On the behaviour of single scale hard small $x$ processes in QCD near the black disc limit

Abstract

We argue that at sufficiently small Bjorken $x$ where pQCD amplitude rapidly increases with energy and violates probability conservation the shadowing effects in the single-scale small $x$ hard QCD processes can be described by an effective quantum field theory of interacting quasiparticles. The quasiparticles are the perturbative QCD ladders. We find, within the WKB approximation, that the smallness of the QCD coupling constant ensures the hierarchy among many-quasiparticle interactions evaluated within physical vacuum and in particular, the dominance in the Lagrangian of the triple quasiparticle interaction. It is explained that the effective field theory considered near the perturbative QCD vacuum contains a tachyon relevant for the divergency of the perturbative QCD series at sufficiently small $x$. We solve the equations of motion of the effective field theory within the WKB approximation and find the physical vacuum and the transitions between the false (perturbative) and physical vacua. Classical solutions which dominate transitions between the false and physical vacua are kinks that cannot be decomposed into perturbative series over the powers of ${\alpha }_s$. These kinks lead to color inflation and the Bose-Einstein condensation of quasiparticles. The account of the quantum fluctuations around the WKB solution reveals the appearance of the "massless" particles-- "phonons". It is explained that "phonons" are relevant for the black disc behaviour of small $x$ processes, leading to a Froissart rise of the cross-section. The condensation of the ladders produces a color network occupying a "macroscopic" longitudinal volume. We discuss briefly the possible detection of new QCD effects.

arXiv comment24 pages, 1 Figure. References added, and several misprints eliminated

References in corpus (34)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• 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
• Factorization for hard exclusive electroproduction of mesons in QCD
• The Intrinsic Glue Distribution at Very Small 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
• Diffractive Leptoproduction of Vector Mesons in QCD
• Small-x physics in perturbative QCD
• Fock Space Distributions, Structure Functions, Higher Twists and Small x
• On Exact Tachyon Potential in Open String Field Theory
• Renormalization Group Improved Small-x Equation
• Classical Gluon Radiation in Ultrarelativistic Nucleus-Nucleus Collisions
• HERA Collider Physics
• Froissart Bound from Gluon Saturation
• No Froissart Bound from Gluon Saturation
• Perturbative Saturation and the Soft Pomeron
• New evidence for the saturation of the Froissart bound
• Signals for black body limit in coherent ultraperipheral heavy ion collisions
• Diffractive Dissociation and Eikonalization in High Energy pp and p $\bar{p}$ Collisions
• Revealing the black-body regime of small-x deep-inelastic scattering through final-state signals
• Can Thermalization in Heavy Ion Collisions be Described by QCD Diagrams?
• Tunneling transition to the Pomeron regime
• On the Triple Pomeron Vertex in Perturbative QCD
• Color coherent phenomena on nuclei and the QCD evolution equation
• p p Elastic Scattering at LHC and Nucleon Structure
• The Role of Screening Corrections in High Energy Photoproduction
• Impact Parameter Dependence in the Balitsky-Kovchegov Equation
• Large distance behaviour of light cone operator product in perturbative and nonperturbative QCD regimes
• On the increase with relative distances of light cone operator product of currents and related phenomena

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