In the extended Nambu\char21{}Jona-Lasinio (NJL) model the total cross sections of the processes ${e}^{+}{e}^{$-${}}$\rightarrow${}[$\eta${},{$\eta${}}^{$'${}},$\eta${}(1295),$\eta${}(1405)]$\gamma${}$ at energies up to 2 GeV are calculated. The intermediate vector mesons $$\rho${}(770)$, $$\omega${}(782)$, $$\phi${}(1020)$, ${$\rho${}}^{$'${}}(1450)$, ${$\omega${}}^{$'${}}(1420),$ and ${$\phi${}}^{$'${}}(1680)$ are taken into account. The latter three mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of polynomial form factors. The calculation results are in satisfactory agreement with the experimental data obtained with the SND detector at VEPP-2M, Novosibirsk. The predictions given for the process ${e}^{+}{e}^{$-${}}$\rightarrow${}[{$\eta${}}^{$'${}},$\eta${}(1295),$\eta${}(1405)]$\gamma${}$ have not been experimentally tested yet.

The total cross section of the process $e^{+}{e}^{-}\to \mathrm{\Lambda }\overline{\mathrm{\Lambda }}$ is calculated within the energy range close to the mass of the $\psi (3770)$ charmonium state. Two different contributions were considered: the $D$-meson loop and the three gluon charmonium annihilation one. Both of them contribute noticeably and in sum, fairly reproduce the data. Large relative phase for these contributions are generated with respect to the pure electromagnetic mechanism. As a by-product, the fit for the electromagnetic form factor of $\mathrm{\Lambda }$ hyperon is obtained for the large momentum transferred region.

The annihilation of proton and antiproton to an electron-positron pair, including radiative corrections due to the emission of virtual and real photons is considered. The results are generalized to leading and next-to leading approximations. The relevant distributions are derived and numerical applications are given in the kinematical range accessible to the PANDA experiment at the FAIR facility.

The process e ⁺ e ⁻ → π⁰ρ⁰ is described in the framework of the expanded NJL model in the energy region from 0.9 to 1.5 GeV. The contribution of intermediate state with vector mesons ω(782), φ(1020), and ω′(1420), where ω′ is the first radial excitation of ω meson, was taken into account. Results obtained are in satisfactory agreement with experimental data.

Antiproton-proton annihilation into light neutral mesons in the few GeV energy domain is investigated in view of a global description of the existing data and predictions for future work at the Antiproton Annihilation at Darmstadt (PANDA) experiment at the Facility for Antiproton and Ion Research (FAIR). An effective meson model earlier developed, with mesonic and baryonic degrees of freedom in $s, t$, and $u$ channels, is applied here to ${\pi }^0{\pi }^0$ production. Form factors with logarithmic $s$ and $t\left(u\right)$ dependencies are applied. A fair agreement with the existing angular distributions is obtained. Applying SU(3) symmetry, it is straightforward to recover the angular distributions for ${\pi }^0\eta$ and $\eta \eta$ production in the same energy range. A good agreement is generally obtained with all existing data.