Applying Bayesian Inference to Galileon Solutions of the Muon Problem

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 $\delta E_{H{e}^3}=1.97_{-1.87}^{+9.28}$ meV and $\delta E_{H{e}^4}=1.69_{-1.61}^{+9.25}$ meV as well as for true muonium, $\delta E_{TM}=0.06_{-0.05}^{+0.46}$ meV.

arXiv comment8 pages, 2 figures, updated to match journal version

References in corpus (25)

• MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics
• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• The galileon as a local modification of gravity
• Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
• Test of lepton universality using $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ decays
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• The Relation between Physical and Gravitational Geometry
• UV-Completion by Classicalization
• Compatibility of the chameleon-field model with fifth-force experiments, cosmology, and PVLAS and CAST results
• Production of the Smallest QED Atom: True Muonium (mu^+ mu^-)
• Measurement of the 1s-2s energy interval in muonium
• Disformal Inflation
• Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
• Constraining Disformally Coupled Scalar Fields
• Nucleon electromagnetic form factors in two-flavour QCD
• Probing extra dimensions using Nambu-Goldstone bosons
• The Lamb Shift of Excited S-Levels in Hydrogen and Deuterium Atoms
• The bound mu+ mu- system
• The Heavy Photon Search experiment at Jefferson Laboratory
• The Production and Discovery of True Muonium in Fixed-Target Experiments
• Decay Rate and Hyperfine Structure of the bound mu+ mu- system
• Explaining the Proton Radius Puzzle with Disformal Scalars
• Electroweak Corrections to the True Muonium Hyperfine Splitting
• Can Galileons solve the muon problem?
• Hyperfine Splitting in True Muonium to $\mathcal{O}(m_{\mu }{\alpha }^6)$: Two Photon Annihilation Contribution from Other Flavors

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• Discovering True Muonium in $K_L\to ({\mu }^{+}{\mu }^{-})\gamma$
• Scouring meson decays for true muonium