Proton Polarization Shifts in Electronic and Muonic Hydrogen

TL;DR

This paper calculates the polarization energy shifts in electronic and muonic hydrogen using a combination of model-independent methods and quark model predictions, incorporating retardation effects and estimating additional contributions.

Contribution

It introduces a hybrid approach combining experimental data and quark models to refine polarization shift calculations in hydrogen isotopes.

Findings

Retardation effects significantly reduce the polarization shifts.

Transverse and seagull contributions are non-negligible.

The approach provides more accurate energy shift estimates with discussions on uncertainties.

Abstract

The contribution of virtual excitations to the energy levels of electronic and muonic hydrogen is investigated combining a model-independent approach for the main part with quark model predictions for the remaining corrections. Precise values for the polarization shifts are obtained in the long-wavelength dipole approximation by numerically integrating over measured total photoabsorption cross sections. These unretarded results are considerably reduced by including retardation effects in an approximate way since the average momentum transfer (together with the mean excitation energy) turns out to be larger than usually assumed. Transverse and seagull contributions are estimated in a simple harmonic oscillator quark model and found to be non-negligible. Possible uncertainties and improvements of the final results are discussed.