Some t-channel aspects of a geometrical Pomeron

We discuss the geometrical scaling in the case of total cross-sections behaving at high energies like (ln s)^η and show that i) the case -1≤η≤0 is inconsistent with t-channel unitarity; ii) the structure of the t-channel partial wave amplitudes is A(t,j)∝ 1 (-t)^1+rH(k≡ (j-1) (-t)^r) with r=η^- and iii) the t-dependence of the j-plane singularities is given for η > 0 by α(t)=1+a(-t) ^{1 η} with a being const.