Dispersive representation of the pion vector form factor in $\tau\to\pi\pi\nu_\tau$ decays

Understand

We propose a dispersive representation of the charged pion vector form factor that is consistent with chiral symmetry and fulfills the constraints imposed by analyticity and unitarity.

• Unknown parameters are fitted to the very precise data on $\tau^-\to\pi^-\pi^0\nu_\tau$ decays obtained by Belle, leading to a good description of the corresponding spectral function up to a $\pi\pi$ squared invariant mass $s\simeq 1.5$ GeV$^2$.
• We discuss the effect of isospin corrections, and obtain the values of low energy observables.
• For larger values of $s$, this representation is complemented with a phenomenological description to allow its implementation in the new TAUOLA hadronic currents.