Semianalytic approach to higherorder corrections in simple muonic bound systems: Vacuum polarization, selfenergy and radiativerecoil
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 ^{3}He^{+}), as well as in the muonic {^4He} 4 He ion ( μ ^{4}He^{+}). Here, we choose a semianalytic approach and evaluate a number of higherorder corrections to vacuum polarization (VP) semianalytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semianalytic results for the secondorder correction, and for the relativistic correction to VP. The selfenergy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiativerecoil correction to the 2S2P Lamb shift of order α( Zα)^{5} μ ^{3}ln( Zα) / ( m _{ μ } m _{ N }) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.
 Publication:

European Physical Journal D
 Pub Date:
 December 2011
 DOI:
 10.1140/epjd/e2011203382
 arXiv:
 arXiv:1112.0556
 Bibcode:
 2011EPJD...65..357J
 Keywords:

 Physics  Atomic Physics;
 High Energy Physics  Phenomenology
 EPrint:
 10 pages