Solutions of the Pion-Pion Partial Wave Dispersion Relations

It is shown that a minimum of 3 parameters are required for a realistic solution of the low-cnergy pion-pion problem. Numerical solutions falling within the uncertainty of present experimental data are presented. The coupled S- and P- wave pion-pion dispersion equations are solved numerically including left-hand cuts satisfying crossing symmetry up to a cutoff point. The remaining left-hand cut of each partial-wave amplitude is replaced by a pole together with a subtraction constant at the symmetry point nu = - 2/3, where nu is the center- of-mass momentum squared in pion units, No further reduction in the number of parameters seems possible if only low waves are kept in all absorptive amplitudes. (L.N.N.)