pi-pi scattering amplitudes constrained by Roy's equations
  The scalar-isoscalar, scalar-isotensor and vector-isovector pi-pi amplitudes have been fitted simultaneously to experimental data and to to Roy's equations. Resulting pi-pi phase shifts up to 1600 MeV and near threshold observables have been analyzed. Only the amplitudes fitted to the "down-flat" set of phase shifts in scalar-isoscalar wave fulfill crossing symmetry conditions and can be regarded as physical. 
R. Kaminski, L. Lesniak, B. Loiseau