Divergence of perturbation series in Reggeon field theory

A lower bound on the contribution of $2n\mathrm{th}$-order perturbation theory to the two-point function for $0\le D<\mathrm{}4\mathrm{}$ ($D$ is the number of spatial dimensions) is given; for zero mass (Pomeranchuk) the lower bound is $c^n{g}^{2n}{\mathrm{}(n!)\mathrm{}}^{3-\frac{D}{2}}$, while for nonzero mass (intercept below 1) it is $c^n{g}^{2n}n!$, where $g$ is the coupling constant and $c$ is an appropriate constant. Subtraction of divergences or restricting ourselves to skeleton diagrams does not change the type of behavior of these terms.