Isospin breaking in the relation between the τ⁻ → ντ π⁻π⁰ and e⁺e⁻ → π⁺π⁻ versions of |Fπ (s)|² and implications for (g − 2)μ

Abstract

We investigate two points related to existing treatments of isospin-breaking corrections to the conserved vector current relation between σ[e+e-→π+π-] and dΓ[τ-→ντπ-π0]/ds. Implications for the value of the hadronic contribution to aμ=(g-2)μ/2 based on those analyses incorporating hadronic τ decay data are also considered. We conclude that the uncertainty on the isospin-breaking correction which must be applied to the τ decay data should be significantly increased, and that the central value of the ρ-ω mixing contribution to this correction may be significantly smaller than indicated by the present standard determination. Such a shift would contribute to reducing the discrepancy between the τ- and electroproduction-based determinations of the leading order hadronic contribution to aμ.