The recoil correction to the proton-finite-size contribution to the Lamb shift in muonic hydrogen

Abstract

The Lamb shift in muonic hydrogen was measured some time ago to a high accuracy. The theoretical prediction of this value is very sensitive to the proton-finite-size effects. The proton radius extracted from muonic hydrogen is in contradiction with the results extracted from elastic electron-proton scattering. That creates a certain problem for the interpretation of the results from the muonic hydrogen Lamb shift. For the latter we need also to take into account the two-photon-exchange contribution with the proton finite size involved. The only way to describe it relies on the data from the scattering, which may produce an internal inconsistency of theory. Recently the leading proton-finite-size contribution to the two-photon exchange was found within the external field approximation. The recoil part of the two-photon-exchange has not been considered. Here we revisit calculation of the external-field part and take the recoil correction to the finite-size effects into account.

References in corpus (26)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• High-precision determination of the electric and magnetic form factors of the proton
• Global analysis of proton elastic form factor data with two-photon exchange corrections
• On the rms-radius of the proton
• Two-photon exchange in elastic electron-nucleon scattering
• High Precision Measurement of the Proton Elastic Form Factor Ratio ${\mu }_p{G}_E/G_M$ at low $Q^2$
• Proton structure effects in muonic hydrogen
• The RMS Charge Radius of the Proton and Zemach Moments
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Higher order proton structure corrections to the Lamb shift in muonic hydrogen
• Realistic Transverse Images of the Proton Charge and Magnetic Densities
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Electromagnetic form factors of the nucleon: new fit and analysis of uncertainties
• Chiral perturbation theory of muonic hydrogen Lamb shift: polarizability contribution
• Nuclear Structure-Dependent Radiative Corrections to the Hydrogen Hyperfine Splitting
• The two-photon exchange contribution to muonic hydrogen from chiral perturbation theory
• Precise determination of low-Q nucleon electromagnetic form factors and their impact on parity-violating e-p elastic scattering
• Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory
• $\mu -H$ Lamb shift: dispersing the nucleon-excitation uncertainty with a finite energy sum rule
• Proton polarizability effect in the Lamb shift of the hydrogen atom
• Proton root-mean-square radii and electron scattering
• Muonic Hydrogen and the Third Zemach Moment
• Comment on "High-Precision Determination of the Electric and Magnetic Form Factors of the Proton"
• Proton polarizability and the Lamb shift in muonic hydrogen
• Model-independent determination of the magnetic radius of the proton from spectroscopy of ordinary and muonic hydrogen
• A self-consistent value of the electric radius of the proton from the Lamb shift in muonic hydrogen

Cited by in corpus (9)

• Theory of the n=2 levels in muonic deuterium
• Parameterization and applications of the low-$Q^2$ nucleon vector form factors
• Comprehensive theory of the Lamb shift in light muonic atoms
• Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
• Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• Theory of the n=2 levels in muonic helium-3 ions
• Precision Nuclear-Spin Effects in Atoms: EFT Methods for Reducing Theory Errors
• Relativistic fine structure of the (He4,mu) ion 2p-levels