Pole position of the $a_1(1260)$ from $\ddot{I}„$-decay

Abstract

We perform an analysis of the three-pion system with quantum numbers $J^{PC}=1^{++}$ produced in the weak decay of $\ddot{I}„$ 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 $\ddot{I}{„}^{-}\to \ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}\hat{I}{½}_{\ddot{I}}„$ decay. We then perform the analytic continuation of the amplitude to the complex energy plane. The singularity structures related to the $\ddot{I}€\ddot{I}€$ subchannel resonances are carefully addressed. Finally, we extract the $a_1(1260)$ pole position $m_p^{(a_1(1260))}-i\hat{I}{“}_p^{(a_1(1260))}/2$ with $m_p^{(a_1(1260))}=(1209\pm 4_{-9}^{+12})\text{MeV}$, $\hat{I}{“}_p^{(a_1(1260))}=(576\pm 11_{-20}^{+89})\text{MeV}$}.

20 pages, 22 figures