# Lamb shift in hydrogen-like muonic atoms to test fractal extra dimensions

## TL;DR

This paper investigates the Lamb shift in hydrogen-like muonic atoms to set bounds on the existence of fractal extra dimensions, suggesting future experiments could reveal evidence of such dimensions.

## Contribution

It introduces a method to estimate bounds on fractal extra dimensions using Lamb shift measurements in muonic atoms, extending previous analyses to higher Z values.

## Key findings

- Stronger bounds on extra dimensions from muonic hydrogen and deuterium.
- Potential for future measurements to detect fractal extra dimensions.
- Highlights the importance of high-Z muonic atom experiments.

## Abstract

From the comparison between the experimental and theoretical results for the energy difference between 2s1/2 and 2p1/2 states in hydrogen and hydrogen-like ions with different values of Z, we estimate bounds for the presence of an extra fractional dimension. These bounds are higher when we work with muonic hydrogen and muonic deuterium, which open the possibility that future measurements of the Lamb shift in muonic atoms with one electron and higher values of Z may show evidence of the extra dimension.