Leading-order hadronic contribution to the electron and muon g − 2

¹ Deutsches Elektronen–Synchrotron (DESY), Platanenallee 6, D–15738 Zeuthen, Germany
² Humboldt–Universität zu Berlin, Institut für Physik, Newtonstrasse 15, D–12489 Berlin, Germany

^a e-mail: fjeger@physik.hu-berlin.de

Published online: 26 April 2016

Abstract

I present a new data driven update of the hadronic vacuum polarization effects for the muon and the electron g − 2. For the leading order contributions I find a_μ^had(1) = (688.57 ± 4.28) [688.91 ± 3.52] × 10⁻¹⁰ based on e⁺e⁻ data [incl. τ data], a_μ^had(2) = (− 9.92 ± 0.10) × 10⁻¹⁰ (NLO) and a_μ^had(3) = (1.23 ± 0.01) × 10⁻¹⁰ (NNLO) for the muon, and a_e^had(1) = (185.11 ± 1.24) × 10⁻¹⁴ (LO), a_e^had(2) = (−22.15 ± 0.16) × 10⁻¹⁴ (NLO) and a_e^had(3) = (−2.80 ± 0.02) × 10⁻¹⁴ (NNLO) for the electron. A problem with vacuum polarization undressing of cross-sections (time-like region) is addressed. I also add a comment on properly including axial mesons in the hadronic light-by-light scattering contribution. My estimate here reads a_μ[a₁, f′₁, f₁] ∼ (7.51 ± 2.71) × 10⁻¹¹. With these updates a_μ^exp – a_μ^the = (31.0 ± 8.2) × 10⁻¹⁰ a 3.8σ deviation, while a_e^exp – a_e^the = (−1.14 ± 08.2) × 10⁻¹² shows no significat deviation.