Proton polarizability contribution: Muonic hydrogen Lamb shift and elastic scattering

The uncertainty in the contribution to the Lamb shift in muonic hydrogen, ΔEsubt 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 ΔEsubt 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.