Elimination of Ambiguities in pi-pi Amplitudes Using Roy's Equations

Roy’s equations are used to check if scalar-isoscalar pi-pi amplitudes fitted to the up-flat'' and down-flat’’ phase shift solutions fulfill crossing symmetry below 1 GeV. It is shown that the amplitude fitted to the down-flat'' solution satisfies crossing symmetry while the up-flat’’ one does not. In such a way the up-down'' ambiguity in the scalar-isoscalar phase shifts is resolved in favour of the down-flat’’ solution.