A Dispersive Analysis on the $f_0(600)$ and $f_0(980)$ Resonances in $\gamma\gamma\to\pi^+\pi^-, \pi^0\pi^0$ Processes

TL;DR

This paper analyzes the di-photon couplings of the $f_0(600)$, $f_0(980)$, and $f_2(1270)$ resonances using dispersive methods, revealing insights into their nature and origins, especially the $f_0(600)$'s non-qqbar character.

Contribution

It introduces a coupled channel dispersive approach to estimate di-photon couplings and reexamines the $f_0(600)$ coupling with improved analyticity, providing new insights into the $f_0(980)$ resonance structure.

Findings

The $f_0(600)$ di-photon coupling is smaller than that expected for a $ar qq$ state.

The $f_0^{III}(980)$ pole may originate from a coupled channel Breit-Wigner description.

The analysis suggests the $f_0(600)$ is unlikely a simple $ar qq$ meson.

Abstract

We estimate the di-photon coupling of $f_0(600)$, $f_0(980)$ and $f_2(1270)$ resonances in a coupled channel dispersive approach. The $f_0(600)$ di-photon coupling is also reinvestigated using a single channel $T$ matrix for $\pi\pi$ scattering with better analyticity property, and it is found to be significantly smaller than that of a $\bar qq$ state. Especially we also estimate the di-photon coupling of the third sheet pole located near $\bar KK$ threshold, denoted as $f_0^{III}(980)$. It is argued that this third sheet pole may be originated from a coupled channel Breit-Wigner description of the $f_0(980)$ resonance.