  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 empiric 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, and, in comparison with the tensorial
degrees of freedom, it couples to matter in a different way. Moreover, as some
stabilization mechanism acts exclusively on the scalar degree of freedom, the
tensor and scalar fields should be treated as phenomenologically independent
quantities. 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.
