Explaining the Proton Radius Puzzle with Disformal Scalars

TL;DR

This paper proposes that disformal scalar interactions can explain the proton radius puzzle by affecting atomic energy levels, especially in muonic atoms, and discusses how non-linear theories and screening mechanisms make this explanation consistent with existing constraints.

Contribution

It introduces a novel disformal scalar field model that accounts for the proton radius discrepancy and integrates non-linear effects to satisfy collider and astrophysical constraints.

Findings

Disformal scalars induce measurable shifts in atomic energy levels.

The model explains the proton radius difference between muonic and electronic hydrogen.

Non-linear theories and screening mechanisms ensure consistency with experimental bounds.

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.