Constraining Born-Infeld-like Nonlinear Electrodynamics Using Hydrogen's Ionization Energy

TL;DR

This paper develops an analytical method to constrain parameters of nonlinear electrodynamics models using hydrogen's ionization energy, providing bounds that improve understanding of these theories' viability.

Contribution

An analytical approach was created to calculate hydrogen ground state energy corrections for generic nonlinear electrodynamics models, enabling new constraints on their parameters.

Findings

Established bounds on parameter b for three nonlinear electrodynamics models.

Compared Born-Infeld constraint with existing literature.

Provided a methodology applicable to other atomic systems.

Abstract

In this work, the hydrogen's ionization energy was used to constrain the free parameter $b$ of three Born-Infeld-like electrodynamics namely Born-Infeld itself, Logarithmic electrodynamics and Exponential electrodynamics. An analytical methodology capable of calculating the hydrogen ground state energy level correction for a generic nonlinear electrodynamics was developed. Using the experimental uncertainty in the ground state energy of the hydrogen atom, the bound $b>5.37\times10^{20}K\frac{V}{m}$, where $K=2$, $4\sqrt{2}/3$ and $\sqrt{\pi}$ for the Born-Infeld, Logarithmic and Exponential electrodynamics respectively, was established. In the particular case of Born-Infeld electrodynamics, the constraint found for $b$ was compared with other constraints present in the literature.