Excitation function of elastic $pp$ scattering from a unitarily extended Bialas-Bzdak model

TL;DR

This paper extends the Bialas-Bzdak model to include real parts in the scattering amplitude, enabling accurate descriptions of elastic $pp$ scattering across a wide energy range and predicting future collider results.

Contribution

The model is extended to incorporate arbitrary real parts while satisfying unitarity, improving its applicability to high-energy elastic $pp$ scattering data.

Findings

Successfully describes elastic $pp$ scattering at ISR and 7 TeV energies.

Predicts differential and total cross-sections at future LHC energies.

Identifies non-exponential features in the differential cross-section.

Abstract

The Bialas-Bzdak model of elastic proton-proton scattering assumes a purely imaginary forward scattering amplitude, which consequently vanishes at the diffractive minima. We extended the model to arbitrarily large real parts in a way that constraints from unitarity are satisfied. The resulting model is able to describe elastic $pp$ scattering not only at the lower ISR energies but also at $\sqrt{s}=$7~TeV in a statistically acceptable manner, both in the diffractive cone and in the region of the first diffractive minimum. The total cross-section as well as the differential cross-section of elastic proton-proton scattering is predicted for the future LHC energies of $\sqrt{s}=$13, 14, 15~TeV and also to 28~TeV. A non-trivial, significantly non-exponential feature of the differential cross-section of elastic proton-proton scattering is analyzed and the excitation function of the non-exponential behavior is predicted. The excitation function of the shadow profiles is discussed and related to saturation at small impact parameters.