Two photon decay and photoproduction of radial excitation of pion $\pi_0'$

TL;DR

This paper calculates the two-photon decay width of the radially excited pion $'$ and estimates its production probabilities in electron-positron colliders and photon interactions, using a non-local quark model.

Contribution

It introduces a polynomial form factor for describing the radial excitation of the pion within a non-local NJL model and provides decay and production estimates.

Findings

Decay width of $'$ is 3.6 keV.

Production cross sections are estimated as 0.14 nb and 0.06 nb.

The model describes the radial excitation with a second-order polynomial form factor.

Abstract

Within the framework of non-local quark model of Nambu--Jona-Lasinio type the two-photon decay of radial excited state of $\pi_0$-meson -- $\pi_0'$ -- is found to be $3.6\KeV$. The radial excitation of pion is described with the use of polynomial formfactor of second order over $\vec q^2$ where $\vec q$ is the transverse momentum, which corresponds to relative motion of quark-antiquark pair within the energy range from 0 up to $1\GeV$. The probabilities of production of $\pi_0'$ and $(\pi_0'+\gamma)$ states in the electron-positron colliders are estimated. The production of $\pi_0'$-meson in the interaction of photon with electron or muon is as well considered (Primakoff effect). The relevant total cross sections are 0.14 or $0.06\nb$.