Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-06-20
Phys.Rev.D78:053005,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
27 pages
Scientific paper
10.1103/PhysRevD.78.053005
We have evaluated the contribution to the anomalous magnetic moment of the electron from six tenth-order Feynman diagrams which contain eighth-order vacuum-polarization function formed by two light-by-light scattering diagrams connected by three photons. The integrals are constructed by two different methods. In the first method the subtractive counter terms are used to deal with ultraviolet (UV) singularities together with the requirement of gauge-invariance. In the second method, the Ward-Takahashi identity is applied to the light-by-light scattering amplitudes to eliminate UV singularities. Numerical evaluation confirms that the two methods are consistent with each other within their numerical uncertainties. Combining the two results statistically and adding small contribution from the muons and/or tau leptons, we obtain $ 0.000 399 9 (18) (\alpha/\pi)^5$. We also evaluated the contribution to the muon $g-2$ from the same set of diagrams and found $ -1.263 44 (14) (\alpha/\pi)^5$.
Aoyama Takahiro
Hayakawa Masahiko
Kinoshita Takahiro
Nio Makiko
Watanabe Naoki
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