Unitary condition and decrease of the differential cross section of multiparticle production with increasing energy

On the basis of the analytic properties of the inelastic process amplitude and the unitarity condition it is shown that the differential cross section of multiparticle production $d\sigma/d\Omega$ for fixed $\theta$ and $\varphi\ne 0, \pi$ decreases with increasing energy. An upper bound for the decrease is established.