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Register a new userHadronic light-by-light scattering in the muon g-2: a new short-distance constraint on pion exchange
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Authors
Andreas Nyffeler
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We summarize our recent new evaluation of the pion-exchange contribution to hadronic light-by-light scattering in the muon g-2. We first derive a new short-distance constraint on the off-shell pion-photon-photon form factor at the external vertex in a_mu which relates the form factor to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints and obtain the new estimate a_{mu}(LbyL;pi^0) = (72 pm 12) x 10^{-11}. Updating our earlier results for the contributions from the exchanges of the eta and eta-prime using simple vector-meson dominance form factors, we get a_{mu}(LbyL; PS) = (99 pm 16) x 10^{-11} for the sum of all light pseudoscalars. Combined with available evaluations for the other contributions to hadronic light-by-light scattering this leads to the estimate a_{mu}(LbyL; had) = (116 pm 40) x 10^{-11}. The corresponding contributions to the anomalous magnetic moment of the electron are also given.
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Recently it was pointed out that for the evaluation of the numerically dominant pion-exchange contribution to the hadronic light-by-light scattering correction in the muon g-2, a fully off-shell pion-photon-photon form factor should be used. Following this proposal, we first derive a new short-distance constraint on the off-shell form factor which enters at the external vertex for the muon g-2 and show that it is related to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints. With a value for the magnetic susceptibility as estimated in the same large-N_C framework, we obtain the result a_{mu}(LbyL; pi^0) = (72 pm 12) x 10^{-11}. Updating our earlier results for the contributions from the exchanges of the eta and eta-prime using simple vector-meson dominance form factors, we obtain a_{mu}(LbyL; PS) = (99 pm 16) x 10^{-11} for the sum of all light pseudoscalars. Combined with available evaluations for the other contributions to hadronic light-by-light scattering this leads to the new estimate a_{mu}(LbyL; had) = (116 pm 40) x 10^{-11}.
We briefly review the current status of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. Based on various model calculations in the literature, we obtain the estimate a_{mu}^{HLbL} = (102 pm 39) x 10^{-11}. Recent developments including more model-independent approaches using dispersion relations and lattice QCD, that could lead to a more reliable estimate, are also discussed.
We review recent developments concerning the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. We first discuss why fully off-shell hadronic form factors should be used for the evaluation of this contribution to the g-2. We then reevaluate the numerically dominant pion-exchange contribution in the framework of large-N_C QCD, using an off-shell pion-photon-photon form factor which fulfills all QCD short-distance constraints, in particular, a new short-distance constraint on the off-shell form factor at the external vertex in g-2, which relates the form factor to the quark condensate magnetic susceptibility in QCD. Combined with available evaluations of the other contributions to hadronic light-by-light scattering this leads to the new result a_{mu}(LbyL; had) = (116 pm 40) x 10^{-11}, with a conservative error estimate in view of the many still unsolved problems. Some potential ways for further improvements are briefly discussed as well. For the electron we obtain the new estimate a_{e}(LbyL; had) = (3.9 pm 1.3) x 10^{-14}.
We give an update on the status of the hadronic light-by-light scattering contribution to the muon g-2. We review recent work by various groups, list some of the open problems and give an outlook on how to better control the uncertainty of this contribution. This is necessary in order to fully profit from planned future muon g-2 experiments to test the Standard Model. Despite some recent developments, we think that the estimate a_{mu}^{HLbL} = (116 pm 40) x 10^{-11} still gives a fair description of the current situation.
In this talk we review the recent progress on the numerical determination of the Hadronic Light-by-Light contribution to the anomalous magnetic moment of the muon and we discuss the role of experimental data on the accuracy of its determination. Special emphasis on the main contribution, the pseudoscalar piece, is made. Gathering recent progress in the light-by-light scattering contribution we consider $a_{mu}^{{mathrm{HLBL}}} = (12.1pm3.0)times10^{-10}$ as a good summary of the state-of-the-art calculations which still claims for a $4sigma$ deviation between theory and experiment for the $(g-2)_{mu}$.
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