Pole position of the $a_1(1260)$ from $\tau$-decay

Understand

We perform an analysis of the three-pion system with quantum numbers $J^{PC}=1^{++}$ produced in the weak decay of $\tau$ leptons.

• The interaction is known to be dominated by the axial meson $a_1(1260)$.
• We build a model based on approximate three-body unitarity and fix the free parameters by fitting it to the ALEPH data on $\tau^-\to \pi^-\pi^+\pi^-\,\nu_\tau$ decay.
• We then perform the analytic continuation of the amplitude to the complex energy plane.