Three-pion contribution to hadronic vacuum polarization

Understand

We address the contribution of the $3\pi$ channel to hadronic vacuum polarization (HVP) using a dispersive representation of the $e^+e^-\to 3\pi$ 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 $\gamma^*\to3\pi$ amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various $e^+e^-\to 3\pi$ data sets.