Scalar radius of the pion and two photons into two pions. Strong Swave final state interactions
Abstract
The quadratic pion scalar radius, <r^2>^\pi_s, plays an important role for present precise determinations of \pi\pi scattering. The solution of the MuskhelishviliOmnès equations for the nonstrange null isospin (I) pion scalar form factor determines that <r^2>^\pi_s=(0.61\pm 0.04) fm^2. However, by using an Omnès representation of this form factor, Ynduráin recently obtains <r^2>^\pi_s=(0.75\pm 0.07) fm^2. A large discrepancy between both values, given the precision, then results. We show that Ynduráin's method is indeed compatible with the determinations from the MuskhelishviliOmnès equations once a zero in the scalar form factor for some Swave I=0 Tmatrices is considered. Once this is accounted for, the resulting value is <r^2>^\pi=(0.63\pm 0.05) fm^2. On the other hand, we perform a theoretical study of the reaction \gamma\gamma\to \pi^0\pi^0 based on dispersion relations. The large source of uncertainty for \sqrt{s}\gtrsim 0.5 GeV, due to variations in the phase used in the Omnès function above the K\bar{K} threshold, is removed by taking one more subtraction in the dispersion relation. This allows us to make sharper predictions for the cross section so that one could use this reaction to distinguish between different low energy \pi\pi parameterizations, once independent experiments are available. We also study the role played by the \sigma or f_0(600) meson in this reaction and determine its width to two photons.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.2125
 Bibcode:
 2007arXiv0711.2125O
 Keywords:

 High Energy Physics  Phenomenology
 EPrint:
 10 pages, 1 figure. Invited talk at the 11th International Conference on MesonNucleon Physics and the Structure of the Nucleon (MENU 2007), September 1014, 2007, IKP, Forschungzentrum J\"ulich, Germany