$\tau \to f_1(1285){\pi }^{-}{\nu }_{\tau }$ decay in the extended Nambu -- Jona-Lasinio model

Abstract

Within the framework of the extended Nambu -- Jona-Lasinio model, we calculate the matrix element of the $\tau \to f_1(1285){\pi }^{-}{\nu }_{\tau }$ decay, obtain the invariant mass distribution of the $f_1\pi$ -system and estimate the branching ratio Br$(\tau \to f_1{\pi }^{-}{\nu }_{\tau })=4.0\times 10^{-4}$. The two types of contributions are considered: the contact interaction, and the axial-vector $I^G(J^{PC})=1^{-}(1^{++})$ resonance exchange. The latter includes the ground $a_1(1260)$ state, and its first radially excited state, $a_1(1640)$. The corrections caused by the $\pi -a_1$ transitions are taken into account. Our estimate is in a good agreement with the latest empirical result Br$(\tau \to f_1{\pi }^{-}{\nu }_{\tau })=(3.9\pm 0.5)\times 10^{-4}$. The distribution function obtained for the decay $\tau \to f_1(1285){\pi }^{-}{\nu }_{\tau }$ shows a clear signal of $a_1(1640)$ resonance which should be compared with future experimental data including our estimate of the decay width $Γ(a_1(1640) \to f_1 π)=14.1\,\mbox{MeV}$.

9 pages, 5 figures, has been accepted for publication in the European Physical Journal A - "Hadrons and Nuclei"

References in corpus (4)

• Pseudocalar meson and vector meson interactions and dynamically generated axial-vector mesons
• Test of the multiquark structure of $a_1(1420)$ in strong two-body decays
• The anomalous decay $f_1(1285)\to \rho \gamma$ and related processes
• A general framework to diagonalize vector--scalar and axial-vector--pseudoscalar transitions in the effective meson Lagrangian

Cited by in corpus (6)

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• Triangle singularity in ${\tau }^{-}\to {\nu }_{\tau }{\pi }^{-}{f}_0(980)$ ($a_0(980)$) decays
• $\tau$ decay into a pseudoscalar and an axial-vector meson
• The decays $\tau \to [\omega (782),\varphi (1020)]K^{-}{\nu }_{\tau }$ in the extended NJL model
• Decay rates $f_1(1285)\to {\rho }^0{\pi }^{+}{\pi }^{-}$ and $a_1(1260)\to \omega {\pi }^{+}{\pi }^{-}$ in the Nambu -- Jona-Lasinio model
• About The Polarized $\tau$ Lepton Radiative Decay