Towards a $^{229}$Th Nuclear Clock for Dark Matter and Beyond Standard Model Physics Searches*

Ever since Dirac published his large number hypothesis, there has been considerable interest in searching for variations in fundamental constants. Many modern theories, including grand unified theories, string theories, and dark matter and energy models, predict some variations in the constants. Of particular interest to nuclear physics are several unified theories' predictions that there might be variations in the fine structure constant $\alpha$ and the strong interaction scale parameter $m_q/\Lambda _{QCD}$ (i.e. the ratio of the average of the quark masses $m_q$ to the quantum chromodynamic scale $\Lambda _{QCD}$).

The anomalously low-lying nuclear isomer transition in $^{229}$Th provides the opportunity to search for variations in both $\alpha$ and $m_q/\Lambda _{QCD}$. Regular comparisons of the $^{229}$Th transition frequency to another narrow linewidth transition (e.g. any atomic clock, which variations in can be ignored owing to the far lower sensitivity) should enable searching for variations in the constants at or below the level of $10^{-20}/$yr. Experimental progress towards the development of a next generation clock utilizing this nuclear isomer transition will be presented.