# Improved Tests of Lorentz Invariance in the Matter Sector using Atomic Clocks

## TL;DR

This paper improves constraints on Lorentz invariance violation in the matter sector by reanalyzing atomic clock data, notably significantly tightening bounds on the isotropic coefficient of the $ ilde{c}_{
ueta}$ tensor.

## Contribution

It introduces an advanced model for frequency shifts due to Lorentz violation, enabling the first constraint on the least well-constrained $ ilde{c}_{TT}$ coefficient with a five-order-of-magnitude improvement.

## Key findings

- New limits on eight $ ilde{c}_{
ueta}$ tensor components.
- First constraint on the isotropic coefficient $ ilde{c}_{TT}$.
- Five orders of magnitude improvement on $ ilde{c}_{TT}$ constraint.

## Abstract

For the purpose of searching for Lorentz-invariance violation in the minimal Standard-Model Extension, we perfom a reanalysis of data obtained from the $^{133}\text{Cs}$ fountain clock operating at SYRTE. The previous study led to new limits on eight components of the $\tilde{c}_{\mu\nu}$ tensor, which quantifies the anisotropy of the proton kinetic energy. We recently derived an advanced model for the frequency shift of hyperfine Zeeman transition due to Lorentz violation and became able to constrain the ninth component, the isotropic coefficient $\tilde{c}_{TT}$, which is the least well-constrained coefficient of $\tilde{c}_{\mu\nu}$. This model is based on a second-order boost Lorentz transformation from the laboratory frame to the Sun-centered frame, and it gives rise to an improvement of five orders of magnitude on $\tilde{c}_{TT}$ compared to the state of the art.