Semi-analytic approach to higher-order corrections in simple muonic bound systems

Vacuum polarization, self-energy and radiative-recoil

U. Jentschura, B. J. Wundt

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)357-366
Number of pages10
JournalEuropean Physical Journal D
Volume65
Issue number3
DOIs
Publication statusPublished - Dec 2011

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vacuum systems
polarization
vacuum
energy
shift
hydrogen
logarithms
mass ratios
deuterium
ions
perturbation
nuclei

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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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.",
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T2 - Vacuum polarization, self-energy and radiative-recoil

AU - Jentschura, U.

AU - Wundt, B. J.

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N2 - 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.

AB - 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.

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