Abstract
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.
Highlights
Experimental data reveal that total cross sections grow with energy
The fast growing hard pomeron leads to a violation of unitarity for values of s smaller than 1
If we assume that the hard pomeron is present in soft data, it will lead to a cross section of the order of 150 mb
Summary
The simplest expression of the unitarity constraints can be obtained from partialwave amplitudes. As ImF ∝ s∆ with ∆ > 0, the scattering amplitude F (s, b) reaches the unitarity bound for some value bu(s) of the impact parameter. We see that the small-t slope of ρ will be one of the most striking features of saturation The scattering amplitude can be represented as In this case, the slope of the differential cross section at small momentum transfer will be BBDL ∼ R2/4 + R4/32 |t|.
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