Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil
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 (μH), muonic deuterium (μD), the muonic 3He ion (denoted here as μ 3He +), as well as in the muonic 4He ion (μ 4He +). 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 α(Zα) 5 μ 3ln(Zα) / (m μ m N ) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.
U. D. Jentschura and B. J. Wundt, "Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil," European Physical Journal D, vol. 65, no. 3, pp. 357-366, Springer New York, Dec 2011.
The definitive version is available at https://doi.org/10.1140/epjd/e2011-20338-2
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