Abstract
It is shown that, if the superconvergence relations appertaining to a two-particle scattering process are saturated by an infinite tower of resonances of mass mJ, where J is the spin, then mJ must increase less quickly than J in all cases. With this observation, it is shown that the complex of all the superconvergence relations for all the processes a(J1) + a(J2) → a(J3) + a(J4), where a(J) is the spin-J member of the same tower of particles, possesses an infinity of solutions for the coupling constants. It is concluded that the superconvergence relations are incomplete, and need to be supplemented by some new physical principle, if they are to be of any practical use. A possible exception to this rule is when all but a finite number of residues are constrained to be positive, with no negative coefficient from the isospin crossing matrices. In this case, a given solution may be unique if mJ increases not more quickly than J½.
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