  We have recently studied the QCD pomeron loop evolution equations in zero
transverse dimensions [Shoshi:2005pf]. Using the techniques developed in
[Shoshi:2005pf] together with the AGK cutting rules, we present a calculation
of single, double and central diffractive cross sections (for large diffractive
masses and large rapidity gaps) in zero transverse dimensions in which all
dominant pomeron loop graphs are consistently summed. We find that the
diffractive cross sections unitarise at asymptotic energies and that they are
suppressed by powers of alpha_s. Our calculation is expected to expose some of
the diffractive physics in hadron-hadron collisions at high energy.
