Applying Bayesian Inference to Galileon Solutions of the Muon Problem

TL;DR

This paper uses Bayesian inference to constrain Galileon theory parameters by analyzing corrections to atomic energy levels, predicting measurable shifts in muonic helium and true muonium.

Contribution

It introduces a novel approach linking Galileon disformal couplings to atomic energy shifts and constrains model parameters using Bayesian methods.

Findings

Predicted energy shifts in muonic helium and true muonium.

Constrained Galileon scale and cutoff radii with Bayesian inference.

Introduced a new parameter $eta$ relating cutoff radii across systems.

Abstract

We derive corrections to atomic energy levels from disformal couplings in Galileon theories. Through Bayesian inference, we constrain the cutoff radii and Galileon scale via these corrections. To connect different atomic systems, we assume the various cutoff radii related by a one-parameter family of solutions. This introduces a new parameter $\alpha$ which is also constrained. In this model, we predict shifts to muonic helium of $\delta E_{He^3}=1.97^{+9.28}_{-1.87}$ meV and $\delta E_{He^4}=1.69^{+9.25}_{-1.61}$ meV as well as for true muonium, $\delta E_{TM}=0.06^{+0.46}_{-0.05}$ meV.