The decays $τ\rightarrow (K, K(1460))ν_τ$ and the value of the weak decay coefficients ${F}_{K}$ and ${{F}_{{K}^{'}}}$ in the extended NJL model
In the extended NJL model, the decay widths of $τ\rightarrow (K, K(1460))ν_τ$, $(K, K(1460))\rightarrow μν_μ$ are calculated. The contributions from intermediate axial-vector mesons ${K}_{1}(1270)$, ${K}_{1}(1400)$ and the first radially excited state ${K}_{1}(1650)$ are taken into account. Estimates for the weak decay coefficients ${F}_{K}$ and ${{F}_{{K}^{'}}}$ are given. Predictions are made for the width of $τ\rightarrow K(1460)ν_τ$ decay and ${{F}_{{K}^{'}}}$ constant.