Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity

Abstract

We study the effects of including a running coupling constant in high-density QCD evolution. For fixed coupling constant, QCD evolution preserves the initial dependence of the saturation momentum $Q_s$ on the nuclear size $A$ and results in an exponential dependence on rapidity $Y$, $Q_s^2(Y)=Q_s^2(Y_0)\exp [{\bar{\alpha }}_{s}d(Y-Y_0)]$. For the running coupling case, we re-derive analytical estimates for the $A$- and $Y$-dependences of the saturation scale and test them numerically. The $A$-dependence of $Q_s$ vanishes $\propto 1/\sqrt{Y}$ for large $A$ and $Y$. The $Y$-dependence is reduced to $Q_s^2(Y)\propto \exp ({\Delta }^{\prime }\sqrt{Y+X})$ where we find numerically ${\Delta }^{\prime }\simeq 3.2$. We study the behaviour of the gluon distribution at large transverse momentum, characterizing it by an anomalous dimension $1-\gamma$ which we define in a fixed region of small dipole sizes. In contrast to previous analytical work, we find a marked difference between the fixed coupling ($\gamma \simeq 0.65$) and running coupling ($\gamma \sim 0.85$) results. Our numerical findings show that both a scaling function depending only on the variable $r{Q}_s$ and the perturbative double-leading-logarithmic expression, provide equally good descriptions of the numerical solutions for very small $r$-values below the so-called scaling window.

LaTeX, 29 pages, 7 eps figures; discussion on DLL enlarged and comparison with sub-leading terms in the rapidity behaviour of the saturation scale added

References in corpus (8)

• Color Glass Condensate at the LHC: hadron multiplicities in $pp$, $pA$ and $AA$ collisions
• Relating high-energy lepton-hadron, proton-nucleus and nucleus-nucleus collisions through geometric scaling
• Universal behavior of QCD amplitudes at high energy from general tools of statistical physics
• Unintegrated gluon distribution from modified BK equation
• Higher Order Effects in Non Linear Evolution from a Veto in Rapidities
• The spread of the gluon k_t-distribution and the determination of the saturation scale at hadron colliders in resummed NLL BFKL
• Inclusive cross-sections for jet production in nucleus-nucleus collisions in perturbative QCD
• Saturation scale from the Balitsky-Kovchegov equation

Cited by in corpus (103)

• Saturation Physics and Deuteron--Gold Collisions at RHIC
• Quark contribution to the small-$x$ evolution of color dipole
• Triumvirate of Running Couplings in Small-x Evolution
• AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks
• Nuclear shadowing
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Non-linear QCD meets data: A global analysis of lepton-proton scattering with running coupling BK evolution
• Review of Jet Measurements in Heavy Ion Collisions
• Solving The High Energy Evolution Equation Including Running Coupling Corrections
• Single Inclusive Hadron Production at RHIC and the LHC from the Color Glass Condensate
• Long range two-particle rapidity correlations in A+A collisions from high energy QCD evolution
• Odderon in the Color Glass Condensate
• A Langevin equation for high energy evolution with pomeron loops
• Color Glass Condensate and Glasma
• Study of the Fundamental Structure of Matter with an Electron-Ion Collider
• Extension of the JIMWLK Equation in the Low Gluon Density Region
• Quark pair production in high energy pA collisions: General features
• Nuclear enhancement and suppression of diffractive structure functions at high energies
• Particle multiplicities in Lead-Lead collisions at the LHC from non-linear evolution with running coupling
• Unintegrated gluon distribution from modified BK equation
• Running coupling and power corrections in nonlinear evolution at the high--energy limit
• Dipole factorization for DIS at NLO: Combining the $q\bar{q}$ and $q\bar{q}g$ contributions
• Confronting impact parameter dependent JIMWLK evolution with HERA data
• The shape of the proton at high energies
• Gluon spectrum in the glasma from JIMWLK evolution
• High Gluon Densities in Heavy Ions Collisions
• Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation
• On the implementation of NLO high energy factorization in single inclusive forward hadron production
• Saturation physics at HERA and RHIC: An unified description
• Limiting fragmentation in hadron-hadron collisions at high energies
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• Summing Pomeron loops in the dipole approach
• Small x physics and RHIC data
• The high energy asymptotics of scattering processes in QCD
• Treading on the cut: Semi inclusive observables at high energy
• Solution for the BFKL Pomeron Calculus in zero transverse dimensions
• Solution to the Balitsky-Kovchegov equation with the collinearly improved kernel including impact-parameter dependence
• The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes
• Color Glass Condensate and Glasma
• Pomeron loop and running coupling effects in high energy QCD evolution
• Running Coupling Corrections to High Energy Inclusive Gluon Production
• First analysis of world polarized DIS data with small-$x$ helicity evolution
• Could saturation effects be visible in a future electron-ion collider?
• The Balitsky-Kovchegov equation in full momentum space
• Comparing AdS/CFT Calculations to HERA F_2 Data
• The neutrino-nucleon cross section at UHE and its astrophysical implications
• Limiting fragmentation in heavy-ion collisions and percolation of strings
• Nuclear size and rapidity dependence of the saturation scale from QCD evolution and experimental data
• On the long-range correlations in hadron-nucleus collisions
• Initial state and thermalization in the Color Glass Condensate framework
• Probing the Color Glass Condensate in an electron-ion collider
• Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
• Percolation Effects in Very High Energy Cosmic Rays
• The BFKL Pomeron Calculus in the dipole approach
• Long range correlations, event simulation and parton percolation
• Heavy quarkonium production: Nontrivial transition from pA to AA collisions
• Impact Parameter Dependence in the Balitsky-Kovchegov Equation
• O(α_s^2)-corrections to JIMWLK evolution from the classical equations of motion
• Exclusive photoproduction of vector meson at next-to-leading order from Color Glass Condensate
• Mutual boosting of the saturation scales in colliding nuclei
• Testing Non-linear Evolution with Running Coupling Corrections in $ep$ and $pp$ collisions
• The Color Glass Condensate: an overview
• Diffractive deep inelastic scattering in an AdS/CFT inspired model: A phenomenological study
• Lecture notes on "Quantum chromodynamics and statistical physics"
• R-Current DIS on a Shock Wave: Beyond the Eikonal Approximation
• On correlations and discreteness in non-linear QCD evolution
• Conformal symmetry and the Balitsky-Kovchegov equation
• BFKL Pomeron: modeling confinement
• Running Coupling Corrections to Nonlinear Evolution for Diffractive Dissociation
• A simple model for the nuclear unintegrated gluon distribution
• Non-linear QCD dynamics in two-photon interactions at high energies
• Compatibility of phenomenological dipole cross sections with the Balitsky-Kovchegov equation
• CGC and initial state effects in Heavy Ion Collisions
• Solutions to the Balitsky-Kovchegov equation including the dipole orientation
• Universality of QCD traveling-waves with running coupling
• Universality of traveling waves with QCD running coupling
• Rare fluctuations of the $S$-matrix at NLO in QCD
• Rapidity gap distribution in diffractive dissociation: predictions for future electron-ion colliders
• Nuclear Shadowing in the Holographic Framework
• Single diffractive production of open heavy flavor mesons
• Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method
• Brief Review of Saturation Physics
• Saturation and linear transport equation
• Resummation of double collinear logs in BK evolution versus HERA data
• Nuclear scattering configurations of onia in different frames
• Solution to the Sudakov suppressed Balitsky-Kovchegov equation and its application to the HERA data
• An analytical solution of Balitsky-Kovchegov equation using homotopy perturbation method
• Parametrization of the nuclear structure function
• A unitarized model of inclusive and diffractive DIS with Q2-evolution
• The Status of Parton Saturation and the CGC
• Infrared instability from nonlinear QCD evolution
• Nuclear Structure Functions at Low-$x$ in a Holographic Approach
• Soft processes at high energy without soft Pomeron: a QCD motivated model
• On the solution of linearized (linear in S-matrix) Balitsky-Kovchegov equation
• Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering
• Saturation momentum at fixed and running QCD coupling
• First correction to JIMWLK evolution from the classical equations of motion
• Evaluating the ratio of the exclusive vector meson photoproduction to inclusive hadron/jet production cross section in ultraperipheral heavy ion collisions
• Particle Multiplicities in Nuclear Collisions at the LHC from Saturation Physics
• Scattering off the Color Glass Condensate
• A predictive phenomenological tool at small Bjorken-x
• Invariant color calculus and generalized Balitsky-Kovchegov hierarchy
• Saturation in nuclei