Thomas Blum
University of Connecticut

Eduardo de Rafael

David Hertzog
University of Washington

Fred Jegerlehner
DESY Zeuten

Lee Roberts
Boston University

Arkady Vainshtein
University of Minnesota

Program Coordinator:
Inge Dolan
(206) 685-4286


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INT Workshop on
The Hadronic Light-by-Light Contribution to the Muon Anomaly

February 28 - March 4, 2011

There is a registration fee of $80 to attend this workshop to cover the expenses for catering and a workshop dinner.

The Workshop Plan:

The workshop will bring together both theorists and experimentalists to focus on one of the outstanding theoretical issues in interpreting the muon anomalous magnetic moment:

  1. Can agreement be reached on the individual and combined theoretical contributions to the hadronic light-by-light (HLbL) contribution to the muon anomalous magnetic moment, aμ, based on QCD-inspired models?
  2. Can the lattice approach lead to a result having sufficient precision to check the models or to independently establish the HLbL value?
  3. Which data that can be obtained at Frascati, and at other facilities, are essential to constrain the theoretical calculations and what theoretical developments are required to connect data to model predictions?
We envision summary talks and working sessions on all topics and will produce a Review style article, signed by the contributors. The goal of the group is not to produce "one number" at this time, but to summarize the state of the art and to design the path to a future meeting, that would have a "one number, one uncertainty" goal as its mission.


The muon anomalous magnetic moment can be calculated and measured to very high precision. Comparison of experiment to theory has been, and will continue to be, a very sensitive test of New Physics. The present uncertainty on the Standard Model contribution is δαμ(SM) = 49 × 10-11. The largest error is an experiment-driven leading-order hadronic term, which has been reduced as higher-precision e+e- → hadrons data have become available, particularly in the low-energy region from threshold to 1.4 GeV. The next largest uncertainty is associated with hadronic light-by-light (HLbL) scattering; the error quoted ranges from ± 26 × 10-11 to ± 40 × 10-11.

The advent of a next-generation muon g-2 experiment at Fermilab, with a goal of δαμ(Expt.) ~ 16 × 10-11 demands improved SM evaluations to fully interpret the measurement. While a program exists worldwide to expand the quality and quantity of the data entering the leading-order hadronic determination, only a broad theory effort can work to reduce the uncertainty on HLbL. It is particularly useful to develop a community of theorists that work together on this problem.

Three thrusts of the Workshop:

Models. The hadronic light-by-light contribution cannot at present be determined from data, but rather must be calculated using hadronic models that correctly reproduce the properties of QCD. A number of authors have calculated portions of this contribution, and recently a synthesis of all contributions has become available from Prades, de Rafael and Vainshtein (PdRV). Additional work on this contribution is underway. We aim to fold the input from all involved groups to develop a combined effort from theorists along the lines started in Bijnens-Pallante-Prades, Knecht-Nyffeler-Perrottet-de Rafael, Melnikov-Vainshtein. The aim is an accuracy of 15% or better. The PdRV paper was only the beginning of this process.

Lattice. In principle, the HLbL amplitude is calculable in QCD using the lattice regularization. Recent efforts, still preliminary, have taken two independent tracks: computation of the entire amplitude using QCD+QED on the lattice; and, computation of the required hadronic four-point correlation function in QCD alone, which is then used as an input to perturbative QED to obtain the contribution to aμ. Both have advantages and drawbacks. A third effort has begun to calculate the two-photon form factors that will also be measured at Frascati. Besides establishing the long term viability of independent lattice calculations of the HLbL contribution to aμ, attendees will also address how to best help test and establish the validity of the current model calculations and their systematic errors.

Data. Unlike the dominant lowest-order hadronic contribution, there are few data on γ*γ* → hadrons to constrain the HLbL model calculations. A number of diagrams contribute: pseudoscalar, pseudovector, scalar, dressed pion loop, etc. which have been calculated by various groups. An interesting development is the new experimental two-photon physics facility under construction at Frascati. This will provide some data on the elusive process γ*γ* → hadrons and provide experimental input to the HLbL evaluations. Theoretical effort will also be devoted to connecting these data to the model calculation predictions and exploring the usefulness of additional data of this type at the higher energies accessible at BES III, BaBar and Belle.