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Published August 27, 2012 | Published
Journal Article Open

Hadronic light-by-light scattering and the pion polarizability


We compute the charged pion loop contribution to the light-by-light scattering amplitude for off-shell photons in chiral perturbation theory through next-to-leading order (NLO). We show that for small photon virtualities (k^2≪m^(2)_(π)) the NLO contributions are relatively more important due to an accidental numerical suppression of the LO terms. This behavior is consistent with previous calculations of the hadronic light-by-light contribution to the muon anomalous magnetic moment, a^(HLBL)_(μ), whose leading order value receives O(1) corrections from models incorporating some of the NLO physics. We also show that models employed thus far for the charged pion loop contribution to a^(HLBL)_(μ) are not fully consistent with low-momentum behavior implied by quantum chromodynamics, having omitted potentially significant contributions from the pion polarizability.

Additional Information

© 2012 American Physical Society. Received 17 January 2012; published 27 August 2012. We thank J. Bijnens, E. de Rafael, and A. Vainshtein for useful conversations and Mark B. Wise for discussions in the formulation of this project. The work is partially supported by U.S. Department of Energy contracts No. DE-FG02-92-ER40701 (K. T. E) and No. DE-FG02-08ER41531 (H. H. P. and M. J. R. M.) and the Wisconsin Alumni Research Foundation (H. H. P. and M. J. R. M.).

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Published - PhysRevD.86.037502.pdf


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