A New Analysis of the pi+pi- and pi0pi0 Data

A joint analysis of the pi+pi- and pi0pi0 S-wave amplitudes including results of three experiments has been performed. Using our theoretical model of the pion-pion production in which not only the pion exchange but also the a1(1260) meson exchange were taken into account we have obtained a unique solution (called "down-flat") for the scalar-isoscalar phase shifts. Thus a long-standing problem of ambiguities in the S-wave isoscalar amplitude has been finally resolved and the second ("up-flat") solution was eliminated.