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

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 $\bar{q}q$ state. Especially we also estimate the di-photon coupling of the third sheet pole located near $\bar{K}K$ 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.

24 pages and 13 eps figures. A nuerical bug in previous version is fixed. Some results changed. References and new figures added. Version to appear in Phys. Rev. D

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Cited by in corpus (12)

• MO analysis of the high statistics Belle results on $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ with chiral constraints
• Comprehensive Amplitude Analysis of $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ and $\overline{K}K$ below 1.5 GeV
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• Two photon couplings of the lightest isoscalars from BELLE data
• Dispersion relations for ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$: helicity amplitudes, subtractions, and anomalous thresholds
• Gluonium nature of the sigma/f_0(600) from its coupling to KK
• sigma and f_0(980) substructures from gamma-gamma to pi-pi, J/psi, phi radiative and D_s semi-leptonic decays
• Dispersive Analysis of Low Energy $\gamma N\to \pi N$ Process and Studies on the $N^{\ast }(890)$ Resonance
• Dispersive analysis of low energy ${\gamma }^{\ast }N\to \pi N$ process
• The sigma and f_0(980) from K_e4+pi-pi, gamma-gamma scatterings, J/psi, phi to gamma sigma_B and D_s to l nu sigma_B
• Advanced parametrisations for hadronic form factors
• Unitarity constraints on chiral perturbative amplitudes