Abstract
We compute the contributions to the electron and muon anomalous magnetic moment induced by heavy leptons up to four-loop order. Asymptotic expansion is applied to obtain three analytic expansion terms which show rapid convergence.
Highlights
Since decades the anomalous magnetic moments of electron and muon, ae and aμ, are used to perform precision tests of QED.1 in the case of the electron the experimental measurements and theoretical predictions have reached a precision which allows for the most precise extraction of the fine structure constant α
In the case of the muon this means that Feynman diagrams have to be considered which contain closed tau loops and both closed muon and tau loops are present for ae
It is based on asymptotic expansion [23] in the ratio of the light and heavy lepton mass, Ml and Mh, which leads to a factorization of the two-scale integrals into simpler ones with at most one mass scale
Summary
Since decades the anomalous magnetic moments of electron and muon, ae and aμ, are used to perform precision tests of QED. in the case of the electron the experimental measurements and theoretical predictions have reached a precision which allows for the most precise extraction of the fine structure constant α. In the case of the muon this means that Feynman diagrams have to be considered which contain closed tau loops and both closed muon and tau loops are present for ae Such contributions appear for the first time at two-loop order (cf Fig. 1) and have been computed in Refs. We want to cross-check these results using a different method which leads to analytic results for ae and aμ It is based on asymptotic expansion [23] in the ratio of the light and heavy lepton mass, Ml and Mh, which leads to a factorization of the two-scale integrals into simpler ones with at most one mass scale. From the parametric point of view the four-loop corrections induced by heavy leptons could be of the same order as the five-loop results obtained in Ref. In the Appendix we present results for the on-shell counterterms for the fine structure constant, the lepton mass and the lepton wave function
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