K(K)over-bar scattering amplitude to one loop in chiral perturbation theory, its unitarization and pion form factors

We have calculated the K (K) over bar --> K (K) over bar scattering amplitu de to next-to-leading order in chiral perturbation theory. Then, making use of a unitarization procedure with one or several coupled channels (pi pi,K (K) over bar in our case) we have calculated the pi --> pi pi, pi pi --> K (K) over bar and K (K) over bar --> K (K) over bar S- and P-waves in good agreement with the experiment up to root s similar or equal to 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 form er chiral perturbation theory calculations. Finally we have employed these amplitudes, making use of an Omnes represent ation, to calculate the scalar and the vector pion form factors, obtaining a good agreement with the available experimental data. (C) 1999 Elsevier Sc ience B.V.