Hadronic vacuum polarization: three-pion channel

Abstract

The 3π-channel contribution to hadronic vacuum polarization (HVP) in the anomalous magnetic moment of the muon (g−2)µ is examined based on a dispersive representation of the γ* → 3π amplitude. This decay amplitude is reconstructed from dispersion relations, fulfilling the low-energy theorem of QCD. The global fit function is applied to the data sets of the 3π channel below 1.8 GeV, which constitutes the secondlargest exclusive contribution to HVP and its uncertainty. The dominant ωand φ-peak regions in the e+e− → 3π cross section as well as the non-resonant regions are precisely described to obtain our best estimate. The final result, $ a_\mu ^{3\pi }\left| { \le 1.8\,{\rm{GeV}}\,{\rm{ = }}\,{\rm{46}}{\rm{.2(6)(6)}} \times {\rm{1}}{{\rm{0}}^{ - 10}}} \right. $, reduces the model dependence owing to the fundamental principles of analyticity and unitarity and provides a cross check for the compatibility of the different e+e− → 3π data sets. A combination of the current analysis and the recent similar treatment of the 2π channel yields a dispersive determination of almost 80% of the entire HVP contribution. Our analysis reaffirms the muon anomaly at 3.4σ level, when the rest of the contributions is taken from the literature.