Test of Lorentz invariance in $\beta$ decay of polarized $^{20}\text{Na}$

TL;DR

This study tests Lorentz invariance in weak interactions by examining potential directional dependence of $^{20}$Na nuclei lifetime, finding no significant sidereal variation and setting a new, more stringent limit on possible violations.

Contribution

It provides the first sensitive test of Lorentz invariance in nuclear beta decay by measuring sidereal variations in $^{20}$Na lifetime, improving previous limits by a factor of 15.

Findings

No significant sidereal variation detected.

Set a limit of $2\times 10^{-4}$ on Lorentz invariance violation.

Improved previous experimental bounds by a factor of 15.

Abstract

We search for a dependence of the lifetime of $^{20}\text{Na}$ nuclei on the nuclear spin direction. Such a directional dependence would be evidence for Lorentz-invariance violation in weak interactions. A difference in lifetime between nuclei that are polarized in the east and west direction is searched for. This difference is maximally sensitive to the rotation of the Earth, while the sidereal dependence is free from most systematic errors. The experiment sets a limit of $2\times 10^{-4}$ at 90 % C.L. on the amplitude of the sidereal variation of the relative lifetime differences, an improvement by a factor 15 compared to an earlier result.