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

Abstract

We obtain a model independent expression for the muonic hydrogen Lamb shift. This expression includes the leading logarithmic $\mathcal{O}(m_{\mu }{\alpha }^6)$ terms, as well as the leading $\mathcal{O}(m_{\mu }{\alpha }^5\frac{m_{\mu }^2}{m_{\rho }^2})$ 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 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 accuracy of our result is limited by uncomputed terms of $\mathcal{O}(m_{\mu }{\alpha }^5\frac{m_{\mu }^3}{m_{\rho }^3},m_{\mu }{\alpha }^6)$. This parametric control of the uncertainties allows us to obtain a model independent determination of the error, which is dominated by hadronic effects.

5 pages, 1 figure. Extensive changes in the discussion. References added. Some numbers changed. Main conclusion unchanged

References in corpus (5)

• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
• Reduction of the proton radius discrepancy by 3 sigma
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory

Cited by in corpus (6)

• Comprehensive theory of the Lamb shift in light muonic atoms
• Proton radius from electron-proton scattering and chiral perturbation theory
• The proton radius (puzzle?) and its relatives
• Point-Particle Effective Field Theory III: Relativistic Fermions and the Dirac Equation
• Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions
• Quantum field theory for multipolar composite bosons with mass defect and relativistic corrections