The muonic hydrogen Lamb shift and the proton radius

TL;DR

This paper provides a model-independent calculation of the muonic hydrogen Lamb shift, incorporating hadronic effects via chiral theory, leading to a precise proton radius measurement that significantly differs from previous values.

Contribution

It introduces a model-independent expression for the Lamb shift including hadronic effects and determines the proton radius with controlled uncertainties.

Findings

Proton radius measured as 0.8412(15) fm

Result differs by 6.8σ from CODATA value

Hadronic effects are fully accounted for in the analysis

Abstract

We obtain a model independent expression for the muonic hydrogen Lamb shift up to $\mathcal O (m_\mu \alpha^6, m_\mu \alpha^5 \frac{m_\mu^2}{m_\rho^2})$. The hadronic effects are controlled by the chiral theory, which allows for their model independent determination. We give their complete expression including the pion and Delta particles. Out of this analysis and the experimental measurement of the muonic hydrogen Lamb shift we determine the electromagnetic proton radius: $r_p$=0.8412(15) fm. This number is at 6.8$\sigma$ variance with respect to the CODATA value. The parametric control of the uncertainties allows us to obtain a model independent determination of the error, which is dominated by hadronic effects.