor sector, showing that the Carroll-Field-Jackiw term naturally emerges as a finite quantum correction, avoiding fine-tuning issues.

Contribution

It demonstrates the natural emergence and finiteness of the Carroll-Field-Jackiw term in Lorentz-breaking theories with higher derivatives, addressing quantum corrections and fine-tuning.

Findings

The Carroll-Field-Jackiw term appears as a finite quantum correction.

The theory avoids ambiguities and fine-tuning problems.

Low-energy Lorentz violations remain controlled and finite.

Abstract

We consider the two-point function of the gauge field in Lorentz-breaking theories with higher-derivative extension of the Dirac Lagrangian. We show that the Carroll-Field-Jackiw term naturally arises in this theory as a quantum correction being perfectly finite and thus displaying no ambiguities. Also, the finiteness of this term at low energy limit and the absence of large Lorentz violating corrections allows to avoid the fine-tuning problem.