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 (lns)^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 $\text{A(t,j)∝}\text{1}\text{(?t)}{}^{\mathrm{1+r}}\text{H(k≡}\text{(j?1)}\text{(?t)}{}^{\mathrm{r}}\text{)}$ with r=η^? and iii) the t-dependence of the j-plane singularities is given for η > 0 by $\text{α(t)=1+a(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>\eta </mtext>}}$ with a being const.