Three-pion contribution to hadronic vacuum polarization

We address the contribution of the 3 pi channel to hadronic vacuum polarization (HVP) using a dispersive representation of the e(+)e(-) -> 3 pi amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon (g - 2)(mu), both to its absolute value and uncertainty. It is largely dominated by the narrow resonances omega and phi, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for (g - 2)(mu) an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying gamma* -> 3 pi amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various e(+)e(-) -> 3 pi data sets. Overall, we obtain a(mu)(3 pi)vertical bar(<= 1.8 GeV) = 46.2(6)(6) x 10(-10) as our best estimate for the total 3 pi contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the 2 pi channel below 1 GeV, this covers nearly 80% of the total HVP contribution, leading to a(mu)(HVP) = 692.3(3.3) x 10(-10) when the remainder is taken from the literature, and thus reaffirming the (g-2)(mu) anomaly at the level of at least 3.4 sigma. As side products, we find for the vacuum-polarization-subtracted masses M-omega = 782.63(3)(1) MeV and M-phi = 1019.20(2)(1) MeV, confirming the tension to the omega mass as extracted from the 2 pi channel.