Radiative decays of pseudoscalar (P) and vector (V) mesons and the process e^+e^- \to \eta' \rho

TL;DR

This paper calculates radiative decays of pseudoscalar and vector mesons using the NJL model, comparing two methods for loop integrals, and applies the results to describe e+e- annihilation producing η' and ρ mesons, aligning with experimental data.

Contribution

It introduces two approaches for evaluating quark loop integrals in meson decays, incorporating momentum dependence to account for quark confinement, and applies these to e+e- annihilation processes.

Findings

Both methods agree qualitatively and with experimental data.

The second method effectively describes e+e- annihilation from 1.6 to 3.5 GeV.

The approach allows for quark confinement effects in decay calculations.

Abstract

Radiative decays of pseudoscalar and vector mesons are calculated in the framework of the chiral Nambu-Jona-Lasinio (NJL) model. We use the amplitude for triangle quark loops of anomalous type. In evaluating these loop integrals we use two methods. In the first one, we neglect the dependence of external momenta by reproducing the Wess-Zumino-Witten terms of effective chiral meson Lagrangian. In the second method, we take into account the momentum dependence of loop integrals omitting their imaginary part. This makes it possible to allow for quark confinement. As applied both the methods is in qualitative agreement with each other and with experimental data. The second method allows us to describe the electron-positron annihilation with production of $\eta'$ and $\rho$ mesons in the center of mass energy range from 1.6 to 3.5$\GeV$. The comparison with the recent experimental data is presented.