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

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 $\text{?}{}_{\mathrm{l}}{}^{\mathrm{(n)}}\text{(s)}$ in the limits $\text{s → ∞, l → ∞ x = l (}\text{μ}\text{√s}\text{)}{}^3\text{=}\text{fixed}$. Assuming the validity of the scaling law in the whole range, allowed by s-channel unitarity — i.e. for $\text{l > L (s) = (α(4μ}{}^2\text{) ? 1) (}\text{s}\text{4μ}\text{)}\text{log}\text{(}\text{s}\text{s}{}_1\text{)}$ we obtain constant production cross sections σ⁽ⁿ⁾(s) at high energies s → ∞ up to s factors.