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

TL;DR

This paper investigates how large extra-dimensional theories, particularly the radion field, influence atomic energy levels and uses recent spectroscopic data to constrain these theories, shedding light on the proton radius puzzle.

Contribution

It provides a novel analysis of muonic helium spectroscopic data within the context of extra-dimensional theories, focusing on the radion's effects and deriving new constraints on fundamental parameters.

Findings

Constraints on the radion's effective energy scale derived from spectroscopic data.

Implications for the proton radius puzzle based on radion-related bounds.

Compatibility of alpha particle charge radius measurements with existing data.

Abstract

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.