Analyticity and scaling property of pp and p\=p forward scattering amplitudes

TL;DR

This paper revisits the analytic properties and scaling behavior of proton-proton and proton-antiproton forward scattering amplitudes using recent LHC data, confirming crossing symmetry and dispersion relation constraints, and providing predictions for higher energies.

Contribution

It introduces a new scaling function within Martin's model, demonstrating data consistency with crossing symmetry at LHC energies and enabling energy-independent amplitude predictions.

Findings

Data are consistent with crossing symmetry at 7 and 8 TeV.

The real part of the amplitude reproduces Martin's zero.

Model predicts behavior at higher and asymptotic energies.

Abstract

We analyse the pp elastic scattering amplitudes using the recent LHC data, revisiting the model proposed by A. Martin based on analytic continuation and crossing symmetry. Introducing a new form for the scaling function we show that the data are consistent with the crossing symmetry of the scattering amplitudes at $\sqrt{s}= $ 7 and 8 TeV. The complex amplitude automatically obeys the constraints of dispersion relations and their derivatives. The real part reproduces the zero predicted by A. Martin, which is crucial to describe with precision the differential cross section in the forward direction at LHC energies. Since the free parameters of the model are energy independent, the analytical form of the amplitude leads to predictions for higher and asymptotic energies.