The alpha particle charge radius, the radion and the proton radius puzzle

Recent measurements of the Lamb shift of muonic helium-4 ions were used to infer the alpha particle charge radius. The value found is compatible with the radius extracted from the analysis of the electron-helium scattering. Thus, the new spectroscopic data put additional empirical bounds on some free parameters of certain physics theories beyond the Standard Model. In this paper, we analyze the new data in the context of large extra-dimensional theories. Specifically, we calculate the influence of the radion, the scalar degree of freedom of the higher-dimensional gravity, on the energy difference between the 2S and 2P levels of this exotic atom. The radion field is related to fluctuations of the volume of the supplementary space. It should be treated as a phenomenologically independent quantity in relation to the tensorial degrees of freedom of the metric within the braneworld scenario. Based on the spectroscopic data of muonic helium, we find constraints for the effective energy scale of the radion as a function of the alpha particle radius. Then, we discuss the implications of these new constraints on the proton radius puzzle. We also establish a new empirical bound for the radion by examining its influence on the isotopic shift in the 2P-2S transition of muonic hydrogen and muonic deuteron. In connection with this discussion, we study the impact of the radion on the tension observed in measurements of the difference between the squared radii of the helion and alpha particle as extracted from muonic and electronic helium isotopes.