Two photons into \pi^0\pi^0

TL;DR

This paper uses dispersion relations and chiral perturbation theory to analyze the b3b3d7b0b0 reaction, clarifying the role of the f_0(980) and c resonance in b3b3d7b0b0 scattering and predicting cross sections.

Contribution

It provides a dispersive analysis of b3b3d7b0b0 scattering, highlighting the f_0(980) signal and c resonance effects, with comparisons to Unitary Chiral Perturbation Theory.

Findings

The c resonance coupling to b3b3 is 8 b1 0.15 KeV.

The dispersive approach constrains the b3b3d7b0b0 cross section at low energies.

The c resonance plays a significant role in b3b3d7b0b0 scattering.

Abstract

We perform a theoretical study based on dispersion relations of the reaction \gamma\gamma\to \pi^0\pi^0 emphasizing the low energy region. We discuss how the f_0(980) signal emerges in \gamma\gamma\to \pi\pi within the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave \gamma\gamma\to \pi\pi amplitude above the K\bar{K} threshold. This allows us to make sharper predictions for the cross section at lower energies and our results could then be used to distinguish between different \pi\pi isoscalar S-wave parameterizations with the advent of new precise data on \gamma\gamma\to\pi^0\pi^0. We compare our dispersive approach with an updated calculation employing Unitary Chiral Perturbation Theory (U\chiPT). We also pay special attention to the role played by the \sigma resonance in \gamma\gamma\to\pi\pi and calculate its coupling and width to gamma\gamma, for which we obtain \Gamma(\sigma\to\gamma\gamma)=(1.68\pm 0.15) KeV.