Constraints on extra dimensions from atomic spectroscopy

We consider a hydrogen atom confined in a thick brane embedded in a higher-dimensional space. Due to effects of the extra dimensions, the gravitational potential is amplified in distances smaller than the size of the supplementary space, in comparison with the Newtonian potential. Studying the influence of the gravitational interaction modified by the extra dimensions on the energy levels of the hydrogen atom, we find independent constraints for the higher-dimensional Planck mass in terms of the thickness of the brane by using accurate measurements of atomic transition frequencies. The constraints are very stringent for narrow branes.

Figure 1

Lower bound for the higher-dimensional Planck mass ${\mathrm{M}}_D$ (expressed in natural units) in terms of $\sigma$ (the wave function width in the transverse directions). The areas below the lines are excluded.

Figure 2

Upper limit for the radius of the extra dimensions in terms of $\sigma$ for $n=3$, 4, 5 and 6. The regions above the lines are excluded.

Figure 3

The energy gap between the $2S-1S$ states in the hydrogen atom due to higher-dimensional gravitational interaction, assuming LHC constraints for $M_D$. The horizontal lines, labeled with $\delta E_{\exp }$ and $\delta E_{\text{th}}$ are the current experimental precision and theoretical uncertainty, respectively, in the $2S-1S$ transition.