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

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).

Comments: 62 pages, 20 figures, 12 tables. Accepted for publication in PRD. Minor changes and a few references added