Solution for the BFKL Pomeron Calculus in zero transverse dimensions

Abstract

In this paper the exact analytical solution is found for the BFKL Pomeron calculus in zero transverse dimensions, in which all Pomeron loops have been included. The comparison with the approximate methods of the solution is given, and the kinematic regions are discussed where they describe the behaviour of the scattering amplitude quite well. In particular, the semi-classical approach is considered, which reproduces the main properties of the exact solution at large values of rapidity ($Y\ge 10$). It is shown that the mean field approximation leads to a good description of the scattering amplitude only if the amplitude at low energy is rather large. However, even in this case, it does not lead to the correct asymptotic behaviour of the scattering amplitude at high energies.

37 pages,19 figures and one table, the revised version

References in corpus (40)

• Saturation and BFKL dynamics in the HERA data at small x
• Geometric scaling as traveling waves
• Traveling wave fronts and the transition to saturation
• Universal features of JIMWLK and BK evolution at small x
• On solutions of the Balitsky-Kovchegov equation with impact parameter
• Small-x physics beyond the Kovchegov equation
• A Langevin equation for high energy evolution with pomeron loops
• Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity
• Extension of the JIMWLK Equation in the Low Gluon Density Region
• From Color Glass to Color Dipoles in high-energy onium--onium scattering
• Towards a symmetric approach to high energy evolution: generating functional with Pomeron loops
• In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term
• Effective Hamiltonian for QCD evolution at high energy
• Unintegrated gluon distribution from modified BK equation
• Rare fluctuations and the high-energy limit of the S-matrix in QCD
• Non-linear QCD evolution with improved triple-pomeron vertices
• A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei
• Interactions of Reggeized Gluons in the Möbius Representation
• From target to projectile and back again: selfduality of high energy evolution
• Balitsky's hierarchy from Mueller's dipole model and more about target correlations
• Pomeron Vertices in Perturbative QCD in Diffractive Scattering
• Towards a new global QCD analysis: low x DIS data from non-linear evolution
• Conformal invariant pomeron interaction in the perurbative QCD with large N_c
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• Remarks on High Energy Evolution
• Dense-Dilute Duality at work: dipoles of the target
• More Remarks on High Energy Evolution
• Towards a New Global QCD Analysis: Solution to the Non-Linear Equation at Arbitrary Impact Parameter
• Higher Order Effects in Non Linear Evolution from a Veto in Rapidities
• Pomeron loops in zero transverse dimensions
• Inclusive Gluon Production In High Energy Onium-Onium Scattering
• On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD
• High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution
• Diffractive dissociation from non-linear evolution in DIS on nuclei
• The Iancu-Mueller factorization and high energy asymptotic behaviour
• Algebraic models for the hierarchy structure of evolution equations at small x
• Color dipoles from Bremsstrahlung in QCD evolution at high energy
• A modified Balitsky-Kovchegov equation
• Conformal invariant equations for nucleus-nucleus scattering in perturbative QCD with $N_c\to \infty$
• Solution to the Balitsky-Kovchegov equation in the saturation domain

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• Soft interactions at high energies: QCD motivated approach
• Dipole-dipole scattering amplitude in CGC approach
• Effects of gluon number fluctuations on photon - photon collisions at high energies
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• Eikonal but not: a complementary view of high energy evolution
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