# Forward scattering amplitudes of pp and p\=p with crossing symmetry and scaling properties

## TL;DR

This paper investigates proton-proton and proton-antiproton elastic scattering amplitudes using crossing symmetry and scaling properties, confirming their consistency across a wide energy range and enabling predictions at higher energies.

## Contribution

It introduces a new scaling function and analytical form for scattering amplitudes that incorporate crossing symmetry and analyticity, extending previous models.

## Key findings

- Data are consistent with crossing symmetry from 23 GeV to 13 TeV.
- The real part of the amplitude reproduces Martin's zero, improving differential cross section descriptions.
- The model's parameters are energy-independent, allowing reliable predictions at higher energies.

## Abstract

We analyse the pp and p\=p elastic scattering amplitudes using the data of several CERN and FERMILAB experiments, revisiting ideas proposed by Andr\'e Martin based on analytic continuation and crossing symmetry. Introducing a new form for the scaling function together with the analytical forms from COMPETE at $t=0$ we show that the data are consistent with the crossing symmetry of the scattering amplitudes from $\sqrt{s}= $ 23 GeV to 13 TeV for $-t\leq 0.2$ GeV$^{2}$. Analiticity and crossing symmetry automatically satisfy the dispersion relations and their derivatives. The real part reproduces the zero predicted by Martin, which is crucial to describe with precision the differential cross section in the forward range at high energies. Since the free parameters of the model are energy independent, the analytical form of the amplitude allows predictions for intermediate and higher energies.