Two photons into π^0π^0

Abstract

We perform a theoretical study based on dispersion relations of the reaction γγ\to π^0π^0 emphasizing the low energy region. We discuss how the f_0(980) signal emerges in γγ\to ππwithin the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave γγ\to ππamplitude 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 ππisoscalar S-wave parameterizations with the advent of new precise data on γγ\toπ^0π^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 σresonance in γγ\toππand calculate its coupling and width to gammaγ, for which we obtain Γ(σ\toγγ)=(1.68\pm 0.15) KeV.

31 pages, 9 figures