Lamb Shift in Muonic Hydrogen. II. Analysis of the Discrepancy of Theory and Experiment

TL;DR

This paper investigates the discrepancy between theory and experiment in muonic hydrogen's Lamb shift and muon g factor, exploring potential explanations like proton structure effects and new particles, but finds existing models insufficient to resolve the differences.

Contribution

The study analyzes various theoretical modifications, including virtual millicharged particles and hidden sector bosons, and concludes they cannot simultaneously explain muonic discrepancies without conflicting with other measurements.

Findings

Millicharged particles conflict with muon g-2 measurements.

No parameterization of hidden bosons explains both discrepancies.

Electron screening may account for muonic hydrogen effects.

Abstract

Currently, both the g factor measurement of the muon as well as the Lamb shift 2S-2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both "muonic" discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification.