The chaotic effects in a nonlinear QCD evolution equation

Abstract

The corrections of gluon fusion to the DGLAP and BFKL equations are discussed in a united partonic framework. The resulting nonlinear evolution equations are the well-known GLR-MQ-ZRS equation and a new evolution equation. Using the available saturation models as input, we find that the new evolution equation has the chaos solution with positive Lyaponov exponents in the perturbative range. We predict a new kind of shadowing caused by chaos, which blocks the QCD evolution in a critical small $x$ range. The blocking effect in the evolution equation may explain the Abelian gluon assumption and even influence our expectations to the projected Large Hadron Electron Collider (LHeC), Very Large Hadron Collider (VLHC) and the upgrade (CppC) in a circular $e^{+}{e}^{-}$ collider (SppC).

58 pages, 23 figures,. Final version to appear in NPB

References in corpus (20)

• Operator expansion for high-energy scattering
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction
• BFKL pomeron in the next-to-leading approximation
• Unitarization of the BFKL Pomeron on a Nucleus
• Saturation in Diffractive Deep Inelastic Scattering
• Unitarity and the BFKL Pomeron
• Manifestations of high density QCD in the first RHIC data
• A unified BFKL and GLAP description of $F_2$ data
• Hadronic final state predictions from CCFM: the hadron-level Monte Carlo generator CASCADE
• Small x Phenomenology: Summary and Status
• Properties of the BFKL equation and structure function predictions for HERA
• A new approach to parton recombination in a QCD evolution equation
• A new modified Altarelli-Parisi evolution equation with parton recombination in proton
• A Numerical Estimate of the Small-$k_T$ Region in the BFKL Pomeron
• Can a chaotic solution in the QCD evolution equation restrain high-energy collider physics?
• Antishadowing effects in the unitarized BFKL equation
• Applications of a nonlinear evolution equation II: the EMC effect
• BFKL equation for an integrated gluon density
• Electron-Ion Physics with the LHeC

Cited by in corpus (16)

• Insights into the Emergence of Mass from Studies of Pion and Kaon Structure
• The gluon condensation at high energy hadron collisions
• The Gluon condensation in high energy cosmic rays
• A possible evidence of the gluon condensation effect in cosmic positron and gamma-ray spectra
• Looking for the gluon condensation signature in proton using the Earth limb gamma-ray spectra
• The gluon condensation in hadron collisions
• Small-x analysis on the effect of gluon recombinations inside hadrons in light of the GLR-MQ-ZRS equation
• Looking for the possible gluon condensation signature in sub-TeV gamma-ray spectra: from active galactic nuclei to gamma ray bursts
• Exploring the possible gluon condensation signature in gamma-ray emission from pulsars
• Gluon Condensation Signature in the GeV Gamma-Ray Spectra of Pulsars
• The current recorded signals of ultrahigh-energy $\gamma$-rays may come from EeVatrons in the galaxy
• Warning: The mini gamma-ray-bursts in planning hadron colliders beyond the LHC energies
• The gluon condensation effect in the cosmic hadron spectra
• Research on electron and positron spectrum in the high-energy region based on the gluon condensation model
• Nonlinear corrections to the nuclear heavy flavor structure functions
• Explaining muon excess in cosmic rays using the gluon condensation model