Lightest scalar and tensor resonances in $\gamma\gamma\to\pi\pi$ after the Belle experiment

TL;DR

This paper analyzes high-statistics Belle data on gamma-gamma to pion-pion reactions to clarify the nature and couplings of light scalar and tensor resonances, revealing small direct couplings and loop-induced decay mechanisms.

Contribution

The study provides a detailed analysis of Belle data showing that the sigma(600) and f0(980) resonances have small direct gamma-gamma couplings, emphasizing loop mechanisms and chiral shielding effects.

Findings

Small direct gamma-gamma coupling constants for sigma(600) and f0(980)

Decay mechanisms dominated by pi+pi- and K+K- loops

Estimated f2(1270) to gamma-gamma decay width of approximately 3.68 keV

Abstract

New high statistics Belle data on the $\gamma\gamma\to\pi^+\pi^-$ reaction cross section measured in the range of pion-pair invariant masses $\sqrt{s}$ between 0.8 GeV and 1.5 GeV are analyzed to clarify the current situation around the $\sigma(600)$, $f_0(980)$, and $f_2(1270)$ resonances in $\gamma\gamma$ collisions. The present analysis shows that the direct coupling constants of the $\sigma(600)$ and $f_0(980)$ resonances to $\gamma\gamma$ are small, and the $\sigma(600)\to\gamma\gamma$ and $f_0(980)\to\gamma\gamma$ decays are four-quark transitions caused by the $\pi^+\pi^-$ and $K^+K^-$ loop mechanisms, respectively. The chiral shielding of the $\sigma(600)$ resonance takes place in the reactions $\gamma\gamma\to\pi\pi$ as well as in $\pi\pi$ scattering. Some results of a simultaneous description of the $\gamma\gamma\to\pi^+\pi^-$ and $\gamma\gamma\to\pi^0\pi^0$ Belle data are also presented. In particular, the following tentative estimate of the $f_2(1270)\to\gamma\gamma$ decay width is obtained: $\Gamma_{f_2\to\gamma\gamma}(m^2_{f_2})\approx 3.68$ keV.