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

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.