Ambiguities in the Solutions of Partial-Wave Dispersion Relations

Abstract

Partial-wave dispersion relations for $s$-wave amplitudes are studied in the approximation where the left-hand singularities are replaced by a finite sequence of poles. Conditions are obtained under which solutions are possible and it is found that when these are satisfied several classes of solutions are obtained, with different behavior in the high-energy physical region. The case of $p$-wave amplitudes is also discussed.