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

Abstract

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 Padé 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 Padé 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.

arXiv comment12 pages, 1 figure, title and abstract changed

References in corpus (4)

• Radiative Corrections to the Muonium Hyperfine Structure. I. The ${\alpha }^2(Z\alpha )$ Correction
• Heavy Quark Current Correlators to O(α_s^2)
• Mass Corrections to the Vector Current Correlator
• Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen

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