Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift and Elastic Scattering

Abstract

The uncertainty in the contribution to the Lamb shift in muonic hydrogen, $\Delta E^{subt}$ arising from proton polarizability effects in the two-photon exchange diagram at large virtual photon momenta is shown large enough to account for the proton radius puzzle. This is because $\Delta E^{subt}$ is determined by an integrand that falls very slowly with very large virtual photon momenta. We evaluate the necessary integral using a set of chosen form factors and also a dimensional regularization procedure which makes explicit the need for a low energy constant. The consequences of our two-photon exchange interaction for low-energy elastic lepton-proton scattering are evaluated and could be observable in a planned low energy lepton-proton scattering experiment planned to run at PSI.