We present an improved method for the precise reconstruction of cosmic-ray air showers above $10^{17}\mathrm{eV}$ with sparse radio arrays. The method is based on the comparison of measured pulses to predictions for radio pulse shapes by CoREAS simulations. We applied our method to the data of Tunka-Rex, a $1{\mathrm{km}}^2$ radio array in Siberia operating in the frequency band of 30–80 MHz. Tunka-Rex is triggered by the air-Cherenkov detector Tunka-133 and by scintillators (Tunka-Grande). The instrument collects air-shower data since 2012. The present paper describes an updated data analysis of Tunka-Rex and details of the new method applied. After quality cuts, when Tunka-Rex reaches its full efficiency, the energy resolution of about 10% given by the new method has reached the limit of systematic uncertainties due to the calibration uncertainty and shower-to-shower fluctuations. At the same time the shower maximum reconstruction has improved compared to the previous method based on the slope of the lateral distribution and reaches a precision of better than $35\mathrm{g}/{\mathrm{cm}}^2$. We also define conditions of the measurements at which the shower maximum resolution of Tunka-Rex reaches a value of $25\mathrm{g}/{\mathrm{cm}}^2$ and becomes competitive to optical detectors. To check and validate our reconstruction and efficiency cuts we compare individual events to the reconstruction of Tunka-133. Furthermore, we compare the mean of the shower maximum as a function of primary energy to the measurements of other experiments.

The process of electron-positron annihilation into $$\eta${}({$\eta${}}^{$'${}})2$\pi${}$ is described within the extended Nambu\char21{}Jona-Lasinio model in the energy range up to about 2 GeV. Contributions of intermediate vector mesons $$\rho${}(770)$ and $$\rho${}(1450)$ are taken into account. Results for the $$\eta${}2$\pi${}$ channel are found to be in a reasonable agreement with experimental data. Predictions for production of ${$\eta${}}^{$'${}}2$\pi${}$ are given. The corresponding estimations for decays $$\tau${}$\rightarrow${}$\eta${}({$\eta${}}^{$'${}})2$\pi${}$\nu${}$ are given in the Appendix.

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.

EPJ Web of Conferences, open-access proceedings in physics and astronomy

The physics motivations and advantages of the new TAIGA (Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy) detector are presented. TAIGA aims at gamma-ray astronomy at energies from a few TeV to several PeV, as well as cosmic ray physics from 100 TeV to several EeV. For the energy range 30 – 200 TeV the sensitivity of 10 km2 area TAIGA array for the detection of local sources is expected to be 5 × 10-14 erg cm-2 sec-1 for 300 h of observations. Reconstruction of the given EAS energy, incoming direction and its core position, based on the timing TAIGA-HiSCORE data, allows one to increase a distance between the IACTs up to 600-1000 m. The low investments together with the high sensitivity for energies ≥ 30-50 TeV make this pioneering technique very attractive for exploring the galactic PeVatrons and cosmic rays. At present the TAIGA first stage has been constructed in Tunka valley, 50 km West from the Lake Baikal. The first experimental results of the TAIGA first stage are presented.