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

Abstract

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. The singularity structures related to the $\pi \pi$ subchannel resonances are carefully addressed. Finally, we extract the $a_1(1260)$ pole position $m_p^{(a_1(1260))}-i{\Gamma }_p^{(a_1(1260))}/2$ with $m_p^{(a_1(1260))}=(1209\pm 4_{-9}^{+12})\text{MeV}$, ${\Gamma }_p^{(a_1(1260))}=(576\pm 11_{-20}^{+89})\text{MeV}$}.

arXiv comment20 pages, 22 figures

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