Testing Lorentz invariance in orbital electron capture

TL;DR

This paper explores testing Lorentz invariance through orbital electron capture, proposing methods to improve limits on Lorentz violation in the weak interaction sector by analyzing specific isotopes with high decay rates.

Contribution

It derives Lorentz-violating decay rate expressions for orbital electron capture and discusses experimental strategies to enhance sensitivity to Lorentz violation.

Findings

Derived decay rate expressions incorporating Lorentz violation.

Identified isotopes suitable for high-rate, low-dose experiments.

Outlined experimental requirements for competitive tests.

Abstract

Searches for Lorentz violation were recently extended to the weak sector, in particular neutron and nuclear $\beta$ decay [1]. From experiments on forbidden $\beta$-decay transitions strong limits in the range of $10^{-6}$-$10^{-8}$ were obtained on Lorentz-violating components of the $W$-boson propagator [2]. In order to improve on these limits strong sources have to be considered. In this Brief Report we study isotopes that undergo orbital electron capture and allow experiments at high decay rates and low dose. We derive the expressions for the Lorentz-violating differential decay rate and discuss the options for competitive experiments and their required precision.