  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.
