Exact two-loop vacuum polarization correction to the Lamb shift in hydrogenlike ions

1998 ◽  
Vol 1 (2) ◽  
pp. 177-185 ◽  
Author(s):  
G. Plunien ◽  
T. Beier ◽  
Gerhard Soff ◽  
H. Persson
Keyword(s):  
Lamb Shift ◽  
Vacuum Polarization ◽  
Polarization Correction

The Vacuum Polarization Correction in Muonic Atoms

1975 ◽  
pp. 191-208 ◽  
Author(s):  
R. Engfer ◽  
J. L. Vuilleumier ◽  
E. Borie
Keyword(s):  
Vacuum Polarization ◽  
Muonic Atoms ◽  
Polarization Correction

scholarly journals Hadronic vacuum polarization and vector-meson resonance parameters from $$\varvec{e^+e^-\rightarrow \pi ^0\gamma }$$

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Bai-Long Hoid ◽  
Martin Hoferichter ◽  
Bastian Kubis
Keyword(s):  
Transition Form Factor ◽  
Vacuum Polarization ◽  
Transition Form ◽  
Isospin Breaking ◽  
Meson Resonance ◽  
Resonance Parameters ◽  
Polarization Correction ◽  
Dispersive Representation ◽  
The Masses ◽  
Good Agreement

AbstractWe study the reaction $$e^+e^-\rightarrow \pi ^0\gamma $$ e + e - → π 0 γ based on a dispersive representation of the underlying $$\pi ^0\rightarrow \gamma \gamma ^*$$ π 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of the $$\pi ^0\gamma $$ π 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find $$a_\mu ^{\pi ^0\gamma }\big |_{\le 1.35\,\text {GeV}}=43.8(6)\times 10^{-11}$$ a μ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of $$\omega $$ ω and $$\phi $$ ϕ . We observe good agreement with the $$e^+e^-\rightarrow 3\pi $$ e + e - → 3 π channel, explaining a previous tension in the $$\omega $$ ω mass between $$\pi ^0\gamma $$ π 0 γ and $$3\pi $$ 3 π by an unphysical phase in the fit function. Combining both channels we find $${\bar{M}}_\omega =782.736(24)\,\text {MeV}$$ M ¯ ω = 782.736 ( 24 ) MeV and $${\bar{M}}_\phi =1019.457(20)\,\text {MeV}$$ M ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The $$\phi $$ ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from the $${\bar{K}} K$$ K ¯ K channel, demonstrating consistency with $$3\pi $$ 3 π and $$\pi ^0\gamma $$ π 0 γ . For the $$\omega $$ ω mass, our result is consistent but more precise, exacerbating tensions with the $$\omega $$ ω mass extracted via isospin-breaking effects from the $$2\pi $$ 2 π channel.

Vacuum polarization in muonic and exotic atoms: the Lamb shift at medium Z and high n

2007 ◽  
Vol 85 (5) ◽  
pp. 551-561 ◽  
Author(s):  
E Yu. Korzinin ◽  
V G Ivanov ◽  
S G Karshenboim
Keyword(s):  
Quantum Number ◽  
Lamb Shift ◽  
Vacuum Polarization ◽  
Principal Quantum Number ◽  
Energy Levels ◽  
Exotic Atoms ◽  
Atomic States

We present new results on various asymptotics for the Uehling contribution to the energy levels in atomic states in hydrogen-like atoms that have a principal quantum number n with a high value. The results may be applied to conventional atoms (with an orbiting electron) as well as to muonic, pionic, antiprotonic, and other exotic atoms.PACS Nos.: 36.10.Gv, 31.30.Jv

scholarly journals Hadronic vacuum polarization and the Lamb shift

1999 ◽  
Vol 59 (5) ◽  
pp. 4061-4063 ◽  
Author(s):  
J. L. Friar ◽  
J. Martorell ◽  
D. W. L. Sprung
Keyword(s):  
Lamb Shift ◽  
Vacuum Polarization

Second-order self-energy–vacuum-polarization contributions to the Lamb shift in highly charged few-electron ions

1996 ◽  
Vol 54 (4) ◽  
pp. 2805-2813 ◽  
Author(s):  
Hans Persson ◽  
Ingvar Lindgren ◽  
Leonti N. Labzowsky ◽  
Günter Plunien ◽  
Thomas Beier ◽  
...  
Keyword(s):  
Lamb Shift ◽  
Vacuum Polarization ◽  
Second Order ◽  
Self Energy

scholarly journals Hadronic vacuum-polarization contribution to various QED observables

2021 ◽  
Vol 75 (2) ◽  
Author(s):  
Savely G. Karshenboim ◽  
Valery A. Shelyuto
Keyword(s):  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Vacuum Polarization ◽  
Muonic Hydrogen ◽  
New Physics ◽  
Order Effects ◽  
Indirect Determination ◽  
Standard Data ◽  
Conservative Estimation

Abstract Due to precision tests of quantum electrodynamics (QED), determination of accurate values of fundamental constants, and constraints on new physics, it is important in a consistent way to evaluate a number of QED observables such as the Lamb shift in hydrogen-like atomic systems. Even in a pure leptonic case, those QED variables are in fact not pure QED ones since hadronic effects are involved through intermediate states while accounting for higher-order effects. One of them is hadronic vacuum polarization (hVP). Complex evaluations often involve a number of QED quantities, for which treatment of hVP is not consistent. The highest accuracy for a calculation of the hVP term is required for the anomalous magnetic moment of a muon. However, a standard data-driven treatment of hVP, based on a dispersion integration of experimental data on electron-positron annihilation to hadrons and some other phenomena, leads to a contradiction with the experimental value of $$a_\mu $$ a μ . This experimental value can be considered as an indirect determination of the hVP contribution to $$a_\mu $$ a μ and the scatter of theory and experiment allows one to obtain a conservative estimation of the related hVP contribution. In this paper, we derive exact and approximate relations between the leading-order (LO) hVP contributions to various observables. Using those relations, we obtain for them a consistent set of the results, based on the scatter of $$a_\mu $$ a μ values. While calculating the LO hVP term, we have to remember that next-to-LO (NLO) hVP corrections are often comparable with the uncertainty of the LO term. Special attention is payed to hVP contribution to simple atoms. In particular, we discuss the NLO contribution to the Lamb shift in ordinary and muonic hydrogen and other two-body atoms for $$Z\le 10$$ Z ≤ 10 . We also consider the NLO contribution of the muonic vacuum polarization to the Lamb shift in hydrogen-like atoms. With the $$a_\mu $$ a μ puzzle unresolved, one may still require present-days values of the hVP contributions to various observable for comparison to experiment etc. the presence of contradicting values and a lack of consistency means an additional uncertainty for $$a_\mu $$ a μ and for key contributions to it, including the LO hVP one. We present here an estimation of such a propagated uncertainty in hVP contributions to different QED observables and recommend a consistent set of the related LO hVP contributions. Graphic Abstract

Coulomb line vacuum polarization corrections to Lamb shift of order α2(Zα)5m

1992 ◽  
Vol 294 (1) ◽  
pp. 115-119 ◽  
Author(s):  
Michael I. Eides ◽  
Howard Grotch ◽  
David A. Owen
Keyword(s):  
Lamb Shift ◽  
Vacuum Polarization ◽  
Line Vacuum
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