Effects of variation of the fine structure constant $\alpha$ and quark mass $m_q$ in M\"ossbauer nuclear transitions

TL;DR

This paper investigates how M"ossbauer nuclear transitions can be highly sensitive probes for detecting potential variations in fundamental constants like the fine-structure constant and quark mass, which could indicate new physics or dark matter effects.

Contribution

It calculates the sensitivity of specific nuclear transitions to variations in fundamental constants, highlighting their potential for precision measurements of such variations.

Findings

M"ossbauer transitions show high sensitivity to quark mass and QCD scale variations.

Enhancement factors $K$ can be large, e.g., $K_q oughly 10^4$ for $^{229}$Th.

Certain nuclear transitions are promising for laser spectroscopy-based tests.

Abstract

High accuracy measurements in M\"ossbauer transitions open up the possibility to use them in the search for temporal and spatial variation of the fine-structure constant $\alpha$, quark mass $m_q$, and dark matter field which may lead to the variation of $\alpha$ and $m_q$. We calculate the sensitivity of nuclear transitions to variation of $\alpha$ and $m_q$. M\"ossbauer transitions have high sensitivity to variation of quark mass $m_q$ and the strong interaction scale $\Lambda_{QCD}$, to which atomic optical clocks are not sensitive. The enhancement factors $K$, defined by $\frac{\delta f}{f} =K_{\alpha }\frac{\delta \alpha}{\alpha}$ and $\frac{\delta f}{f} =K_{q }\frac{\delta m_q}{m_q}$ where $f$ is the transition energy, may be large in some transitions. The 8~eV nuclear clock transition in $^{229}$Th ($K_q \approx 10^4$) and 76~eV transition in $^{235}$U ($K_\alpha \approx K_q \approx 10^3$) may be investigated using laser spectroscopy methods.