KK bar scattering amplitude to one loop in chiral perturbation theory, its unitarization and pion form factors

Abstract

We have calculated the KK bar --> KK bar scattering amplitude to next to leading order in Chiral Perturbation Theory. Then, making use of a unitarization procedure with one or several coupled channels (\pi\pi, KK bar in our case) we have calculated the \pi\pi --> \pi\pi, \pi\pi --> KK bar and KK bar --> KK bar S and P waves in good agreement with the experiment up to \sqrt{s}= 1.2 GeV. The \pi\pi scattering lengths with isospin and spin (I,J) equal to (0,0), (1,1) and (2,0) are also calculated in agreement with experiment and former Chiral Perturbation Theory calculations. Finally we have employed these amplitudes, making use of an Omnes representation, to calculate the scalar and the vector pion form factors, obtaining a good agreement with the available experimental data.