Abstract
We argue that if the elastic proton–proton cross section increases with energy, the Froissart-like high energy behaviour of the elastic amplitude (which corresponds to a ‘black disk’ of radius R(s)=clns−βln(lns)) is the only possibility to satisfy the unitarity equation at each value of the impact parameter, b. Otherwise the cross section of events with Large Rapidity Gaps grows faster than the total cross section at the same b. That is, these ‘gap’ events require maximal growth of the high-energy (asymptotic) cross section and of the interaction radius R(s) in order to be consistent with unitarity.
Highlights
It was shown long ago [1] that in the so-called ‘strong coupling’ regime √(where the cross section increases with energy) the high energy, s, dependence of the total and elastic cross sections takes the form σtot = Ctη, dσel dt =Cel(ln s)2η F (B(s)t) (1)with the function F chosen to describe the t dependence of the elastic cross section, with the “slope”B(s) = B0(ln s)γ, (2)where the parameters η and γ are limited to the intervals 0 ≤ η ≤ γ and 0 ≤ γ ≤ 2.Note that processes with Large Rapidity Gaps (LRG) were not considered specially in [1]
When we consider the contribution of LRG events at the edge of disk we find that the radius of the disk must grow as
We emphasise that when high-energy pp cross sections grow with energy, black disk absorption is the only cure of the Finkelstein–Kajantie disease (FK) disease
Summary
It was shown long ago [1] that in the so-called ‘strong coupling’ regime √(where the cross section increases with energy) the high energy, s, dependence of the total and elastic cross sections takes the form σtot = Ct (ln s)η, dσel dt. In a recent paper [2] we argued that when we account for events with LRG the only possibility to satisfy unitarity is to make the disk completely black. There we show that only in the case of γ = 2 (that is R(s) ∝ ln s) does there exist a possibility of screening an increasing LRG cross section in such a way that it does not exceed the total cross section at the same partial wave, that is at the same value of b
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