Effects of gravity in extra dimensions in atomic phenomena

TL;DR

This paper investigates how extra spatial dimensions affect atomic energy levels by comparing theoretical predictions with experimental data, leading to tighter constraints on the size of extra dimensions than previous methods.

Contribution

It introduces a novel approach using Dirac equations to set more stringent limits on extra dimensions in the Arkani-Hamed-Dimopoulos-Dvali model based on atomic phenomena.

Findings

Stronger limits on extra dimension size than molecular spectra methods

Perturbation theory is inadequate for this analysis

Solving Dirac equations yields more reliable results

Abstract

We use the difference between theory and experiment for energy intervals in simple atomic systems (hydrogen, muonium, positronium and deuteron) to find limits on the size of extra space dimensions in the Arkani-Hamed - Dimopoulos - Dvali model for gravitation potential on short distances. As an additional experimental fact we use absence of the small size gravitational bound states of elementary particles. We demonstrate that the perturbation theory approach does not work and more reliable results are obtained by solving the Dirac equations for an electron in Coulomb and gravitational fields. These results probe smaller distances than distance between nuclei in molecules and the limits are significantly stronger than the limits on the size of extra dimensions obtained using spectra of hydrogen molecules.