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arXiv · 1708.02879

The Stationary Points and Structure of High-Energy Scattering Amplitude

A. P. Samokhin·V. A. Petrov
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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 $ dσ/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 $ dσ/dt$ at 13 TeV and $ 0.05 < |t| < 3.4\, \mathrm{GeV}^{2}$ and predict the values of $ dσ/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 $ dσ/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.

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A. P. Samokhin, V. A. Petrov. 2018-05-04. The Stationary Points and Structure of High-Energy Scattering Amplitude. https://doi.org/10.1016/j.nuclphysa.2018.03.009

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