Accuracy of Calculations Involving $α^3$ Vacuum-Polarization Diagrams: Muonic Hydrogen Lamb Shift and Muon $g-2$

Details Accuracy of Calculations Involving $α^3$ Vacuum-Polarization Diagrams: Muonic Hydrogen Lamb Shift and Muon $g-2$ Accuracy of Calculations Involving $α^3$ Vacuum-Polarization Diagrams: Muonic Hydrogen Lamb Shift and Muon $g-2$

1998-12-21

arxiv.org/abs/hep-ph/9812443v4

Phys.Rev. D60 (1999) 053008

Physics

High Energy Physics

High Energy Physics - Phenomenology

12 pages, 1 figure, title and abstract changed

Scientific paper

10.1103/PhysRevD.60.053008

The contribution of the $\alpha^3$ single electron-loop vacuum-polarization diagrams to the Lamb shift of the muonic hydrogen has been evaluated recently by two independent methods. One uses the exact parametric representation of the vacuum-polarization function while the other relies on the Pad\'{e} approximation method. High precision of these values offers an opportunity to examine the reliability of the Monte-Carlo integration as well as that of the Pad\'{e} method. Our examination covers both muonic hydrogen atom and muon $g-2$. We tested them further for the cases involving two-loop vacuum polarization, where an exact analytic result is known. Our analysis justifies the result for the Lamb shift of the muonic hydrogen and also resolves the long-standing discrepancy between two previous evaluations of the muon $g-2$ value.

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