Pole position of the a1 (1260) from τ -decay

We perform an analysis of the three-pion system with quantum numbers JPC=1++ produced in the weak decay of τ leptons. The interaction is known to be dominated by the axial meson a1(1260). We build a model based on approximate three-body unitary and fix the free parameters by fitting it to the ALEPH data on τ-→π-π+π-ντ decay. We then perform the analytic continuation of the amplitude to the complex energy plane. The singularity structures related to the ππ subchannel resonances are carefully addressed. Finally, we extract the a1(1260) pole position mp(a1(1260))-iΓp(a1(1260))/2 with mp(a1(1260))=(1209±4-9+12) MeV, Γp(a1(1260))=(576±11-20+89) MeV.