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.
Highlights
A tantalizing discrepancy of 3–4 standard deviations between the experiment [1] and the standard model (SM) prediction of the muon anomalous magnetic moment aμ = (g − 2)μ/2 triggers advents of the new measurements [2, 3] concurrent with progresses on the SM calculation
As the SM uncertainty is dominated by hadronic contributions in hadronic vacuum polarization (HVP) and hadronic light-by-light (HLbL) scattering topologies, dedicated efforts have been put both into lattice QCD [4,5,6,7,8,9,10,11,12,13] and dispersion theory [14,15,16,17,18,19,20,21,22,23] beyond hadronic modelings
In view of a downward shift of 0.13 MeV and an upward shift of 0.06 MeV for the mass and width of the ω, this analysis solidifies the tension with the vacuum polarization (VP)-subtracted ω mass extracted from the 2π channel [30]
Summary
The leading hadronic contribution, HVP, can be evaluated using e+e− → hadrons cross section data as input into a dispersion integral [24, 25]. For low-multiplicity channels like 2π, a reconstruction of global fit functions from analyticity, unitarity, and low-energy theorems make it possible to confront the data with constraints from QCD. Such an investigation has been recently completed for the 2π channel below 1 GeV [30]
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