Explaining the Proton Radius Puzzle with Disformal Scalars

Abstract

We analyse the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cut-off scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic Hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in non-linear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where non-perturbative effects in vacuum are present ensure that unitarity is preserved in high energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

17 pages, typos corrected and references added

References in corpus (11)

• Resummation of Massive Gravity
• Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios
• Lunar Laser Ranging Tests of the Equivalence Principle
• Compatibility of the chameleon-field model with fifth-force experiments, cosmology, and PVLAS and CAST results
• Muonic hydrogen and MeV forces
• New Parity-Violating Muonic Forces
• Proton size anomaly
• Spectroscopy as a test of Coulomb's law - A probe of the hidden sector
• Constraining Disformally Coupled Scalar Fields
• Atomic Precision Tests and Light Scalar Couplings
• Reduction of the proton radius discrepancy by 3 sigma

Cited by in corpus (3)

• Disformal Theories of Gravity: From the Solar System to Cosmology
• Standard Electroweak Interactions in Gravitational Theory with Chameleon Field and Torsion
• Applying Bayesian Inference to Galileon Solutions of the Muon Problem