On correlations and discreteness in non-linear QCD evolution

Abstract

We consider modifications of the standard non-linear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities $y=({\alpha }_s{N}_c/\pi )Y<10$. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut-off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cut-off evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cut-off. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients.

20 pages, LaTeX, 18 eps figures included using epsfig; changes in v3: new kind of averaging added, 5 new plots, discussions and conclusions extended, final version

References in corpus (64)

• 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
• Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction
• The Wilson renormalization group for low x physics: towards the high density regime
• Green's Functions in the Color Field of a Large Nucleus
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• The Renormalization Group Equation for the Color Glass Condensate
• The Intrinsic Glue Distribution at Very Small x
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Unitarity at small Bjorken x
• Relating different approaches to nonlinear QCD evolution at finite gluon density
• The Energy Dependence of the Saturation Momentum
• Geometric Scaling above the Saturation Scale
• Geometric scaling as traveling waves
• Solution to the evolution equation for high parton density QCD
• Traveling wave fronts and the transition to saturation
• Relating high-energy lepton-hadron, proton-nucleus and nucleus-nucleus collisions through geometric scaling
• Structure function of the nucleus in the perturbative QCD with $N_c\to \infty$ (BFKL pomeron fan diagrams)
• Universal features of JIMWLK and BK evolution at small x
• Energy Dependence of the Cronin Effect from Non-Linear QCD Evolution
• Vector potential versus colour charge density in low-x evolution
• Universal behavior of QCD amplitudes at high energy from general tools of statistical physics
• Small-x physics beyond the Kovchegov equation
• A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts
• A Langevin equation for high energy evolution with pomeron loops
• Diffusion into infra-red and unitarization of the BFKL pomeron
• Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity
• Studies of Unitarity at Small~$x$ Using the Dipole Formulation
• Universality and tree structure of high energy QCD
• A Simple Derivation of the JIMWLK Equation
• Extension of the JIMWLK Equation in the Low Gluon Density Region
• Parton densities and dipole cross-sections at small x in large nuclei
• Towards a symmetric approach to high energy evolution: generating functional with Pomeron loops
• Effective Hamiltonian for QCD evolution at high energy
• In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term
• Non-linear QCD evolution with improved triple-pomeron vertices
• A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei
• From target to projectile and back again: selfduality of high energy evolution
• Non linear gluon evolution in path-integral form
• Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large N_c
• Balitsky's hierarchy from Mueller's dipole model and more about target correlations
• Scaling phenomena from non-linear evolution in high energy DIS
• Nuclear A-dependence near the Saturation Boundary
• Remarks on High Energy Evolution
• Dense-Dilute Duality at work: dipoles of the target
• The high energy asymptotics of scattering processes in QCD
• Parton densities and saturation scale from non-linear evolution in DIS on nuclei
• Fluctuations effects in high-energy evolution of QCD
• Pomeron loops in zero transverse dimensions
• Duality and Pomeron effective theory for QCD at high energy and large N_c
• On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD
• Nuclear size and rapidity dependence of the saturation scale from QCD evolution and experimental data
• On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture
• Gluon shadowing in the low x region probed by the LHC
• Color dipoles from Bremsstrahlung in QCD evolution at high energy
• Consequences of strong fluctuations on high-energy QCD evolution
• QCD saturation in the dipole sector with correlations
• Chaos in the Color Glass Condensate
• Traveling waves in discretized Balitsky-Kovchegov evolution
• Saturation scale from the Balitsky-Kovchegov equation
• Dipole amplitude correlation in saturation model beyond mean field approximation

Cited by in corpus (13)

• Angular Correlations in Gluon Production at High Energy
• Angular and long range rapidity correlations in particle production at high energy
• Diffusive scaling and the high-energy limit of deep inelastic scattering in QCD at large N_c
• On Angular Correlations and High Energy Evolution
• Treading on the cut: Semi inclusive observables at high energy
• On the probability distribution of the stochastic saturation scale in QCD
• Correlation of small-x gluons in impact parameter space
• Quenching of Leading Jets and Particles: the p_t Dependent Landau-Pomeranchuk-Migdal effect from Nonlinear k_t Factorization
• Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
• O(α_s^2)-corrections to JIMWLK evolution from the classical equations of motion
• Antishadowing effects in the unitarized BFKL equation
• Dense-dilute factorization for a class of stochastic processes and for high energy QCD
• First correction to JIMWLK evolution from the classical equations of motion