Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accuracy of Calculations Involving $\alpha^3$ Vacuum-Polarization
  Diagrams: Muonic Hydrogen Lamb Shift and Muon $g-2$   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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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th