Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift and Elastic Scattering

TL;DR

This paper investigates the proton polarizability's impact on the muonic hydrogen Lamb shift and elastic scattering, revealing uncertainties that could explain the proton radius puzzle and suggesting observable effects in upcoming experiments.

Contribution

It provides a detailed evaluation of proton polarizability effects on the Lamb shift and elastic scattering, highlighting their significance in resolving the proton radius puzzle.

Findings

Proton polarizability effects are large enough to account for the proton radius discrepancy.

The integral evaluation uses form factors and dimensional regularization to quantify uncertainties.

Predicted observable effects in low-energy lepton-proton scattering experiments at PSI.

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.