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

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 Standard Model contribution uncertainty is approximately 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 a small, higher-order hadronic loop, the hadronic light-by-light (HLbL) scattering contribution; the error is quoted aggressively at ± 26 × 10-11. The HLbL contribution must be calculated, and below we discuss the approaches used. The uncertainty quoted above is not presently agreed to by all of the experts working in the field, with others in the community preferring a value closer to δαμ(HLbL) ~ 40 × 10-11.

The advent of a next-generation muon g-2 experiment at Fermilab, with a goal of δαμ (Expt.) ~ 16 × 10-11 clearly demonstrates that the SM theory contributions must be improved 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 to work on this problem now.

The aim of our Workshop is to gather most of the leading participants, along with new faces, to start the process that will lead to an improved, and agreed on, value for HLbL in the timeline of the new g-2 experiment. The Workshop will be organized around three themes: Models, Lattice efforts, and Related Experimental Input. We propose a product outcome of a Review style article, signed by the contributors. The goal of the group is not to produce "1 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 "1 number, 1 uncertainty" goal as its mission.

Background on the HLbL situation. The hadronic light-by-light contribution to the muon anomaly is about 0.9 ppm of the anomaly. The present relative experimental error is ±0.54 ppm, and the proposed Fermilab experimental goal is ±0.14 ppm. Unlike the dominant lowest-order hadronic contribution, which can be determined from experimental data of e+e- → hadrons and a dispersion relation, 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. We expect theoretical effort to be devoted to connecting these data to the model calculation predictions. In principle, it might be worth encouraging additional data of this type at the higher energies accessible at BES III, BaBar and Belle.

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 g-2. 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 g-2, attendees will also address how to best help test and establish the validity of the current model calculations and their systematic errors.

The Workshop Plan: The workshop will bring together both theorists and experimentalists to focus on the outstanding issues:

  1. Can agreement be reached on the individual and combined theoretical contributions to the HLbL contribution, 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 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. The aim is to produce a review style summary article.