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