Constraints on Extra-Dimension Gravity by Muonic Hydrogen and Deuterium Spectroscopy

In the early 2010s, the discrepancy between the measured proton radius of muonic and normal hydrogen, i.e. the proton radius puzzle, led to investigations into Quantum Electrodynamics and new physics. One such explanation is the Large Extra Dimension (LED) Model. The LED Model introducces a short-range extra graviational force between the muon and the proton, shifting the energy levels in atoms. This paper aims to utilize recently refined measurements of proton and deuteron radii from spectroscopy experiments to provide new, stringent constraints on the LED model’s fundamental parameters: the compactification radius (R n ) and the Planck scale (M pl(4+n) ). Our analysis is performed on muonic hydrogen and muonic deuterium. While dealing with individual atoms, a differential analysis is applied to minizize systematic and theoretical uncertainties. The calculated M pl(4+n) values are found to be several orders of magnitude below the experimental lower limit of 2 TeV, consistent with previous studies despite a smaller residual energy discrepancy. Such result indicates that the LED model is highly constrained or untenable.