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

Abstract

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 $\varphi$ 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 $\varphi$ 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 $|\delta {\Lambda }_{\text{QCD}}/{\Lambda }_{\text{QCD}}|<2\times 10^{-9}$ over that time span, corresponding to the linear drift limit $|{\dot{\Lambda }}_{\text{QCD}}/{\Lambda }_{\text{QCD}}|<1\times 10^{-18}{\text{yr}}^{-1}$, 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.

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