Hadronic vacuum polarization (HVP) and hadronic light-by-light scattering (HLbL)
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The International Theory Initiative was founded to bring together the worldwide community of theoretical and experimental physicists working on the determination of the Standard Model value of the muon magnetic anomaly $a_\mu$. The goal is to produce a single consensus theoretical value of $a_\mu$ to be compared with the experimental value obtained by the Fermilab and J-PARC experiments.

The coordination and leadership of this effort is provided by the Steering Committee. Its role is to organize the international workshops and to coordinate the writing of the Whitepaper and its updates. The Steering Committee’s membership draws upon expertise from all of the different theoretical areas and experimental efforts that contribute to the Standard Model value of $a_\mu$. While it is not intended to represent each individual theoretical collaboration, it has the responsibility to ensure that the entire international community working on the various Standard Model contributions to $a_\mu$ is included in the workshops and in the preparation of the Whitepaper and its updates. The current members of the Steering Committee$^*$ are:

  • Gilberto Colangelo (University of Bern)
  • Michel Davier (University of Paris-Saclay and CNRS, Orsay) co-chair
  • Aida X. El-Khadra (University of Illinois) chair
  • Martin Hoferichter (University of Bern)
  • Christoph Lehner (University of Regensburg) co-chair
  • Laurent Lellouch (Marseille)
  • Tsutomu Mibe (KEK)
  • Lee Roberts (Boston University)
  • Thomas Teubner (University of Liverpool)
  • Hartmut Wittig (University of Mainz)
$^*$Simon Eidelman, a founding member of the Theory Initiative, served on the Steering Committee until he passed away in June 2021.


The anomalous magnetic moment of the muon has, for over twenty ten years now, provided an enduring hint for new physics, in the form of tantalizing tensions between Standard Model (SM) theory and experiment. It is currently measured to a precision of about 0.35 ppm, commensurate with the theoretical uncertainty in its SM prediction. The E989 experiment at Fermilab started running in 2018, and plans to reduce the experimental uncertainty by a factor of four. The E34 experiment at J-PARC plans to start its first run in 2025.

However, without improvements on the theoretical side, the discovery potential of these efforts may be limited. To leverage the experimental efforts at Fermilab and J-PARC and hence unambiguously discover whether or not new-physics effects contribute to this quantity, the theory errors must be reduced to the same level as the experimental uncertainties. In the SM, $a_\mu$ is calculated from a perturbative expansion in the fine-structure constant $\alpha$, which starts at $O(\alpha)$ with the Schwinger term and has been carried out up to and including $O(\alpha^5)$. Its uncertainty, dominated by the unknown $O(\alpha^6)$ term, is completely negligible. Electroweak corrections have been evaluated at full two-loop order, with dominant three-loop effects estimated from the renormalization group. Their uncertainty, mainly arising from nonperturbative effects in two-loop diagrams involving the light quarks, is still negligible compared to the experimental precision. The dominant sources of theory error are by far the hadronic contributions, in particular, the $O(\alpha^2)$ HVP term and the $O(\alpha^3)$ HLbL term. There are a number of complementary theoretical efforts underway to better understand and quantify the hadronic corrections, including using dispersive methods, lattice QCD, and effective field theories, as well as a number of different experimental efforts to provide inputs to dispersive, data- driven evaluations.