Abstract
The problem of the asymptotic behaviour of partial wave scattering amplitudes in pion-pion scattering is investigated in relation to the role of the double spectral functions. It is stressed that in view of the insensitivity of the low-energy theory to the distant left-hand discontinuity, the solutions obtained byBransden andMoffat in the low-energy region are independent of the existence of a cut-off. Results of a calculation of the double spectral functions in the two-pion intermediate state approximation are briefly described. The consistency of the inverse amplitude solutions with crossing symmetry is examined, and a calculation of theP-wave solution is described using theN/D method. It is shown that if real ghost poles appear on the left cut in theP-wave solutions, then these poles will occur well beyond the region of validity of the approximations.
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