The Pomeron and Odderon in elastic, inelastic and total cross sections at the LHC

TL;DR

This paper presents a simple model analyzing elastic, inelastic, and total cross sections in proton-proton and antiproton-proton scattering at the LHC, focusing on the dip-bump structure and Regge trajectory effects.

Contribution

It introduces a simple, controlled model to analyze the interplay of C-even and C-odd components in scattering amplitudes, including non-linearity of Regge trajectories, for LHC energies.

Findings

Predicted ratios of real to imaginary parts of the forward amplitude.

Estimated elastic and inelastic cross sections at LHC energies.

Analyzed the dip-bump structure and its sensitivity to model parameters.

Abstract

A simple model for elastic diffractive hadron scattering, reproducing the dip-bump structure is used to analyze PP and $\bar PP$ scattering. The main emphasis is on the delicate and non-trivial dynamics in the dip-bump region, near t=-1 GeV$^2$. The simplicity of the model and the expected smallness of the absorption corrections enables one the control of various contributions to the scattering amplitude, in particular the interplay between the C-even and C-odd components of the amplitude, as well as their relative contribution, changing with s and t. The role of the non-linearity of the Regge trajectories is scrutinized. The ratio of the real to imaginary parts of the forward amplitude, the ratio of elastic to total cross sections and the inelastic cross section are calculated. Predictions for the LHC energy region, where most of the exiting models will be either confirmed or ruled out, are presented.