# Probing of violation of Lorentz invariance by ultracold neutrons in the Standard Model Extension

## TL;DR

This paper investigates potential violations of Lorentz invariance using ultracold neutrons in quantum gravitational states, providing theoretical estimates for experimental bounds on Lorentz violation parameters within the Standard Model Extension.

## Contribution

It introduces a method to analyze Lorentz invariance violation effects on ultracold neutrons using quantum gravitational states and estimates new experimental bounds on SME parameters.

## Key findings

- Estimated upper bounds on Lorentz violation parameters in neutron sector.
- Proposed analysis of transition frequencies to improve constraints.
- Theoretical framework linking SME interactions to quantum gravitational states.

## Abstract

We analyze a dynamics of ultracold neutrons (UCNs) caused by interactions violating Lorentz invariance within the Standard Model Extension (SME) (Colladay and Kostelecky, Phys. Rev. D55, 6760 (1997) and Kostelecky, Phys. Rev. D69, 105009 (2004)). We use the effective non-relativistic potential for interactions violating Lorentz invariance derived by Kostelecky and Lane (J. Math. Phys. 40, 6245 (1999)) and calculate contributions of these interactions to the transition frequencies of transitions between quantum gravitational states of UCNs bouncing in the gravitational field of the Earth. Using the experimental sensitivity of qBounce experiments we make some estimates of upper bounds of parameters of Lorentz invariance violation in the neutron sector of the SME which can serve as a theoretical basis for an experimental analysis. We show that an experimental analysis of transition frequencies of transitions between quantum gravitational states of unpolarized and polarized UCNs should allow to place some new constraints in comparison to the results adduced by Kostelecky and Russell in Rev. Mod. Phys. 83, 11 (2011); edition 2019, arXiv: 0801.0287v12 [hep-ph].