Energy Conservation and Saturation in Small-x Evolution

Abstract

Important corrections to BFKL evolution are obtained from non-leading contributions and from non-linear effects due to unitarisation or saturation. It has been difficult to estimate the relative importance of these effects, as NLO effects are most easily accounted for in momentum space while unitarisation and saturation are easier in transverse coordinate space. An essential component of the NLO contributions is due to energy conservation effects, and in this paper we present a model for implementing such effects together with saturation in Mueller's dipole evolution formalism. We find that energy conservation severely dampens the small-x rise of the gluon density and, as a consequence, the onset of saturation is delayed. Using a simple model for the proton we obtain a reasonable qualitative description of the x-dependence of F2 at low Q^2 as measured at HERA even without saturation effects. We also give qualitative descriptions of the energy dependence of the cross section for gamma*-gamma* and gamma*-nucleus scattering.

References in corpus (26)

• Operator expansion for high-energy scattering
• 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
• BFKL pomeron in the next-to-leading approximation
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Energy Scale(s) and Next-to-leading BFKL Equation
• Single and Double BFKL Pomeron Exchange and a Dipole Picture of High Energy Hard Processes
• Deep-Inelastic Inclusive ep Scattering at Low x and a Determination of alpha_s
• Saturation and BFKL dynamics in the HERA data at small x
• Unitarity and the BFKL Pomeron
• A Modification of the Saturation Model: DGLAP evolution
• Solution to the evolution equation for high parton density QCD
• Renormalization Group Improved Small-x Equation
• Small x Phenomenology: Summary and Status
• Measurement of the Proton Structure Function F_2 at Very Low Q^2 at HERA
• Studies of Unitarity at Small~$x$ Using the Dipole Formulation
• Large multiplicity fluctuations and saturation effects in onium collisions
• On the Rise of the Proton Structure Function F_2 Towards Low x
• Extracting the dipole cross-section from photo- and electro-production total cross-section data
• Dijet Production at Hadron--Hadron Colliders in the BFKL Approach
• The Linked Dipole Chain Monte Carlo
• OEDIPUS: Onium Evolution, Dipole Interaction and Perturbative Unitarisation Simulation
• Soft emissions and the equivalence of BFKL and CCFM final states
• Investigations into the BFKL Mechanism with a Running QCD Coupling
• Energy Consumption and Jet Multiplicity from the Leading Log BFKL Evolution

Cited by in corpus (39)

• General-purpose event generators for LHC physics
• The Angantyr model for Heavy-Ion Collisions in PYTHIA8
• Improving the kinematics for low-x QCD evolution equations in coordinate space
• Effects of Colour Reconnection on Hadron Flavour Observables
• Inclusive and Exclusive observables from dipoles in high energy collisions
• Small x Phenomenology - summary of the 3rd Lund Small x Workshop in 2004
• Numerical solution of the nonlinear evolution equation at small x with impact parameter and beyond the LL approximation
• Multiparton Interactions with an x-dependent Proton Size
• Eccentricity and elliptic flow in proton-proton collisions from parton evolution
• Exact kinematics in the small x evolution of the color dipole and gluon cascade
• Small x nonlinear evolution with impact parameter and the structure function data
• Diffractive and non-diffractive wounded nucleons and final states in pA collisions
• Small-x Dipole Evolution Beyond the Large-N_c Limit
• Elastic and quasi-elastic $pp$ and ${\gamma }^{\star }p$ scattering in the Dipole Model
• Reggeon Field Theory for Large Pomeron Loops
• Correlations in double parton distributions at small x
• Soft gluons away from jets: distribution and correlation
• Exclusive vector meson production and small-x evolution
• Measurement of the inelastic cross section in proton-lead collisions at a centre-of-mass energy per nucleon pair of 5.02 TeV
• Diffractive Excitation in DIS and pp Collisions
• Fluctuations, Saturation, and Diffractive Excitation in High Energy Collisions
• QCD Challenges from pp to A-A Collisions
• On the role of NLL corrections and Energy Conservation in the High Energy Evolution of QCD
• CCFM Evolution with Unitarity Corrections
• Constraining high energy interaction mechanisms by studying forward hadron production at the LHC
• Geometric Scaling and QCD Dynamics in DIS
• Correlations in impact-parameter space in a hierarchical saturation model for QCD at high energy
• Exclusive final states in diffractive excitation
• Dipole evolution: perspectives for collectivity and ${\gamma }^{\ast }$A collisions
• On the different forms of the kinematical constraint in BFKL
• Travelling waves and impact-parameter correlations
• On the Dipole Swing and the Search for Frame Independence in the Dipole Model
• The BFKL Pomeron in the weak and strong coupling limits and kinematical constraints
• Gluon density fluctuations in dilute hadrons
• Coherent and incoherent diffractive hadron production in pA collisions and gluon saturation
• On the High Energy Behaviour of The Total Cross Section in the QCD Dipole Model
• Probing the low-x structure of nuclear matter with diffractive hadron production in pA collisions
• Anti-de Sitter D-brane dynamics
• Four-jet double parton scattering production in proton-nucleus collisions within the PYTHIA8 framework