Tenth-order electron anomalous magnetic moment: Contribution of diagrams without closed lepton loops

Abstract

This paper presents a detailed account of evaluation of the electron anomalous magnetic moment a e which arises from the gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte-Carlo integration routine VEGAS is 8.726 (336)(α/π) 5 , which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795 (336)(α/π) 5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to a e (theory) = 1 159 652 181.643 (25)(23)(16)(763) × 10 −12 , where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from α −1 = 137.035 999 049 (90), the fine-structure constant derived from the rubidium recoil measurement. Thus, a e (experiment) − a e (theory) = −0.91 (0.82) × 10 −12 .Assuming the validity of the standard model, we obtain the fine-structure constant α −1 (a e ) = 137.035 999 1570 (29)(27)(18)(331), where uncertainties are from the eighth-order term, tenthorder term, hadronic and electroweak terms, and the measurement of a e . This is the most precise value of α available at present and provides a stringent constraint on possible theories beyond the standard model.

The coannihilation codex

“…The anomaly in the gyromagnetic ratio of the electron, a e ≡ (g−2) e /2, is conventionally used to determine the fine-structure constant α [215,216]. However, as pointed out in ref.…”

Leading-order hadronic contributions to the electron and tau anomalous magnetic moments

“…This leads to the electron magnetic moment being one of the most precisely determined quantities in nature. The difference between the latest experimental [2] and SM values [3,4] This constitutes one of the cornerstone results for quantum field theories to be recognised as the correct mechanism for a e-mail: florian.burger@physik.hu-berlin.de b e-mail: karl.jansen@desy.de c e-mail: marcus.petschlies@hiskp.uni-bonn.de d e-mail: grit.hotzel@physik.hu-berlin.de describing particle interactions. The very good agreement of the electron magnetic moment between experiment and SM calculations is not matched by the muon anomalous magnetic moment.…”

Next-to-leading order prediction for the decay μ → e e + e − ν ν ¯ $$ \mu \to e\kern0.22em \left({e}^{+}{e}^{-}\right)\;\nu \kern0.2em \overline{\nu} $$

“…2) where G F = 1.166 378 7(6) × 10 −5 GeV −2 [34] is the Fermi constant, defined from the muon lifetime, and α = 1/137.035 999 157 (33) is the fine-structure constant [35,36]. Calling m µ and m e the masses of the muon and the electron (neutrinos are considered to be massless), we define the ratio r = m e /m µ .…”