Elastic proton-proton scattering from ISR to LHC energies, focusing on the dip region

TL;DR

This paper analyzes elastic proton-proton scattering across ISR to LHC energies using a quark-diquark model, revealing that the total cross-section increase is linked to quark-diquark separation and proposing relations to predict the dip position in the differential cross-section.

Contribution

It introduces a generalized quark-diquark model and phenomenological relations connecting total cross-section, particle sizes, and dip position, aiding future predictions.

Findings

Total cross-section increase linked to quark-diquark separation.

Derived model-independent relation: t(dip) * sigma(tot) ~ const.

Predicted dip positions for future collider energies.

Abstract

The differential cross-section of elastic proton-proton collisions is studied at ISR and LHC energies, utilizing a quark-diquark model, that generalizes earlier models of Bialas and Bzdak, and, in addition, a model of Glauber and Velasco. These studies suggest that the increase of the total pp cross-section is mainly due to an increase of the separation of the quark and the diquark with increasing energies. Within the investigated class of models, two simple and model-independent phenomenological relations were found, that connect the total pp scattering cross-section to the effective quark, diquark size and their average separation, on one hand, and to the position of the dip of the differential cross-section, on the other hand. The latter t(dip) sigma(tot) ~ const relation can be used to predict t(dip), the position of the dip of elastic pp scattering for future colliding energies, and for other reactions, where sigma(tot) is either known or can be reliably estimated.