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

Author

Ulrich D. Jentschura, Missouri University of Science and TechnologyFollow
Benedikt J. Wundt

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 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.

Recommended Citation

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

Department(s)

Physics

International Standard Serial Number (ISSN)

1434-6060

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2011 Springer New York, All rights reserved.

Publication Date

01 Dec 2011