Elimination of ambiguities in ππ phase shifts using crossing symmetry

Royʹs equations, which incorporate crossing symmetry of the ππ 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 Royʹs equations and consequently crossing symmetry while the other solution called “up-flat” does not and thus should be eliminated.