We study variation of the proton-to-electron mass ratio [Formula: see text] by incorporating Standard Model (SM) of particle physics into an extended Brans–Dicke theory. We show that the evolution of the Higgs vacuum expectation value (VEV), with expansion of the Universe, leads to the variation of the proton-to-electron mass ratio. This is because the electron mass is proportional to the Higgs VEV, while the proton mass is mainly dependent on the quantum chromodynamics (QCD) energy scale, i.e. [Formula: see text]. Therefore, using the experimental and cosmological constraints on the variation of the [Formula: see text], we can constrain the variation of the Higgs VEV. This study is important in understanding the recent claims of the detection of a variation of the proton-to-electron mass ratio in quasar absorption spectra.
Proton mass decomposition: Naturalness and interpretations
