Semi-analytic approach to higher-order corrections in simple muonic bound systems: Vacuum polarization, self-energy and radiative-recoil
Department of Physics, Missouri University of Science and
2 Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
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Published online: 22 November 2011
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 ion (denoted here as μ 3He+), as well as in the muonic 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)5μ3ln(Zα) / (mμmN) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2011