Narrow Results

In this paper, the width of the decay $\tau \to K^{-}{\pi }^0{\nu }_{\tau }$ is calculated in the framework of the Nambu–Jona-Lasinio (NJL) model. The contributions of the intermediate vector $K^{\ast }(892)$ and scalar $K_0^{\ast }(800)$ mesons are taken into account. It is shown that the main contribution to the width of this decay is given by the subprocesses with the intermediate $W$-boson and vector $K^{\ast }(892)$ meson. The scalar channel with the intermediate $K_0^{\ast }(800)$ meson gives an insignificant contribution. In Appendix A, it is shown that the contribution of the subprocess with the intermediate ${K^{\ast }}^{\prime }(1410)$ meson is negligible as well. The obtained results are in satisfactory agreement with the experimental data.

The full and differential widths of the decay $\tau \to K^0{K}^{-}{\nu }_{\tau }$ are calculated in the framework of the extended Nambu–Jona-Lasinio model.The contributions of the subprocesses with the intermediate vector mesons $\rho$(770) and $\rho$(1450) are taken into account. The obtained results are in satisfactory agreement with the experimental data.

The branching fractions of the decays ${\eta }^{\prime }\to \pi \rho$ and $\rho \to \pi \eta$ are calculated in the chiral quark NJL model. The decays exist due to the mass difference between $u$- and $d$-quarks leading to ${\pi }^0-{\eta }^{\prime }$ and ${\pi }^0-\eta$ mixing. Two different approaches are applied: the approximate calculation of this process, taking into account the transitions ${\pi }^0-{\eta }^{\prime }$ and ${\pi }^0-\eta$ explicitly without diagonalization and a more precise approach consisting in the diagonalization of the singlet and octet states leading to the physical fields ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$. The obtained results are in satisfactory agreement with current experimental data.

The processes $e^{+}{e}^{-}\to K^{\pm }{K}^{\ast \mp }(892)$ and $e^{+}{e}^{-}\to \eta \varphi (1020)$ are calculated in the framework of the extended Nambu–Jona-Lasinio model. The intermediate vector mesons $\rho (770)$, $\omega (782)$, $\varphi (1020)$ and their first radially excited states are taken into account. The obtained results are in satisfactory agreement with the experimental data. The predictions for the cross-sections of the reactions $e^{+}{e}^{-}\to K^{\pm }{K}^{\ast \mp }(1410)$, $e^{+}{e}^{-}\to {\eta }^{\prime }(958)\varphi (1020)$ and $e^{+}{e}^{-}\to \eta \varphi (1680)$ were made.

The processes $e^{+}{e}^{-}\to (f_1(1285),a_1(1260))\gamma$ in the threshold domain are considered in the framework of the extended Nambu–Jona-Lasinio model. The channels with the ground $\rho (770)$, $\omega (782)$ and radially excited $\rho (1450)$, $\omega (1420)$ intermediate meson states are taken into account. It is shown that in the process $e^{+}{e}^{-}\to f_1(1285)\gamma$, the probability of the subprocesses with $\rho$-mesons significantly exceeds the probability of the subprocesses with $\omega$-mesons, whereas, in the process $e^{+}{e}^{-}\to a_1(1260)\gamma$, $\rho$- and $\omega$-channels give approximately equal contributions. The mechanism of this effect is discussed. The radiative decay widths of $\rho (1450)\to f_1(1285)\gamma$, $\omega (1420)\to f_1(1285)\gamma$, $\rho (1450)\to a_1(1260)\gamma$ and $\omega (1420)\to a_1(1260)\gamma$ are calculated.

In the extended Nambu–Jona-Lasinio (NJL) model, the decay widths of $\tau \to (K,K(1460)){\nu }_{\tau }$, $(K,K(1460))\to \mu {\nu }_{\mu }$ 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 constants $F_K$ and $F_{K^{\prime }}$ are given. Predictions are made for the width of $\tau \to K(1460){\nu }_{\tau }$ decay and $F_{K^{\prime }}$ constant.

In the extended Nambu–Jona-Lasinio model, the branching fraction of $\tau \to K^{\ast 0}(892)K^{-}{\nu }_{\tau }$ is calculated. The contributions from the contact diagram and the diagrams with intermediate axial-vector, vector and pseudoscalar mesons in the ground and first radially excited states are taken into account. It is shown that an axial-vector and vector channel with a contact diagram give a dominant contribution to the branching fraction. The obtained results for the branching fraction $\tau \to K^{\ast 0}(892)K^{-}{\nu }_{\tau }$ are in satisfactory agreement with experimental data. A prediction for the differential distribution over the invariant mass of the meson pair $K^{\ast 0}(892)K^{-}$ is given.

The effect of the interaction of mesons in the final state is additionally considered within the description of $\tau \to \pi \eta ({\eta }^{\prime }){\nu }_{\tau }$ decays. This interaction is taken into account at the level of production of intermediate pions. One of them, in turn, might be transited into $\eta$ or ${\eta }^{\prime }$ mesons. Our results do not exceed the experimentally established branching fractions, and they are in agreement with the results of other theoretical studies.