Model-independent determination of the Lamb shift in muonic hydrogen and the proton radius

We obtain a model-independent expression for the Lamb shift in muonic hydrogen. This expression includes the leading logarithmic O(m_μα⁶) terms, as well as the leading O(m_μα⁵(m_μ²)/(m_ρ²)) hadronic effects. The latter are controlled by the chiral theory, which allows for their model-independent determination. In this paper we give the missing piece for their complete expression including the pion and Delta particles. Out of this analysis, and the experimental measurement of the Lamb shift in muonic hydrogen, we determine the electromagnetic proton radius: r_p=0.8412(15) fm. This number is at 6.8σ variance with respect to the CODATA value. The accuracy of our result is limited by uncomputed terms of O(m_μα⁵(m_μ³)/(m_ρ³),m_μα⁶). This parametric control of the uncertainties allows us to obtain a model-independent estimate of the error, which is dominated by hadronic effects. (orig.)