Abstract
Abstract The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is re-analyzed in both the unitary gauge and the ’t Hooft–Feynman gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the ’t Hooft–Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_\mu^2/m_Z^2$. The results are compared with those obtained by the asymptotic expansion method.
Highlights
A discrepancy of 3.3σ still remains between experiment and the standard model (SM) prediction for the muon anomalous magnetic moment aμ ≡/2 [1]
In Ref. [7], for a concrete illustration of the asymptotic expansion method, Czarnecki and Marciano, coauthors of Refs.[2,3], showed in detail the calculation of the diagrams with top quark triangle loops connected to the muon line by a photon and a Z boson
Study of a specific subset of the two-loop electroweak contributions shown in Fig. 1 is interesting due to the fact that its fermionic triangle loop subdiagrams have the Adler–Bell–Jackiw
Summary
A discrepancy of 3.3σ still remains between experiment and the standard model (SM) prediction for the muon anomalous magnetic moment aμ ≡ (gμ − 2)/2 [1]. [7], for a concrete illustration of the asymptotic expansion method, Czarnecki and Marciano, coauthors of Refs.[2,3], showed in detail the calculation of the diagrams with top quark triangle loops connected to the muon line by a photon and a Z boson. [8] and Rosenberg [9] for the fermionic triangle subdiagrams, which reads in terms of the momenta shown in Fig. 1 as fermionic triangle subdiagrams and found that the loop contributions of leptons, i.e., e, μ and τ , were enhanced by large logarithms of the form ln(mZ /mμ ) or ln(mZ /mτ ).
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