Nuclear structure contribution to the Lamb shift in muonic deuterium

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 $\Delta E_{2P-2S}=2.01\pm 0.74$ 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 quenching this uncertainty significantly.

10 pages, 11 figures, 4 tables; acknowledgements and references updated; accepted to publication in Phys. Rev. A

References in corpus (8)

• High-precision determination of the electric and magnetic form factors of the proton
• The size of the proton - closing in on the radius puzzle
• Muonic hydrogen and MeV forces
• New Parity-Violating Muonic Forces
• Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory
• Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron Resonance Region Transverse Cross Sections
• Nuclear polarization corrections in the mu-4He+ Lamb shift
• Nuclear Polarization Corrections to mu-d Atoms in Zero-Range Approximation

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