Nuclear-structure contribution to the Lamb shift in muonic deuterium

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 T₁(ν,Q²) is related to the deuteron magnetic polarizability β(Q²). Based on phenomenological information, we obtain for the Lamb shift ΔE_2P-2S=2.01±0.74 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 in quenching this uncertainty significantly.