Elimination of ambiguities in pion-pion phase shifts using crossing   symmetry
  Roy's equations, which incorporate crossing symmetry of the pion-pion scattering amplitudes, are used to resolve the present ambiguity between two solutions for the scalar-isoscalar phase shifts below 1 GeV. It is shown that the "down-flat" solution satisfies well Roy's equations and consequently crossing symmetry while the other solution called "up-flat" does not and thus should be eliminated. 
R. Kaminski, L. Lesniak and B. Loiseau