New <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>-based evaluation of the hadronic contribution to the vacuum polarization piece of the muon anomalous magnetic moment
Jael Miranda, Pablo Roig
Abstract
We revisit the isospin-breaking and electromagnetic corrections to the decay ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, 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 appearing at the next order. As a result, we improve agreement between the two-pion tau decay and ${e}^{+}{e}^{\ensuremath{-}}$ data and reduce the discrepancy between experiment and the Standard Model prediction of ${a}_{\ensuremath{\mu}}$ (using $\ensuremath{\tau}$ input) to the approximately $2\ensuremath{\sigma}$ level.