The discrepancy between τ and e + e − spectral functions revisited and the consequences for the muon magnetic anomaly

Abstract

We revisit the procedure for comparing the ππ spectral function measured in τ decays to that obtained in e⁺e⁻ annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input and find improved agreement between the τ⁻→π⁻π⁰ν_τ branching fraction measurement and its prediction using the isospin-breaking-corrected e⁺e⁻→π⁺π⁻ spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g−2 using e⁺e⁻ and τ data with the new corrections and find a reduced difference between the two evaluations. The new tau-based estimate of the muon magnetic anomaly is found to be 1.9 standard deviations lower than the direct measurement.