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 ( μH), muonic deuterium ( μD), the muonic {^3He} 3 He ion (denoted here as μ 3He+), as well as in the muonic {^4He} 4 He 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.
- Publication:
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European Physical Journal D
- Pub Date:
- December 2011
- DOI:
- 10.1140/epjd/e2011-20338-2
- arXiv:
- arXiv:1112.0556
- Bibcode:
- 2011EPJD...65..357J
- Keywords:
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- Physics - Atomic Physics;
- High Energy Physics - Phenomenology
- E-Print:
- 10 pages