Compatibility between $e^+e^-$ and $\tau$ decay data in the di-pion channel and implications for $a_\mu^\mathrm{SM}$ and CVC tests

TL;DR

This paper reassesses isospin-breaking corrections linking $e^+e^-$ and tau decay data in the di-pion channel, confirming uncertainties are manageable for precise muon g-2 predictions and CVC tests.

Contribution

It provides a refined analysis of isospin-breaking corrections, validating the use of tau data for accurate muon anomalous magnetic moment calculations.

Findings

Uncertainty in isospin-breaking corrections is well-controlled.

Tau data can reliably predict the leading hadronic contribution to $a_$.

Supports precision tests of conserved vector current (CVC).

Abstract

We have revisited the isospin-breaking corrections relating $\sigma(e^+e^-\to\pi^+\pi^-)$ and $\Gamma(\tau^-\to\pi^-\pi^0\nu_\tau)$. We confirm that the associated uncertainty is under control, so that tau data can also be used to predict accurately the leading hadronic contribution to the muon anomalous magnetic moment and precision conserved vector current tests can be carried out.