Description of the decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>τ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:mi>π</mml:mi><mml:mi>π</mml:mi><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mi>τ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> in the NJL-type chiral quark model
M. K. Volkov, А. А. Pivovarov, K. Nurlan
Abstract
The branching fractions of the decays ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ are calculated in the $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$ Nambu--Jona-Lasinio-type chiral model. Four intermediate channels are considered: the contact channel and the channels with the intermediate axial-vector, vector, and pseudoscalar mesons. The additional resonance states ${K}^{*}\ensuremath{\pi}$ and $K\ensuremath{\rho}$ are taken into account in all channels. We show that the main contributions to the widths of these decays are given by the axial-vector channel. In the axial-vector channel, the intermediate resonances ${K}_{1}(1270)$ and ${K}_{1}(1400)$ are taken into account. The obtained results are in satisfactory agreement with the known experimental data.