Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil

Abstract

The current discrepancy of theory and experiment observed recently in muonic hydrogen necessitates a reinvestigation of all corrections to contribute to the Lamb shift in muonic hydrogen muH, muonic deuterium muD, the muonic 3He ion, as well as in the muonic 4He ion. Here, we choose a semi-analytic approach and evaluate a number of higher-order corrections to vacuum polarization (VP) semi-analytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semi-analytic results for the second-order correction, and for the relativistic correction to VP. The self-energy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiative-recoil correction to the 2S-2P Lamb shift of order alpha (Zalpha)^5 mu^3 ln(Zalpha)/(m_mu m_N) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.

10 pages; svjour style; to appear in the European Physical Journal D

References in corpus (3)

• Production of the Smallest QED Atom: True Muonium (mu^+ mu^-)
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Relativistic Reduced-Mass and Recoil Corrections to Vacuum Polarization in Muonic Hydrogen, Muonic Deuterium and Muonic Helium Ions

Cited by in corpus (13)

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• Theory of the n=2 levels in muonic deuterium
• Non-perturbative evaluation of some QED contributions to the muonic hydrogen $\mathbf{n}=2$ Lamb shift and hyperfine structure
• Comprehensive theory of the Lamb shift in light muonic atoms
• Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift
• The Lamb shift in muonic hydrogen and the proton radius from effective field theories
• The ${\alpha }^2(Z\alpha {)}^{4}m$ contributions to the Lamb shift and the fine structure in light muonic atoms
• Lamb shift in muonic ions of lithium, beryllium and boron
• Theory of the n=2 levels in muonic helium-3 ions
• Why three-body physics do not solve the proton radius puzzle
• Model independent determination of the muonic hydrogen Lamb shift and proton radius
• Irreducible Three-Loop Vacuum-Polarization Correction in Muonic Bound Systems
• Reexamination of vacuum-polarization corrections to the self-energy in muonic bound systems