Constraints on the Variation of the QCD Interaction Scale $\Lambda_{\text{QCD}}$

Laboratory and astrophysical tests of ''constant variation'' have so far concentrated on the dimensionless fine-structure constant $\alpha$ and on the electron or quark mass ratios $X_{e,q}=m_{e,q}/\Lambda_{\text{QCD}}$, treating the QCD scale $\Lambda_{\text{QCD}}$ as unchangeable. Certain beyond Standard Model frameworks, most notably those with a dark matter or dark energy scalar field $\phi$ coupling with the gluon field, would make $\Lambda_{\text{QCD}}$ itself time dependent while leaving $\alpha$ and the electron mass untouched. Under the minimal assumption that this gluonic channel is the sole $\phi$ interaction, we recast state-of-the-art atomic clock comparisons into $\dot{\Lambda}_{\text{QCD}}/\Lambda_{\text{QCD}}=(3.2 \pm 3.5) \times 10^{-17} \ \text{yr}^{-1}$ limits, translate the isotope yields of the 1.8-Gyr-old Oklo natural reactor into a complementary geophysical limit of $|\delta\Lambda_{\text{QCD}}/\Lambda_{\text{QCD}}|<2\times10^{-9}$ over that time span, corresponding to the linear drift limit $|\dot{\Lambda}_{\text{QCD}}/\Lambda_{\text{QCD}}|<1\times10^{-18} \text{yr}^{-1}$, and show that the proposed $8.4$ eV $^{229}$Th nuclear clock would amplify a putative $\Lambda_{\text{QCD}}$ drift by four orders of magnitude compared with present atomic clocks. We also obtain constraints from quasar absorption spectra and Big Bang Nucleosynthesis data.