decay in the extended Nambu-Jona-Lasinio model

M. K. Volkov; A. A. Pivovarov; A. A. Osipov

doi:10.1140/epja/i2018-12503-9

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2023 Impact factor 2.6

Hadrons and Nuclei

Eur. Phys. J. A (2018) 54: 61
https://doi.org/10.1140/epja/i2018-12503-9

Regular Article - Theoretical Physics

$\tau \rightarrow f_{1}(1285) \pi^{-}\nu_{\tau}$ decay in the extended Nambu-Jona-Lasinio model

M. K. Volkov, A. A. Pivovarov and A. A. Osipov^*

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia

^* e-mail: osipov@nu.jinr.ru

Received: 30 January 2018
Accepted: 27 March 2018
Published online: 24 April 2018

Abstract

Within the framework of the extended Nambu-Jona-Lasinio model, we calculate the matrix element of the $\tau \rightarrow f_{1}(1285) \pi^{-} \nu_{\tau}$ decay, obtain the invariant mass distribution of the $f_{1}\pi$ -system and estimate the branching ratio $\mathrm{Br}(\tau \rightarrow f_{1} \pi^{-}\nu_{\tau}) = 4.0\times 10^{-4}$ . 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 $\mathrm{Br}(\tau \rightarrow f_{1} \pi^{-} \nu_{\tau})=(3.9\pm 0.5)\times 10^{-4}$ . The distribution function obtained for the decay $\tau \rightarrow f_{1}(1285) \pi^{-} \nu_{\tau}$ shows a clear signal of $a_{1}(1640)$ resonance which should be compared with future experimental data including our estimate of the decay width $\Gamma (a_{1}(1640) \rightarrow f_{1} \pi)=14.1$ MeV.