Conformal invariant saturation

Abstract

We show that, in onium-onium scattering at (very) high energy, a transition to saturation happens due to quantum fluctuations of QCD dipoles. This transition starts when the order ${\alpha }^2$ correction of the dipole loop is compensated by its faster energy evolution, leading to a negative interference with the tree level amplitude. After a derivation of the the one-loop dipole contribution using conformal invariance of the elastic 4-gluon amplitude in high energy QCD, we obtain an exact expression of the saturation line in the plane (Y,L) where Y is the total rapidity and L, the logarithm of the onium scale ratio. It shows universal features implying the Balitskyi - Fadin - Kuraev - Lipatov (BFKL) evolution kernel and the square of the QCD triple Pomeron vertex. For large L, only the higher BFKL Eigenvalue contributes, leading to a saturation depending on leading log perturbative QCD characteristics. For initial onium scales of same order, however, it involves an unlimited summation over all conformal BFKL Eigenstates. In all cases, conformal invariance is preserved for the saturation mechanism based on dipole loops.

15 pages,3 eps figures; Version to be published in Nucl.Phys.B., one more figure, writing improvements, results and conclusion unchanged

References in corpus (8)

• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Saturation and Universality in QCD at small x
• New Scaling at High Energy DIS
• High-Energy QCD and Wilson Lines
• Impact parameter dependent S-matrix for dipole-proton scattering from diffractive meson electroproduction
• Nonlinear evolution and saturation for heavy nuclei in DIS
• Saturation model for two-photon interactions at high energies
• The Color Glass Condensate and Small x Physics: 4 Lectures

Cited by in corpus (29)

• Towards a symmetric approach to high energy evolution: generating functional with Pomeron loops
• From target to projectile and back again: selfduality of high energy evolution
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• Summing Pomeron loops in the dipole approach
• Treading on the cut: Semi inclusive observables at high energy
• More Remarks on High Energy Evolution
• Solution for the BFKL Pomeron Calculus in zero transverse dimensions
• High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution
• QCD Saturation in the Semi-classical Approach
• The Iancu-Mueller factorization and high energy asymptotic behaviour
• From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy
• Unitarisation of the hard pomeron and black-disk limit at the LHC
• The BFKL Pomeron Calculus in the dipole approach
• Perturbative QCD and beyond: azimuthal angle correlations in deuteron-deuteron scattering from Bose-Einstein correlations
• CGC/saturation approach for high energy soft interactions: `soft' Pomeron structure and $v_n$ in hadron and nucleus collisions from Bose-Einstein correlation
• CGC/saturation approach for high energy soft interactions: ${\mathbf{v}}_2$ in proton-proton collisions
• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
• Stretched String with Self-Interaction at High Resolution: Spatial Sizes and Saturation
• Streched String with Self-Interaction at the Hagedorn Point: Spatial Sizes and Black Hole
• Survival probability in diffractive Higgs production in high density QCD
• On the anomalous dimensions of the multiple pomeron exchanges
• Azimuthal angle correlations at large rapidities: revisiting density variation mechanism
• The BFKL Pomeron calculus: summing enhanced diagrams
• Summing loops in QCD: Exclusive Higgs production and the survival probability
• Pomeron loop summation in perturbative QCD and the survival probability
• The Schwinger-Dyson equation on Pomeron loop summation and renormalization
• Energy evolution and the Bose-Einstein enhancement for double parton densities
• `Effective' Pomeron model at large $\mathbf{b}$
• A geometrical scaling solution to the BFKL Pomeron Calculus in the saturation domain