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

TL;DR

The work addresses whether the QCD scale $Λ_{\text{QCD}}$ can drift in time due to a gluon-coupled scalar field, and develops a framework to translate diverse data sets into limits on $\dot{Λ}_{\text{QCD}}/Λ_{\text{QCD}}$ using dimensionless combinations. It analyzes atomic clock frequency ratios, hyperfine and nuclear observables, a proposed $^{229}$Th nuclear clock, Big Bang Nucleosynthesis, the Oklo reactor, and quasar absorption spectra to derive complementary constraints. Key results include $\dot{Λ}_{\text{QCD}}/Λ_{\text{QCD}}=(3.2±3.5)×10^{-17}$ yr$^{-1}$ from atomic clocks, $|δΛ_{\text{QCD}}/Λ_{\text{QCD}}|<2×10^{-9}$ over 1.8 Gyr from Oklo, and a four-order-of-magnitude enhancement in sensitivity for the $^{229}$Th nuclear clock, with additional bounds from BBN and quasar data. Collectively, the paper demonstrates the extreme stability of $Λ_{\text{QCD}}$ over cosmological timescales within this beyond-Standard-Model framework and highlights the potential of nuclear-clock and astrophysical probes as powerful cross-checks.

Abstract

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.