Towards more precise parameters of the $a_1(1260)$ resonance

We explore the experimental data on the three-pion decay of the $\tau$ lepton and on the electron-positron annihilation into four pions in an effort to improve the knowledge about the $a_1(1260)$ resonance and their interactions. Our models of those two processes are based on the same main ingredients. These include the running-mass propagators of the $a_1$ and $\rho$ resonances and an effective two-component interaction Lagrangian among the $a_1$, $\rho$, and pion fields. The $a_1$ mass and width are obtained together with the Lagrangian mixing parameter from a common fit to several sets of data on both processes.