Hadron diffractive scattering at ultrahigh energies, real part of the amplitude and Coulomb interaction

TL;DR

This paper analyzes the real and imaginary parts of proton-proton scattering amplitudes at ultrahigh energies, considering unitarity, analyticity, and Coulomb effects, predicting behaviors beyond 100 TeV and calculating cross sections at 7 TeV.

Contribution

It provides new predictions for scattering amplitudes at energies above 100 TeV and discusses the impact of Coulomb interactions using the $K$-matrix approach.

Findings

Real part of amplitude concentrates at the black disk border.

Predictions for amplitudes at energies >100 TeV.

Calculated 7 TeV cross section including Coulomb effects.

Abstract

On the basis of requirements of unitarity and analyticity we analyze the real and imaginary parts of the $pp^\pm$ scattering amplitudes at recent ultrahigh energies, 1-100 TeV. The predictions for the region $\sqrt s > 100$ TeV and ${\bf q}^2<0.4$ GeV$^2$ are given supposing the black disk asymptotic regime. It turns out that the real part of the amplitude is concentrated in the impact parameter space at the border of the black disk. The interplay of hadron and Coulomb interactions is discussed in terms of the $K$-matrix function. The $pp$ diffractive scattering cross section at 7 TeV is calculated with Coulomb interaction taken into account.