Froissart Bound from Gluon Saturation

Abstract

We demonstrate that the dipole-hadron cross-section computed from the non-linear evolution equation for the Colour Glass Condensate saturates the Froissart bound in the case of a fixed coupling and for a small dipole (Q^2 >> Lambda_{QCD}^2). That is, the cross-section increases as the logarithm squared of the energy, with a proportionality coefficient involving the pion mass and the BFKL intercept (alpha_s N_c/pi)4 ln 2. The pion mass enters via the non-perturbative initial conditions at low energy. The BFKL equation emerges as a limit of the non-linear evolution equation valid in the tail of the hadron wavefunction. We provide a physical picture for the transverse expansion of the hadron with increasing energy, and emphasize the importance of the colour correlations among the saturated gluons in suppressing non-unitary contributions due to long-range Coulomb tails. We present the first calculation of the saturation scale including the impact parameter dependence. We show that the cross-section at high energy exhibits geometric scaling with a different scaling variable as compared to the intermediate energy regime.

42 pages, 5 included figures. A few references and explanations added. Some recent arguments concerning the role of the "white region" are clarified. Final version to appear in Nuclear Physics A

References in corpus (40)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• 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
• Green's Functions in the Color Field of a Large Nucleus
• The BFKL Equation from the Wilson Renormalization Group
• BFKL pomeron in the next-to-leading approximation
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Unitarization of the BFKL Pomeron on a Nucleus
• The Renormalization Group Equation for the Color Glass Condensate
• Unitarity at small Bjorken x
• Energy Scale(s) and Next-to-leading BFKL Equation
• Geometric scaling for the total gamma^* p cross section in the low x region
• Unitarity and the BFKL Pomeron
• The Energy Dependence of the Saturation Momentum
• Geometric Scaling above the Saturation Scale
• Parton Saturation at Small x and in Large Nuclei
• Solution to the evolution equation for high parton density QCD
• Saturation and Universality in QCD at small x
• Structure function of the nucleus in the perturbative QCD with $N_c\to \infty$ (BFKL pomeron fan diagrams)
• New Scaling at High Energy DIS
• Diffusion into infra-red and unitarization of the BFKL pomeron
• Hadronic scattering amplitudes: medium-energy constraints on asymptotic behaviour
• A Simple Derivation of the JIMWLK Equation
• Parton densities and dipole cross-sections at small x in large nuclei
• High-Energy QCD and Wilson Lines
• Nonlinear QCD Evolution: Saturation without Unitarization
• Nonlinear evolution in high-density QCD
• Nonlinear evolution and saturation for heavy nuclei in DIS
• Perturbative Saturation and the Soft Pomeron
• Properties of the BFKL equation and structure function predictions for HERA
• Inclusive and Diffractive Structure Functions at Small x
• Nuclear Structure Functions and Heavy Flavour Leptoproduction Off the Nucleus at Small x in Perturbative QCD
• Scaling phenomena from non-linear evolution in high energy DIS
• Long-Range Forces of QCD
• Non-linear evolution and parton distributions at LHC and THERA energies
• Froissart boundary for deep inelastic structure functions
• Gluon Radiation in Diffractive Electroproduction

Cited by in corpus (72)

• New Forms of QCD Matter Discovered at RHIC
• Saturation Physics and Deuteron--Gold Collisions at RHIC
• Evolution at small x_bj: The Color Glass Condensate
• 50 Years of Quantum Chromodynamics
• On solutions of the Balitsky-Kovchegov equation with impact parameter
• Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large N_c
• From DIS to proton-nucleus collisions in the Color Glass Condensate model
• A Gaussian effective theory for gluon saturation
• Exclusive vector meson production at HERA from QCD with saturation
• Shockwaves and deep inelastic scattering within the gauge/gravity duality
• Towards a New Global QCD Analysis: Solution to the Non-Linear Equation at Arbitrary Impact Parameter
• Saturation effects in exclusive rhoT, rhoL meson electroproduction
• Solution for the BFKL Pomeron Calculus in zero transverse dimensions
• How can the Odderon be detected at RHIC and LHC
• The Balitsky-Kovchegov equation in full momentum space
• Traveling waves and geometric scaling at non-zero momentum transfer
• The QCD Pomeron in ultraperipheral heavy ion collisions: III. Photonuclear production of heavy quarks
• High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution
• QCD Saturation in the Semi-classical Approach
• The Dipole Picture and Saturation in Soft Processes
• Scattering of color dipoles: from low to high energies
• Survival probability for exclusive central diffractive production of colorless states at the LHC
• CGC/saturation approach: a new impact-parameter dependent model in the next-to-leading order of perturbative QCD
• BFKL Pomeron with massive gluons
• Gluon saturation and the Froissart bound: a simple approach
• CGC/saturation approach: a new impact-parameter dependent model
• Geometric scaling in exclusive processes
• Impact Parameter Dependence in the Balitsky-Kovchegov Equation
• Finite-size effects on small-$x$ evolution and saturation in proton and nuclear targets
• How Pomerons Meet in Coloured Glass
• Heisenberg's Universal (lns)**2 Increase of Total Cross Sections
• Asymptotic Energy Dependence of Hadronic Total Cross Sections from Lattice QCD
• Liouville field theory for gluon saturation in QCD at high energy
• Hadronic total cross sections at high energy and the QCD spectrum
• Froissart bound and gluon number fluctuations
• BFKL Pomeron: modeling confinement
• Conformal symmetry and the Balitsky-Kovchegov equation
• QCD Saturation and ${\gamma }^{\ast }-{\gamma }^{\ast }$ Scattering
• Universal Rise of Hadronic Total Cross Sections based on Forward pi p and pbarp(pp) Scatterings
• Solution to the Balitsky-Kovchegov equation in the saturation domain
• Strongly Interacting Matter at High Energy Density
• Geometric Scaling in Mueller-Navelet Jets
• Gribov-Zwanziger confinement, high energy evolution and large impact parameter behaviour of the scattering amplitude
• Improvements to the Froissart bound from AdS/CFT
• Evolution equation for soft physics at high energy
• Test of Universal Rise of Hadronic Total Cross Sections based on pi p, Kp and pbar p,pp Scatterings
• Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops
• Semiclassical solution to the BFKL equation with massive gluons
• The Colour Glass Condensate
• Comments on high-energy total cross sections in QCD
• Large impact parameter behaviour in the CGC/saturation approach: a new non-linear equation
• On the High Energy Behaviour of The Total Cross Section in the QCD Dipole Model
• Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data
• The Froissart--Martin Bound for $\pi \pi$ Scattering in QCD
• Dipole-dipole scattering amplitude in CGC approach
• Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections
• BFKL pomeron with massive gluons and running coupling
• On the behaviour of single scale hard small $x$ processes in QCD near the black disc limit
• CGC/saturation approach: an impact-parameter dependent model for diffraction production in DIS
• Soft Pomeron in the Colour Glass Condensate approach
• Homotopy solution to non-linear evolution for heavy nuclei
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• CGC and saturation approach: Impact-parameter dependent model of perturbative QCD and combined HERA data
• Can $1/N_c$ corrections destroy the saturation of dipole densities?
• Rise of Kp Total Cross Section and Universality
• CGC for Ultra-Peripheral Pb+Pb Collisions at the Large Hadron Collider: a more realistic calculation
• Can Froissart Bound Explain Hadron Cross-Sections at High Energies?
• High energy evolution for Gribov-Zwanziger confinement: solution to the equation
• Dipole-pion cross section in the saturation regime
• Analytic Amplitudes for Hadronic Forward Scattering and the Heisenberg ln**2 Behaviour of Total Cross Section
• `Effective' Pomeron model at large $\mathbf{b}$
• Some remarks on geometric scaling