Muonic hydrogen and MeV forces

TL;DR

This paper investigates whether a new MeV-scale force between muons and protons can explain the proton radius discrepancy observed in muonic hydrogen and its implications for other muonic systems.

Contribution

It proposes a new force carrier with MeV mass that could account for the proton radius puzzle and muon g-2 anomaly, with predictions for other muonic systems.

Findings

A new MeV-scale force can explain the proton radius discrepancy.

Constraints require suppressed couplings to electrons and neutrons.

Predictions made for muonic deuterium, helium, and true muonium.

Abstract

We explore the possibility that a new interaction between muons and protons is responsible for the discrepancy between the CODATA value of the proton radius and the value deduced from the measurement of the Lamb shift in muonic hydrogen. We show that a new force carrier with roughly MeV mass can account for the observed energy shift as well as the discrepancy in the muon anomalous magnetic moment. However, measurements in other systems constrain the couplings to electrons and neutrons to be suppressed relative to the couplings to muons and protons, which seems challenging from a theoretical point of view. One can nevertheless make predictions for energy shifts in muonic deuterium, muonic helium, and true muonium under the assumption that the new particle couples dominantly to muons and protons.