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

JPAC Collaboration; M. Mikhasenko; A. Pilloni; M. Albaladejo; C. Fernandez-Ramirez; A. Jackura; V. Mathieu; J. Nys; A. Rodas; B. Ketzer; A. P. Szczepaniak

doi:10.1103/physrevd.98.096021

arXiv · 1810.00016

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

JPAC Collaboration·M. Mikhasenko·A. Pilloni·M. Albaladejo·C. Fernandez-Ramirez·A. Jackura·V. Mathieu·J. Nys·A. Rodas·B. Ketzer·A. P. Szczepaniak

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Abstract

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 $τ^-\to π^-π^+π^-\,ν_τ$ 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 $a_1(1260)$ pole position $m_p^{(a_1(1260))}-iΓ_p^{(a_1(1260))}/2$ with $m_p^{(a_1(1260))} = (1209 \pm 4^{+12}_{-9})\text{MeV}$, $Γ_p^{(a_1(1260))} = (576 \pm 11 ^{+89}_{-20})\text{MeV}$}.

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JPAC Collaboration, M. Mikhasenko, A. Pilloni, M. Albaladejo, C. Fernandez-Ramirez, A. Jackura, V. Mathieu, J. Nys, A. Rodas, B. Ketzer, A. P. Szczepaniak. 2019-01-10. Pole position of the $a_1(1260)$ from $τ$-decay. https://doi.org/10.1103/physrevd.98.096021

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