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Black disk radius constrained by unitarity.

Khoze, V.A. and Martin, A.D. and Ryskin, M.G. (2018) 'Black disk radius constrained by unitarity.', Physics letters B., 787 . pp. 167-170.


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) = c ln s −βln(ln s)) 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.

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Publisher statement:© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (
Date accepted:29 October 2018
Date deposited:14 November 2018
Date of first online publication:01 November 2018
Date first made open access:14 November 2018

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