The interaction region of high energy protons

TL;DR

This paper analyzes high-energy proton-proton collisions at the LHC, revealing how the interaction region's shape and opacity evolve with energy, and estimates the real-to-imaginary ratio of the scattering amplitude outside the diffraction cone.

Contribution

It introduces a unitarity-based method to determine the interaction region's shape and opacity at LHC energies, providing new estimates of the scattering amplitude ratio outside the diffraction cone.

Findings

Protons become fully absorptive at small impact parameters at LHC energies.

The shape of the interaction region may evolve from a dark core to a transparent torus.

The real-to-imaginary ratio of the scattering amplitude outside the diffraction cone is estimated for the first time.

Abstract

New experimental data about proton-proton collisions obtained atthe LHC allow to widen strongly the energy interval where one gets some knowledge about the structure of their interaction region. Using the unitarity relation in combination with experimental data about the elastic scattering in the diffraction cone, it is shown how the shape and the darkness of the interaction region of colliding protons change with increase of their energies. In particular, the collisions become fully absorptive at small impact parameters at LHC energies that results in some special features of inelastic processes as well. Possible evolution of the shape from the dark core at the LHC to the fully transparent one is discussed that implies the terminology of the black disk would be replaced by the black torus. The parameter which determines the opacity of central collisions also plays a crucial role in the behavior of the differential cross section of elastic scattering outside the diffraction cone where the predictions of all phenomenological models failed at LHC energies. The role of the ratio of real to imaginary part of the elastic scattering amplitude at non-forward scattering becomes decisive there as seen from the unitarity condition. The obtained results allow to estimate this ratio outside the diffraction cone for the first time by comparison with experiment at LHC energies which happens to be drastically different from its values measured at forward scattering. Moreover, the behaviors of the real and imaginary parts separately differ in different phenomeno- logical models and in the approach based on the unitarity condition. This problem is still waiting for its resolution. All the conclusions are only obtained in the framework of the indubitable unitarity condition using experimental data about the elastic scattering.