Dispersive analysis of $\tau^-\to\pi^-\pi^0\nu_\tau$ Belle data

TL;DR

This paper employs a dispersive approach to analyze Belle data on tau decay into pions, accurately extracting low-energy constants while respecting fundamental symmetries and considering isospin breaking effects.

Contribution

It introduces a dispersive representation of the vector form factor for tau decay that aligns with chiral symmetry, analyticity, and unitarity, providing precise parameter extraction.

Findings

Determined low-energy pion observables from Belle data.

Validated the dispersive method against experimental results.

Discussed isospin breaking effects in tau decay analysis.

Abstract

We analyse Belle data on the decay $\tau^- \to \pi^- \pi^0 \nu_\tau$ using a dispersive representation of the vector form factor which is consistent with chiral symmetry and preserves analyticity and unitarity exactly. We fit the unknown theoretical parameters from the data, determining the values of the related low-energy observables $\left\langle r^2\right\rangle^\pi_V$ and $c_V^\pi$. The implementation of isospin breaking effects is also discussed.