Theoretical analysis of the $\gamma\gamma^{(*)} \to \pi^0\eta$ process

TL;DR

This paper provides a theoretical analysis of the $ o ext{pi}^0 ext{eta}$ process involving photon interactions, describing resonances and predicting decay widths within an energy range up to 1.4 GeV, including the first dispersive prediction for the single-virtual process.

Contribution

It introduces a coupled channel dispersive framework for the $a_0(980)$ resonance and offers the first dispersive prediction for the single-virtual $ ext{gamma} ext{gamma}^*$ process in the spacelike region.

Findings

Pole of $a_0(980)$ on the IV Riemann sheet

Two-photon decay width $ o 0.27(4)$ keV

Dispersive prediction for $ ext{gamma} ext{gamma}^*(Q^2) o ext{pi}^0 ext{eta}$ up to $Q^2=1$ GeV$^2$

Abstract

The theoretical analysis of the $\gamma\gamma \to \pi^0\eta$ process is presented within the energy range up to 1.4 GeV. The $S$-wave resonance $a_0(980)$ is described involving the coupled channel dispersive framework and the $D$-wave $a_2(1320)$ is approximated as a Breit-Wigner resonance. For the $a_0(980)$ the pole is found on the IV Riemann sheet resulting in a two-photon decay width of $\Gamma_{a_0\to\gamma\gamma}=0.27(4)$ keV. The first dispersive prediction is provided for the single-virtual $\gamma\gamma^*(Q^2)\to\pi^0\eta$ process in the spacelike region up to $Q^2=1$ GeV$^2$.