Pion scalar form factor with correct mass and width of scalar mesons f0(500) and f0(980)

Construction of the pion scalar isoscalar form factor Gamma(pi)(t) in the elastic region, with an emphasis on the values of the S-wave isoscalar pi pi scattering length a(0)(0) and the quadratic pion scalar radius < r(2)>(pi)(s) to be in conformity with predictions of the chiral perturbation theory, is presented. It is based on a precise S-wave isoscalar pi pi scattering phase shift generated by dispersive analysis of experimental data with and imposed crossing symmetry condition. The final result for values of the f(0)(500) scalar meson mass and width is m(sigma) = (487 +/- 31) MeV; Gamma(sigma) = (542 +/- 60) MeV and for values of the f(0)(980) scalar meson mass and width is m(f)(980) = (988 +/- 78) MeV; Gamma(f(980)) = (97 +/- 29) MeV. The f(0)(500) scalar meson parameters are compatible with the results from dispersive analyses of the BERN and MADRID/CRACOW groups to be considered now as the most reliable values of the f(0)(500) scalar meson parameters, though in presented analysis another, unusual way has been applied. The f(0)(980) meson parameters agree well with values given by the Particle Data Group.