Dense-Dilute Duality at work: dipoles of the target

Abstract

We explore the properties of the QCD high energy evolution in the limit of a dilute target. Using the recently established property of selfduality of the evolution operator (hep-ph/0502119), we show how to properly define the target gluon and dipole creation operators in terms of dual Wilson lines (dual eikonal factors). We explain how to expand these operators in terms of the functional derivatives of the color charge density, in the situation when they act on the eikonal factors of the projectile partons. We explicitly calculate the expansion of the high energy evolution operator to fourth order in the functional derivatives. Our result is infrared and ultraviolet finite, but does not coincide with the formula given in hep-ph/0501088. We resolve this discrepancy by showing that the identification of the dipole creation and annihilation operators used in hep-ph/0501088 is incomplete, and provide the required corrections to these definitions. The use of the corrected operators in the calculational framework of hep-ph/0501088 reproduces our result. We also prove that there is no discrepancy between the expansion of the JIMWLK equation and the dualization of the expansion of the weak field limit.

arXiv comment18 pages, Explanations added. Version to appear in PRD

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• On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture
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• Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
• The BFKL Pomeron Calculus in the dipole approach
• QCD unitarity constraints on Reggeon Field Theory
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• Langevin equation in effective theory of interacting QCD pomerons in the limit of large $N_c$
• Small-x QCD effects in forward-jet and Mueller-Navelet jet production
• CGC formalism with two sources
• On the Wess-Zumino term in high energy QCD
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• JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence
• Reggeon Field Theory and Self Duality: Making Ends Meet
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• On the anomalous dimensions of the multiple pomeron exchanges
• CGC for Ultra-Peripheral Pb+Pb Collisions at the Large Hadron Collider: a more realistic calculation
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• First correction to JIMWLK evolution from the classical equations of motion