Fine-tuning problems in quantum field theory and Lorentz invariance: A scalar-fermion model with a physical momentum cutoff

TL;DR

This paper investigates how a physical momentum cutoff in a scalar-fermion quantum field theory can be compatible with low-energy Lorentz invariance, analyzing the fine-tuning needed for suppression of violations and light scalar particles.

Contribution

It demonstrates the conditions and fine-tuning necessary for Lorentz invariance to emerge at low energies despite high-energy violations in a scalar-fermion model.

Findings

Lorentz invariance suppression at low momenta is achievable with fine-tuning.

A physical momentum cutoff can render the theory finite while maintaining approximate Lorentz invariance.

Light scalar particles can coexist with high-energy Lorentz violation under specific conditions.

Abstract

We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale, a physical cutoff rendering the quantum field theory finite, can be made compatible with a suppression of Lorentz invariance violations at low momenta. The fine tuning required to get this suppression and to have a light scalar particle in the spectrum is determined at one loop.