Evolution equation for elastic scattering of hadrons

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.

arXiv comment6 pages, 3 figures and 2 tables

References in corpus (26)

• Operator expansion for high-energy scattering
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• The Wilson renormalization group for low x physics: towards the high density regime
• The BFKL Equation from the Wilson Renormalization Group
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Unitarity at small Bjorken x
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Relating different approaches to nonlinear QCD evolution at finite gluon density
• Geometric scaling as traveling waves
• Vector potential versus colour charge density in low-x evolution
• On solutions of the Balitsky-Kovchegov equation with impact parameter
• Perturbative Odderon in the Dipole Model
• Elastic differential cross-section measurement at $\sqrt{s}=13$ TeV by TOTEM
• Elastic differential cross-section $\mathrm{d}\sigma /\mathrm{d}t$ at $\sqrt{s}=$2.76 TeV and implications on the existence of a colourless 3-gluon bound state
• A theorem on the real part of the high-energy scattering amplitude near the forward direction
• The interaction region of high energy protons
• Onium-Onium scattering at fixed impact parameter: exact equivalence between the color dipole model and the BFKL Pomeron
• Evidence of Odderon-exchange from scaling properties of elastic scattering at TeV energies
• Traveling waves and geometric scaling at non-zero momentum transfer
• Proton structure and hollowness from Lévy imaging of $pp$ elastic scattering
• Observation of Odderon Effects at LHC energies -- A Real Extended Bialas-Bzdak Model Study
• Scaling properties of elastic proton-proton scattering at LHC energies
• Large impact parameter behaviour in the CGC/saturation approach: a new non-linear equation
• Traveling wave solution of the Reggeon Field Theory
• Analytical representation for amplitudes and differential cross section of pp elastic scattering at 13 TeV