\[\huge
\mathcal{L}_{\rm int.} = \phi \left[ {d_e \, F_{\mu\nu}F^{\mu\nu}} + {d_{m_f} \, \bar\psi\psi} + {d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
\]
\[\huge
\mathcal{L}_{\rm int.} = \phi \left[ {\color{yellow}d_e \, F_{\mu\nu}F^{\mu\nu}} + {d_{m_f} \, \bar\psi\psi} + {d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
\]
\[\huge
\mathcal{L}_{\rm int.} = \phi \left[ {\color{yellow}d_e \, F_{\mu\nu}F^{\mu\nu}} + {\color{orange}d_{m_f} \, \bar\psi\psi} + {d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
\]
\[\huge
\mathcal{L}_{\rm int.} = \phi \left[ {\color{yellow}d_e \, F_{\mu\nu}F^{\mu\nu}} + {\color{orange}d_{m_f} \, \bar\psi\psi} + {\color{red}d_g \, G^a_{\mu\nu}G^{a\mu\nu}}\right]
\]
\[\large
{\color{yellow}\alpha \to \alpha(1 + d_e \phi(r,t))}
\]
• nb: $d_e = d_\gamma = d_\alpha = 1/\Lambda_\gamma$
\[\large
{\color{orange}m_e \to m_e(1 + d_{m_e} \phi(r,t))}
\]
• electron and quark masses
\[\large
{\color{red}m_p \to m_p(1 + d_{g} \phi(r,t))}
\]
• Proton mass: binding energy: QCD scale $\Lambda_{\rm QCD}$
• Nuclear moments + radius: depend on $\Lambda_{\rm QCD}$, $m_q$
• Optical clock
\[
\begin{align*}\large
\omega &\propto R_y \, F_{\rm rel}(Z\alpha) \sim \alpha^{(2+K_{\rm rel})}m_e \\
\frac{\delta\omega}{\omega} &= (2+K_{\rm rel}){\color{yellow}d_e} +{\color{orange}d_{m_e}}
\end{align*}
\]
• Microwave (hyperfine) clock
\[
\begin{align*}\large
\omega &\propto R_y \, [\alpha^2 F_{\rm rel}(Z\alpha)] \, (\mu \, m_e/m_p) \\
\frac{\delta\omega}{\omega} &= (4+K_{\rm rel}'){\color{yellow}d_e} + {\color{orange}d_{m_e}} + ({\color{orange}d_{m_e}} - {\color{red}d_g}) + \kappa\, ({\color{orange}d_{m_q}} - {\color{red}d_g})
\end{align*}
\]
• Cavity-stabilised laser
\[
\begin{align*}\large
\omega &\propto 1/a_0 \\
\frac{\delta\omega}{\omega} &= {\color{yellow}d_e} + {\color{orange}d_{m_e}}
\end{align*}
\]