S-wave unitarization of high energy multileg tree graphs

Abstract

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⩾ λ −⪢1, with λ 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) Σ N> λ −1 σ 2→ N is always small for λ⪡ 1, of order exp ( −const. λ ); (2) for N⩾ λ −1, σ few→ N ≈exp(− βN), where β=0(1) (in agreement with field theoretical results found by other methods); (3) rates for N ′→ N, N ′≈ N⩾ λ −1, are not suppressed.