On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD

Abstract

We study some structural aspects of the evolution equations with Pomeron loops recently derived in QCD at high energy and for a large number of colors, with the purpose of clarifying their probabilistic interpretation. We show that, in spite of their appealing dipolar structure and of the self-duality of the underlying Hamiltonian, these equations cannot be given a meaningful interpretation in terms of a system of dipoles which evolves through dissociation (one dipole splitting into two) and recombination (two dipoles merging into one). The problem comes from the saturation effects, which cannot be described as dipole recombination, not even effectively. We establish this by showing that a (probabilistically meaningful) dipolar evolution in either the target or the projectile wavefunction cannot reproduce the actual evolution equations in QCD.

31 pages, 2 figures

References in corpus (23)

• Evolution at small x_bj: The Color Glass Condensate
• Universal behavior of QCD amplitudes at high energy from general tools of statistical physics
• Odderon in the Color Glass Condensate
• A Langevin equation for high energy evolution with pomeron loops
• Extension of the JIMWLK Equation in the Low Gluon Density Region
• 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
• 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
• Conformal invariant pomeron interaction in the perurbative QCD with large N_c
• High-enegy effective action from scattering of QCD shock waves
• Dense-Dilute Duality at work: dipoles of the target
• The high energy asymptotics of scattering processes in QCD
• More Remarks on High Energy Evolution
• Fluctuations effects in high-energy evolution of QCD
• Duality and Pomeron effective theory for QCD at high energy and large N_c
• Inclusive Gluon Production In High Energy Onium-Onium Scattering
• High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution
• On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture
• Color dipoles from Bremsstrahlung in QCD evolution at high energy
• QCD saturation in the dipole sector with correlations

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• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
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• Soft Pomeron in the Colour Glass Condensate approach
• Resummation of projectile-target multiple scatterings and parton saturation
• Spin-glass model of QCD near saturation
• High energy scattering in QCD: dipole approach with Pomeron loops
• From QCD at high energy to statistical physics and back