# Renormalization in a Lorentz-violating model and higher-order operators

## TL;DR

This paper investigates the renormalization properties of a Lorentz-violating scalar-spinor model with higher derivatives, demonstrating improved convergence and super-renormalizability, and analyzing how Lorentz violation affects physical pole masses.

## Contribution

It introduces a higher-derivative Lorentz-violating model that is super-renormalizable and analyzes the impact of Lorentz violation on propagator poles and renormalization.

## Key findings

- The model is super-renormalizable with no divergences beyond four loops.
- Higher-order Lorentz violation shifts the physical pole masses away from standard on-shell values.
- Lorentz-breaking operators significantly modify the two-point functions and renormalization conditions.

## Abstract

The renormalization in a Lorentz-breaking scalar-spinor higher-derivative model involving $\phi^4$ self-interaction and the Yukawa-like coupling is studied. We explicitly de- monstrate that the convergence is improved in comparison with the usual scalar-spinor model, so, the theory is super-renormalizable, with no divergences beyond four loops. We compute the one-loop corrections to the propagators for the scalar and fermionic fields and show that in the presence of higher-order Lorentz invariance violation, the poles that dominate the physical theory, are driven away from the standard on-shell pole mass due to radiatively induced lower dimensional operators. The new operators change the standard gamma-matrix structure of the two-point functions, introduce large Lorentz-breaking corrections and lead to modifications in the renormalization conditions of the theory. We found the physical pole mass in each sector of our model.