High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution

Abstract

In this paper an analytical solution for the high energy scattering amplitude is suggested. This solution has several unexpected features:(i) the asymptotic amplitude is a function of dipole sizes and, therefore, this amplitude shows the gray disc structure at high energy, instead of black disc behaviour which was expected; (ii) the amplitude approaches the asymptotic limit in the same way as the solution to the Balitsky-Kovchegov equation does ($\propto \exp (-C{Y}^2)$), but the coefficient $C$ in eight times smaller than for the Balitsky-Kovchegov equation; (iii) the process of merging of two dipoles into one, only influences the high energy asymptotic behaviour by changing the initial condition from $Z(Y;[u_i=1])=1$ to $Z(Y;[u_i=1-{\gamma }_{0,i}])=1$. The value of ${\gamma }_0$ is determined by the process of merging of two dipoles into one. With this new initial condition the Balitsky-JIMWLK approach describes the high energy asymptotic behaviour of the scattering amplitude without any modifications recently suggested.

37 pages with 4 figures in eps format, this version will appear in Nucl.Phys.A, a couple of references is added as well as comments on physics of the solution

References in corpus (17)

• 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
• In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term
• Effective Hamiltonian for QCD evolution at high energy
• 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
• Pomeron Vertices in Perturbative QCD in Diffractive Scattering
• Duality and Pomeron effective theory for QCD at high energy and large N_c
• 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
• QCD Saturation Equations including Dipole-Dipole Correlation

Cited by in corpus (25)

• Towards a symmetric approach to high energy evolution: generating functional with Pomeron loops
• Effective Hamiltonian for QCD evolution at high energy
• A QCD motivated model for soft interactions at high energies
• High-enegy effective action from scattering of QCD shock waves
• Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution
• One gluon, two gluon: multigluon production via high energy evolution
• Summing Pomeron loops in the dipole approach
• Treading on the cut: Semi inclusive observables at high energy
• Solution for the BFKL Pomeron Calculus in zero transverse dimensions
• The BFKL Pomeron Calculus in zero transverse dimensions: summation of Pomeron loops and generating functional for the multiparticle production processes
• Pomeron loops in zero transverse dimensions
• On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD
• QCD Reggeon Field Theory for every day: Pomeron loops included
• From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy
• The Yin and Yang of High Energy Chromodynamics: Scattering in Black and White
• The BFKL Pomeron Calculus in the dipole approach
• The BFKL Pomeron Calculus in zero transverse dimensions: diffractive processes and survival probability for central diffractive production
• Soft interactions at high energies: QCD motivated approach
• Dipole-dipole scattering amplitude in CGC approach
• On the anomalous dimensions of the multiple pomeron exchanges
• Soft Pomeron in the Colour Glass Condensate approach
• Eikonal but not: a complementary view of high energy evolution
• Fluctuating pulled fronts & Pomerons
• High energy scattering in QCD: dipole approach with Pomeron loops
• A geometrical scaling solution to the BFKL Pomeron Calculus in the saturation domain