Elastic scattering of protons from sqrt{s}=23.5 GeV to 7 TeV from a generalized Bialas-Bzdak model

TL;DR

This paper extends the Bialas-Bzdak model to include a non-zero real part of the scattering amplitude, improving its fit to experimental data across a wide energy range and revealing energy-dependent proton structure changes.

Contribution

The model is generalized to account for a non-vanishing real part of the scattering amplitude, enhancing its accuracy in describing elastic scattering data at various energies.

Findings

The generalized model fits ISR and LHC data well.

The increase in total cross-section is linked to larger quark-diquark distances.

Two phenomenological relations connect cross-section, dip position, and proton radius.

Abstract

The Bialas-Bzdak model of elastic proton-proton scattering is generalized to the case when the real part of the parton-parton level forward scattering amplitude is non-vanishing. Such a generalization enables the model to describe well the dip region of the differential cross-section of elastic scattering at the ISR energies, and improves significantly the ability of the model to describe also the recent TOTEM data at sqrt{s} = 7 TeV LHC energy. Within this framework, both the increase of the total cross-section, as well as the decrease of the location of the dip with increasing colliding energies, is related to the increase of the quark-diquark distance and to the increase of the "fragility" of the protons with increasing energies. In addition, we present and test the validity of two new phenomenological relations: one of them relates the total p+p cross-section to an effective, model-independent proton radius, while the other relates the position of the dip in the differential elastic cross-section to the measured value of the total cross-section.