New $\tau$-based evaluation of the hadronic contribution to the vacuum polarization piece of the muon anomalous magnetic moment

TL;DR

This paper refines the calculation of the hadronic vacuum polarization contribution to the muon g-2 by improving the isospin-breaking corrections in tau decay data, leading to better agreement with e+e- data and the Standard Model.

Contribution

It extends a resonance chiral Lagrangian analysis by including next subleading terms, enhancing the precision of the tau decay input for muon g-2 calculations.

Findings

Improved agreement between tau decay and e+e- data.

Reduced discrepancy between experiment and SM prediction of muon g-2.

Enhanced accuracy in the hadronic vacuum polarization contribution.

Abstract

We revisit the isospin-breaking and electromagnetic corrections to the decay $\tau^-\to\pi^-\pi^0\nu_\tau$, which allow its use as input in the two-pion contribution to the (leading order) hadronic vacuum polarization part of the muon anomalous magnetic moment. We extend a previous resonance chiral Lagrangian analysis, which included those operators saturating the next-to-leading order chiral low energy constants, by including the contributions of the next subleading terms. As a result, we improve agreement between the two-pion tau decay and $e^+e^-$ data and reduce the discrepancy between experiment and the SM prediction of $a_\mu$ (using $\tau$ input).