# Classical Lagrangians for the nonminimal Standard-Model Extension at higher orders in Lorentz violation

## TL;DR

This paper derives classical Lagrangians for relativistic particles with Lorentz violation in the nonminimal SME, extending previous methods to higher orders and including spin effects, aiding phenomenological and gravitational studies.

## Contribution

It introduces a perturbative expansion technique for classical Lagrangians in the nonminimal SME fermion sector at third order in Lorentz violation, incorporating spin effects.

## Key findings

- Lagrangians obtained at third order for multiple SME operators
- Demonstrates the influence of spin on particle propagation
- Provides tools for phenomenological and gravitational research

## Abstract

The current paper is dedicated to determining perturbative expansions for Lagrangians describing classical, relativistic, pointlike particles subject to Lorentz violation parameterized by the nonminimal Standard-Model Extension (SME). An iterative technique recently developed and applied to a Lorentz-violating scalar field theory is now adopted to treat the spin-degenerate SME fermion sector. Lagrangians are obtained at third order in Lorentz violation for the operators $\hat{a}_{\mu}$, $\hat{c}_{\mu}$, $\hat{e}$, $\hat{f}$, and $\hat{m}$ for arbitrary mass dimension. The results demonstrate the impact of nonzero spin on classical particle propagation. They will be useful for phenomenological studies of modified gravity and could provide useful insights into explicit Lorentz violation in curved spacetimes.