The Stationary Points and Structure of High-Energy Scattering Amplitude

Abstract

The ISR and the 7 TeV LHC data indicate that the differential cross-section of elastic proton-proton scattering remains almost energy-independent at the transferred momentum $t\approx -0.21{\mathrm{GeV}}^2$ at the level of $\approx 7.5\mathrm{mb}/{\mathrm{GeV}}^2$. This property of $d\sigma /dt$ (the "first" stationary point) appears due to the correlated growth of the total cross-section and the local slope parameter and can be expressed as a relation between the latter quantities. We anticipate that this property will be true up to 13 TeV. This enables us to normalize the preliminary TOTEM data for $d\sigma /dt$ at 13 TeV and $0.05<|t|<3.4{\mathrm{GeV}}^2$ and predict the values of $d\sigma /dt$ at this energy. These data give an evidence of the second stationary point at $t\approx -2.3{\mathrm{GeV}}^2$ at the level of $\approx 33\mathrm{nb}/{\mathrm{GeV}}^2$. The energy evolution of $d\sigma /dt$ looks as if the high energy elastic scattering amplitude is a sum of two similar terms. We argue that the existence of the two stationary points and the two-component structure of the high energy elastic scattering amplitude are general properties for all elastic processes.

17 pages, 5 figures, 2 tables; published version

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• Two diffraction cones of elastic scattering and structural symmetry conjecture
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• Model-independent Odderon results based on new TOTEM data on elastic pp collisions at 8 TeV
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• Signs of universality in the behavior of elastic $\text{pp}$ scattering cross-sections at high energies