Processes of $e^+e^- \to (\eta, \eta', \eta(1295), \eta(1475))\gamma$ in the extended Nambu -- Jona-Lasinio model

TL;DR

This paper calculates the cross sections of specific electron-positron annihilation processes involving eta mesons and a photon within the extended Nambu--Jona-Lasinio model, aligning well with existing experimental data and providing new predictions.

Contribution

It extends the NJL model to include radial excited vector mesons using polynomial form factors, enabling accurate predictions of cross sections for these processes up to 2 GeV.

Findings

Calculated cross sections agree with experimental data from VEPP-2M.

Predicted cross sections for untested processes provide new experimental targets.

Incorporated excited vector mesons as polynomial form factors in the NJL model.

Abstract

In the extended NJL model the total cross sections of the processes $e^+e^- \to (\eta, \eta', \eta(1295), \eta(1405))\gamma$ 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 the VEPP-2M, Novosibirsk. The predictions given for the process $e^+e^- \to (\eta',\eta(1295), \eta(1405)) \gamma$ have not been experimentally tested yet.