The decays ρ−→ηπ−\rho^{-}\to\eta\pi^{-} and τ−→η(η′)π−ν\tau^{-}\to\eta(\eta')\pi^{-}\nu in the NJL model

The widths of the decays $\rho^{-}\to\eta\pi^{-}$ and $\tau^{-}\to\eta(\eta')\pi^{-}\nu$ are calculated in the framework of the NJL model. It is shown that these decays are defined by the $u$ and $d$ quark mass difference. It leads to the suppression of these decays in comparison with the main decay modes. In the process $\rho^{-}\to\eta\pi^{-}$ the intermediate scalar $a_0^{-}$ state is taken into account. For the $\tau$ decays the intermediate states with $a_0^{-}$, $\rho^{-}(770)$ and $\rho^{-}(1450)$ mesons are used. Our estimates are compared with the results obtained in other works.Comment: 6 pages, 5 figures, 1 tabl

The processes e+e−→ππ(π′)e^{+}e^{-} \to \pi\pi(\pi') in the extended NJL model

The process $e^{+}e^{-} \to \pi^{+}\pi^{-}$ is described in the framework of the extended NJL model. Intermediate vector mesons $\rho^0(770)$, $\omega(782)$ and \rho'(1450)$are taken into account. Our results are in satisfactory agreement with experimental data. The prediction for the process$e^{+}e^{-} \to \pi\pi'(1300)$is given. Here the main contribution is given by the diagram with intermediate$\rho'(1450)$ meson.Comment: 7 pages, 5 figure

τ−→π−π0ντ\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau decay in the extended NJL model

The width of the decay $\tau^{-} \to \pi^{-} \pi^{0} \nu_\tau$ was calculated in the extended NJL model. Contact interaction of $W$ boson with pion pair as well as the contribution of the $\rho$ mesons in ground and first radial-exited states are taken into account. The sum of the contact diagram and diagram with intermediate $\rho$ meson in the ground state leads to the result which coincides with the result of the vector-dominance model. Our results are in satisfactory agreement with experimental data.Comment: 5 pages, 3 figures, 1 tabl

Pion Polarizability in the NJL model and Possibilities of its Experimental Studies in Coulomb Nuclear Scattering

The charge pion polarizability is calculated in the Nambu-Jona-Lasinio model, where the quark loops (in the mean field approximation) and the meson loops (in the $1/N_c$ approximation) are taken into account. We show that quark loop contribution dominates, because the meson loops strongly conceal each other. The sigma-pole contribution $(m^2_\sigma-t)^{-1}$ plays the main role and contains strong t-dependence of the effective pion polarizability at the region $|t|\geq 4M_\pi^2$. Possibilities of experimental test of this sigma-pole effect in the reaction of Coulomb Nuclear Scattering are estimated for the COMPASS experiment.Comment: 11 pages, 8 figure

Even and odd symplectic and K\"ahlerian structures on projective superspaces

Supergeneralization of \DC P(N) provided by even and odd K\"ahlerian structures from Hamiltonian reduction are construct.Operator $\Delta$ which used in Batalin-- Vilkovisky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered.Comment: 19 page

Excited scalar mesons in a chiral quark model

First radial excitations of the isoscalar and isovector scalar mesons f_0(400-1200), f_0(980) and a_0(980) are investigated in the framework of a nonlocal version of a chiral quark model of the Nambu--Jona-Lasinio type. It is shown that f_0(1370), f_J(1710) and a_0(1450) are the first radially excited states of f_0(400-1200), f_0(980) and a_0(980) which are ground states of the scalar meson nonet. The mesons' masses and strong decay widths are calculated. The scalar resonance f_0(1500) is supposed to be a glueball. The status of K_0^*(1430) is discussed.Comment: LaTeX, 1 figure, minor misprints eradicate

Production of π0ρ0\pi^0\rho^0 pair in electron-positron annihilation in the Nambu-Jona-Lasinio model

The process $e^+e^- \to \pi^0\rho$ is described in the framework of the expanded NJL model in the energy region from 0.9 GeV to 1.5 GeV. The contribution of intermediate state with vector mesons $\omega(782), \,\,\phi(1020)$, and $\omega'(1420)$, where $\omega'$ is the first radial excitation of $\omega$ - meson was taken into account. Results obtained are in satisfactory agreement with experimental data.Comment: 5 pages, 1 figure, 1 tabl

rho(omega)-> pi^0 pi^0 gamma, rho(omega) -> eta pi^0 gamma decays in the local quark Nambu--Jona-Lasinio model

The branching ratios and photon spectra of the rare processes rho(omega)-> pi^0 pi^0 gamma, rho(omega) -> eta pi^0 gamma are calculated in the framework of the standard local quark Nambu--Jona-Lasinio (NJL) model. Three types of diagrams are considered: the quark box and the pole diagrams with scalar (sigma,a_0(980)) and vector (rho,omega) mesons. The obtained estimations for the widths of the processes rho(omega)-> pi^0 pi^0 gamma are in satisfactory agreement with existing experimental data. Predictions are made for the widths of the processes rho(omega) -> eta pi^0 gamma.Comment: 6 pages, 5 figure