Modeling the elastic differential cross-section at LHC

TL;DR

This paper proposes an empirical model for the proton-proton elastic differential cross section at LHC energies, combining exponential components and proton form factors to fit data and predict higher energy behaviors.

Contribution

It introduces a novel parametrization of the scattering amplitude inspired by earlier work, applicable to LHC and ISR data, and capable of making predictions at higher energies.

Findings

Model fits LHC7 and ISR data well

Enables predictions for higher LHC energies

Provides insights into asymptotic behavior of scattering

Abstract

An empirical model for the $pp$ elastic differential cross section is proposed. Inspired by early work by Barger and Phillips, we parametrize the scattering amplitude in building blocks, comprising of two exponentials with a relative phase, supplementing the dominant term at small $-t$ with the proton form factor. This model suitably applies to LHC7 and ISR data, enabling to make simple predictions for higher LHC energies and to check whether asymptotia might be achieved.