Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV

TL;DR

This paper analyzes LHC measurements of elastic proton-proton scattering at 7 and 8 TeV, confirming a zero in the real part of the amplitude near the forward region and making predictions for 13 TeV.

Contribution

It provides a detailed analysis of the scattering amplitudes, confirming theoretical predictions and identifying universal features in the elastic scattering process.

Findings

Confirmed the existence of a zero in the real part of the amplitude near the forward region.

Identified universal features and regularities in the scattering amplitudes.

Made quantitative predictions for elastic scattering at 13 TeV.

Abstract

Recent measurements of the differential cross sections in the forward region of pp elastic scattering at 7 and 8 TeV show precise form of the $t$ dependence. We propose a detailed analysis of these measurements including the structures of the real and imaginary parts of the scattering amplitude. A good description is achieved, confirming in all experiments the existence of a zero in the real part in the forward region close to the origin, in agreement with the prediction of a theorem by A. Martin, with important role in the observed form of $d\sigma/dt$. Universal value for the position of this zero and regularity in other features of the amplitudes are found, leading to quantitative predictions for the forward elastic scattering at 13 TeV.