The Stationary Points and Structure of High-Energy Scattering Amplitude

TL;DR

This paper investigates the energy-independent stationary points in high-energy elastic proton-proton scattering, revealing a two-component structure of the scattering amplitude and predicting its behavior at 13 TeV.

Contribution

It introduces the concept of stationary points in the differential cross-section and links them to a two-component structure of the scattering amplitude, extending understanding of high-energy elastic scattering.

Findings

Identification of a first stationary point at $t oughly -0.21$ GeV$^2$

Evidence for a second stationary point at $t oughly -2.3$ GeV$^2$

Prediction of differential cross-section behavior at 13 TeV

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.