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

We perform an analysis of the three-pion system with quantum numbers $J^{PC}=1^{++}$ produced in the weak decay of τ 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 $m_p^{(a_1(1260))} = (1209 \pm 4^{+12}_{-9})\text{MeV}$.


Publication Date:
Nov 28 2018
Date Submitted:
Jun 28 2019
Pagination:
96021
Citation:
Physical Review D
D98
9
External Resources:




 Record created 2019-06-28, last modified 2019-07-11


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