Unitarisation and black-disk limit at the LHC in the presence of a hard pomeron

Recent models of soft diffraction include a hard pomeron pole besides the usual soft term. Such models violate the black-disk limit around Tevatron energies, so that they need to be supplemented by a unitarisation scheme. Two standard schemes are considered in this Letter, and we show that they lead to an uncertainty at the LHC much larger than previously estimated. We also examine the signature of unitarisation on various small-t observables, the slope in t of the elastic cross section, or the ratio of the real to imaginary parts of the scattering amplitude, and show that the existence of a unitarised hard pomeron in soft scattering may be confirmed by LHC data.