Vanishing of Total Cross Sections at Infinite Energy

We have examined the scattering amplitude of two scalar particles in scalar electrodynamics for arbitrary order of perturbation, and found uncanceled terms proportional to $s{\left(\ln \mathrm{s}\right)}^n$, for $n$ any positive integer. This suggests a branch point or an essential singularity at $J=1\mathrm{}$, and that total cross sections vanish at infinite energy as some negative power of lns. This form fits very well the sum of the measured ${\pi }^{+}p$ and ${\pi }^{-}p$ cross sections between 8 and 22 BeV/c.