Properties of the hard pomeron with a running coupling constant and the   high-energy scattering
  The equation for the hard pomeron with a running coupling introduced on the basis of the bootstrap requirement is solved numerically. Two supercritical pomerons are found with the intercept minus 1 of the leading one of the order 0.35-0.5 and that of the subleading one half as large. The contribution of multipomeron exchanges is found to be essential only at extremely high energies of the order of 100 TeV. Comparison of the cross-sections and structure functions to the present experimental data seems to indicate that the asymptotical regime has not yet been achieved. 
Mikhail Braun, Gian Paolo Vacca, Giovanni Venturi