To the theory of high-energy elastic nucleon collisions

TL;DR

This paper critiques the West and Yennie formula for elastic nucleon scattering, introduces a more general interference model, and discusses implications for luminosity measurements at the LHC.

Contribution

It presents a generalized interference formula based on the eikonal model, overcoming limitations of the West and Yennie approach, and analyzes its impact on high-energy elastic scattering predictions.

Findings

West and Yennie formula requires constant phase assumption

Generalized eikonal model does not have this limitation

Luminosity determination errors could reach 5% using traditional methods

Abstract

The commonly used West and Yennie integral formula for the relative phase between the Coulomb and elastic hadronic amplitudes requires for the phase of the elastic hadronic amplitude to be constant at all kinematically allowed values of t. More general interference formula based on the eikonal model approach does not exhibit such limitation. The corresponding differences will be demonstrated and some predictions of different phenomenological models for elastic pp scattering at energy of 14 TeV at the LHC will be given. Special attention will be devoted to determination of luminosity from elastic scattering data; it will be shown that the systematic error might reach till 5 % if the luminosity is derived from the values in the center of the interference region with the help of West and Yennie formula.