ππ scattering amplitudes constrained by Roy's equations ⁎†

The scalar-isoscalar, scalar-isotensor and vector-isovector ππ amplitudes have been fitted simultaneously to experimental data and to to Roy's equations. Resulting ππ 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.