New Physics and the Proton Radius Problem

TL;DR

This paper investigates whether finely tuned new particles with specific couplings could explain the proton radius discrepancy observed in Lamb shift measurements, considering experimental constraints from muon magnetic moments and kaon decays.

Contribution

It introduces two fine-tuned models with scalar-pseudoscalar and vector-axial couplings to explore their viability in explaining the proton radius problem.

Findings

Scalar-pseudoscalar model excludes masses 100-200 MeV.

Vector model excludes masses below 200 MeV.

Coupling strengths approach electrodynamics levels at around 2 GeV.

Abstract

Background: The recent disagreement between the proton charge radius extracted from Lamb shift measurements of muonic and electronic hydrogen invites speculation that new physics may be to blame. Several proposals have been made for new particles that account for both the Lamb shift and the muon anomalous moment discrepancies. Purpose: We explore the possibility that new particles' couplings to the muon can be fine-tuned to account for all experimental constraints. Method: We consider two fine-tuned models, the first involving new particles with scalar and pseudoscalar couplings, and the second involving new particles with vector and axial couplings. The couplings are constrained by the Lamb shift and muon magnetic moments measurements while mass constraints are obtained by kaon decay rate data. Results: For the scalar-pseudoscalar model, masses between 100 to 200 MeV are not allowed. For the vector model, masses below about 200 MeV are not allowed. The strength of the couplings for both models approach that of electrodynamics for particle masses of about 2 GeV. Conclusions: New physics with fine tuned couplings may be entertained as a possible explanation for the Lamb shift discrepancy.