In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term

TL;DR

Addresses how to extend the JIMWLK evolution to dilute hadronic systems where Pomeron loops are important. By boosting the hadronic wave function and employing a functional integral with a Wess-Zumino term, the authors derive a corrected evolution equation for the weight functional W[ρ], including a resummed path-ordered exponential of functional derivatives that encodes low-density corrections. The main result reveals a second term in ∂W/∂Y involving a path-ordered exponential that acts on the ρ-dependence, hinting at a duality between high- and low-density regimes. The work clarifies the role of noncommutativity in high-energy QCD and establishes a framework for more accurate evolution across density regimes, with implications for unitarization and Pomeron loop dynamics.

Abstract

We derive corrections to the JIMWLK equation in the regime where the charge density in the hadronic wave function is small. We show that the framework of the JIMWLK equation has to be significantly modified at small densities in order to properly account for the noncommutativity of the charge density operators. In particular the weight function for the calculation of averages can not be real, but is shown to contain the Wess-Zumino term. The corrections to the kernel of the JIMWLK evolution which are leading at small density are resummed into a path ordered exponential of the functional derivative with respect to the charge density operator, thus hinting at intriguing duality between the high and the low density regimes.