S-WAVE UNITARIZATION OF HIGH-ENERGY MULTILEG TREE GRAPHS

Recently several authors have made quantitative estimates of the factorial divergences (N!) in tree-level amplitudes where a few particles go to N and N greater-than-or-equal-to lambda-1 >> 1, with lambda the coupling, and various arguments have been given for non-perturbative control of these divergences. We explore numerically a simple S-wave unitarization scheme for these and other large-N amplitudes, proposed earlier by one of us. We find that for S-wave processes (1) SIGMA(N > lambda-1)sigma(2 --> N) is always small for lambda << 1, of order exp(- const./lambda); (2) for N greater-than-or-equal-to lambda-1, sigma(few --> N) approximately exp(- betaN), where beta = O(1) (in agreement with field theoretic results found by other methods); (3) rates for N' --> N, N' approximately N greater-than-or-equal-to lambda-1, are not suppressed.