Hadron diffractive production at ultrahigh energies
  Diffractive production is considered in the ultrahigh energy region where pomeron exchange amplitudes are transformed into black disk ones due to rescattering corrections. The corresponding corrections in hadron reactions $h_1+h_3\to h_1+h_2+h_3$ with small momenta transferred ($q^2_{1\to 1}\sim m^2/\ln^2s$, $q^2_{3\to 3}\sim m^2/\ln^2s$) are calculated in terms of the $K$-matrix technique modified for ultrahigh energies. Small values of the momenta transferred are crucial for introducing equations for amplitudes. The three-body equation for hadron diffractive production reaction $h_1+h_3\to h_1+h_2+h_3$ is written and solved precisely in the eikonal approach. In the black disk regime final state scattering processes do not change the shapes of amplitudes principally but dump amplitudes in a factor $\sim\frac 14$. 
V.V. Anisovich, M.A. Matveev, V.A. Nikonov
hep-ph