Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds

TL;DR

This paper investigates how the Generalized Uncertainty Principle in braneworld models influences the fine structure constant, deriving constraints on quantum gravity parameters from atomic physics measurements.

Contribution

It introduces a novel analysis of GUP effects on atomic spectra within braneworld scenarios, deriving bounds on deformation parameters and higher-dimensional Planck length.

Findings

Constraints on the GUP deformation parameter β.

Bounds on the D-dimensional Planck length l_D.

Predicted deviations in the fine structure constant.

Abstract

The Generalized Uncertainty Principle (GUP) has been discussed in the thick braneworld scenario. By considering Rydberg atoms in this background, we show that the spacetime geometry affects Maxwell equations inducing an effective dielectric constant on the space. In its turn, the corrected Coulomb potential by the gravitational interaction yields a deviation on the $3$-dimensional Bohr radius. Then, we compute the corrections on the fine structure constant owing to the GUP in higher-dimensional spacetime. We also found constraints for the deformation parameter $\beta$ and $D$-dimensional Planck length $l_{D}$ by comparing the predicted deviations with the recent empirical data of the fine structure constant. We compute the intermediate length scale, which in principle may be larger than the Planck length scale. It is conjectured that below such scale Quantum Gravity effects should take place.