Fundamental Constant Observational Bounds on the Variability of the QCD Scale

Many physical theories beyond the Standard Model predict time variations of basic physics parameters. Direct measurement of the time variations of these parameters is very difficult or impossible to achieve. By contrast, measurements of fundamental constants are relatively easy to achieve, both in the laboratory and by astronomical spectra of atoms and molecules in the early universe. In this work measurements of the proton to electron mass ratio $\mu$ and the fine structure constant $\alpha$ are combined to place mildly model dependent limits on the fractional variation of the Quantum Chromodynamic Scale and the sum of the fractional variations of the Higgs Vacuum Expectation Value and the Yukawa couplings on time scales of more than half the age of the universe. The addition of another model parameter allows the fractional variation of the Higgs VEV and the Yukawa couplings to be computed separately. Limits on their variation are found at the level of less than $5 \times 10^{-5}$ over the past seven gigayears. A model dependent relation between the expected fractional variation of $\alpha$ relative to $\mu$ tightens the limits to $10^{-7}$ over the same time span. Limits on the present day rate of change of the constants and parameters are then calculated using slow roll quintessence. A primary result of this work is that studies of the dimensionless fundamental constants such as $\alpha$ and $\mu$, whose values depend on the values of the physics parameters, are excellent monitors of the limits on the time variation of these parameters.