Radiative decays of radially excited mesons ${\pi^0}'$, ${\rho^0}'$, $\omega'$ in NJL model

TL;DR

This paper investigates the radiative decay processes of radially excited mesons using a non-local NJL model, providing predictions consistent with known data and proposing new measurable decay widths for future experiments.

Contribution

It introduces a polynomial form factor to describe radially excited mesons within the non-local NJL model, extending the understanding of meson decay processes beyond the ground states.

Findings

Decay widths of $ ho^0$ and $ ho^0'$ are consistent with experimental data.

Predictions for decay widths of excited mesons are provided for future experimental verification.

The model successfully describes both ground and excited meson decay processes.

Abstract

Radiative decays $\pi^0({\pi^0}')\to\gamma+\gamma$, ${\pi^0}'\to\rho^0(\omega)+\gamma$, ${\rho^0}'(\omega')\to\pi^0+\gamma$, and ${\rho^0}'(\omega')\to{\pi^0}'+\gamma$ are considered in the framework of the non-local SU(2)$\times$SU(2) NJL model. Radially excited mesons are described with the help of polynomial form factor $f({k^\bot}^2)$, where $k^\bot$ is the quark momentum transverse to the external meson momentum. In spite of mixing of the ground and excited meson states in this model, the decay widths of $\pi^0\to\gamma+\gamma$ and $\rho^0(\omega)\to\pi^0+\gamma$ are found to be in good agreement with experimental data as in the standard local NJL model. Our predictions for decay widths of radially excited mesons can be verified in future experiments.