Isospin breaking corrections in $2\pi$ production in tau decays and $e^+e^-$ annihilation: consequences for the muon $g-2$ and CVC tests

TL;DR

This paper refines isospin-breaking corrections between $e^+e^-$ and tau decay data for the di-pion channel, crucial for accurate muon $g-2$ calculations, by testing form factors and analyzing data consistency.

Contribution

It provides a detailed comparison of electromagnetic and weak form factors, demonstrating their accuracy and consistency in describing tau and $e^+e^-$ data for muon $g-2$ predictions.

Findings

Both form factor approaches describe data well, with some limitations when including KLOE measurements.

The isospin-breaking corrections align with previous results, supporting tau data use in muon $g-2$ estimates.

Results improve the precision of Standard Model predictions for muon $g-2$.

Abstract

We revisit the isospin-breaking corrections relating the $e^+e^-$ hadronic cross-section and the tau decay spectral function, focusing on the di-pion channel, that gives the dominant contribution to the hadronic vacuum polarization piece of the muon $g-2$. We test different types of electromagnetic and weak form factors and show that both, the Gounaris-Sakurai and a dispersive-based approach, describe accurately $\tau$ lepton and $e^+e^-$ data (less when KLOE measurements are included in the fits) and comply reasonably well with analyticity constraints. From these results we obtain the isospin-breaking contribution to the conserved vector current (CVC) prediction of the ${\rm BR}(\tau \to \pi\pi\nu_{\tau})$ and to the $2\pi$ hadronic vacuum polarization (HVP) contribution to the muon $g-2$, in agreement with previous determinations and with similar precision. Our results abound in the convenience of using tau data-based results in the updated data-driven prediction of the muon $g-2$ in the Standard Model.