---
abstract: |
    We consider the two-photon exchange contribution to the $2P-2S$ Lamb shift in muonic deuterium in the framework of forward dispersion relations. The dispersion integrals are evaluated using experimental data on elastic deuteron form factors and inelastic electron-deuteron scattering, both in the quasielastic and hadronic range. The subtraction constant that is required to ensure convergence of the dispersion relation for the forward Compton amplitude $T_1(\nu,Q^2)$ is related to the deuteron magnetic polarizability $\beta(Q^2)$. Based on phenomenological information, we obtain for the Lamb shift $\Delta
    E_{2P-2S}=2.01\pm0.74$ meV. The main source of the uncertainty of the dispersion analysis is due to lack of quasielastic data at low energies and forward angles. We show that a targeted measurement of the deuteron electrodesintegration in the kinematics of upcoming experiments A1 and MESA at Mainz can help quenching this uncertainty significantly.
author:
- 'Carl E. Carlson'
- Mikhail Gorchtein
- Marc Vanderhaeghen
title: Nuclear structure contribution to the Lamb shift in muonic deuterium
---

Introduction
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The proton radius puzzle—that the proton radius obtained from the Lamb shift in muonic hydrogen [@pohlmuH; @antogninimuH] is different from what should be the same radius obtained from data involving electrons [@Mohr:2012tt; @bernauer]—has attracted much attention in 