Extra dimensions and atomic transition frequencies

TL;DR

This paper proposes a novel method to constrain the size of large extra dimensions by analyzing their effects on atomic transition energies, providing constraints that improve upon some recent experimental bounds.

Contribution

It introduces a new approach using atomic spectroscopy to limit the size of gravity-only large extra dimensions, especially for three LEDs related to dark matter.

Findings

Constraints on LED size less than 10^-5 meters for three LEDs.

Current atomic spectroscopy data can improve existing bounds.

Method offers a complementary approach to gravitational tests.

Abstract

New unification theories predict Large Extra Dimensions (LEDs). If that is the case, gravity would be stronger at short ranges than what Newtonian gravity predicts. LEDs could also have effects at atomic level. In this paper we propose a new method to constrain the size of gravity-only LEDs by analyzing how these LEDs modify the energy of the atomic transitions 1s-2s and 2s-2p (Lamb shift), for the particular case of the hydrogen and muonium atoms. We estimate these effects by using Bethe's non-relativistic treatment of Lamb shift. For the particular case of three LEDs, which may be a candidate to explain the interaction mechanism of dark matter particles, we have found that current knowledge in atomic spectroscopy could constrain their sizes to be less than 10 * 10^(-6) m. Although our contributions do not reach the sensitivity given by SN1987a, they are still slightly better than recent constraints given by Inverse Square Law tests of Eot-Wash group at Washington University, which gave R3 < 36.6 * 10^(-6) m.