Scaling laws for inelastic partial-wave amplitudes and the high-energy behaviour of multiparticle production

Abstract

t-channel unitarity equations are derived for n-particle overlap functions. Together with s-channel unitarity they lead to scaling laws for the inelastic s-channel partial-wave amplitudes ƒ l (n)(s) in the limits s → ∞, l → ∞ x = l ( μ √s ) 3 = fixed . Assuming the validity of the scaling law in the whole range, allowed by s-channel unitarity — i.e. for l > L (s) = (α(4μ 2) − 1) ( s 4μ ) log ( s s 1 ) we obtain constant production cross sections σ ( n) ( s) at high energies s → ∞ up to s factors.