Processes $e^+e^-\to\pi^0({\pi^0}')\gamma$ in the NJL model

TL;DR

This paper models electron-positron annihilation into neutral pions and their excitations with a focus on intermediate vector mesons using the NJL model, providing predictions consistent with experimental data below 2 GeV.

Contribution

It extends the NJL model to include radial excited vector mesons via polynomial form factors for accurate cross section predictions.

Findings

Predicted cross sections align with experimental data between 600 and 1020 MeV.

Incorporated excited vector mesons as radial states in the NJL model.

Provided numerical results for processes below 2 GeV energy range.

Abstract

The processes of electron-positron annihilation into $\pi^0\gamma$ and into $\pi'(1300)\gamma$ are considered within the NJL model. Intermediate vector mesons $\rho^0$, $\omega$, $\rho'(1450)$, and $\omega'(1420)$ are taken into account. The latter two mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of a polynomial form factor. Numerical predictions for the cross sections of these processes are received for the center-of-mass energies below 2 GeV. Our results for the $\pi^0\gamma$ production are in agreement with experimental data received in the energy region 600 -- 1020 MeV.