Evolution equation for elastic scattering of hadrons

TL;DR

This paper develops an evolution equation based on Regge Field Theory to model high energy elastic hadron scattering, successfully matching experimental data and predicting nonlinear effects and novel phenomena.

Contribution

It introduces a complex nonlinear reaction-diffusion evolution equation for hadron scattering, incorporating data-driven initial conditions and capturing nonlinear effects at current energies.

Findings

Numerical results agree with LHC data for pp differential cross sections.

Nonlinear effects are significant at current energies, nearing the unitarity bound.

Predictions include nuclear matter hollowness and stationary points in momentum transfer.

Abstract

We turn high energy elastic scattering of hadrons into an initial value problem using an evolution equation based on the Regge Field Theory, which has a form of the complex nonlinear reaction-diffusion equation, with time being played by the logarithm of energy. The initial conditions are provided by the data-driven models for the real and imaginary parts of the amplitude. Numerical calculations of pp differential cross sections and forward quantities for LHC energies agree very well with experimental data extending up to, and including the diffractive cone. Furthermore, we show that at current accessible energies the non-linear effects play an important role, as the impact parameter space profiles approach the unitarity bound. The equation also predicts some other effects discussed in the literature, like the hollowness of nuclear matter or existence of stationary points in momentum transfer t.