New observables to test the Color Glass Condensate beyond the large-N_c limit

TL;DR

This work develops a practical framework to test the Color Glass Condensate beyond the large-$N_c$ limit by focusing on meson production in DIS, where four-point Wilson-line correlators enter naturally. The authors introduce the Gaussian truncation (GT) of the JIMWLK evolution, which yields BK-like dynamics for two-point functions while enabling controlled access to higher-point correlators and their $Y$-dependence. They derive explicit GT-based evolution for two-, three-, and four-point correlators, formulating a matrix evolution for the four-Wilson-line correlator relevant to inclusive vector-meson production and detailing how initial conditions are constrained by coincidence limits. Crucially, they show that the difference between inclusive and exclusive vector-meson production isolates correlator-factorization violations, offering a concrete observable to probe beyond-BK, beyond-large-$N_c$ physics. The framework provides a path to test nontrivial JIMWLK features in future experiments and to extend the approach to other observables such as heavy meson production or dijets.

Abstract

The JIMWLK framework offers a powerful tool to calculate the energy dependence of QCD observables at high energies. Despite a growing number of observables considered for phenomenological analysis, few features of JIMWLK evolution beyond its evolution speed are yet well constrained by experiment. We argue that meson production cross-sections have the potential to provide qualitatively new insights and allow to address issues both beyond the large-N_c limit and at higher twist. These cross-sections generically contain four point functions whose evolution is shown to follow from the JIMWLK framework. The Gaussian truncation is used to provide an efficient and practical means of calculating the evolution of four point correlators beyond the large-N_c limit.

Figures (4)

• Figure 1: Diagrammatic representation of the amplitude for $\gamma^* A$ scattering at small $x$ at momentum transfer $Q^2=-q^2$. Light cone "time" $x^-$ runs from right to left. The interacting "out-state" (left diagram) contains nontrivial interactions between projectile and target. The interaction region is indicated by a vertical bar (blue online) at $x^-=0$ with superimposed explicit markers for the Wilson lines picked up by each projectile constituent. An arrow to the left indicates a $U$, an arrow to the right a $U^{-1}$. Arrows on gluon lines stand for Wilson lines in the adjoint representation. The non-interacting "in-state" (right diagram) instead has no interactions and correspondingly constant Wilson line factors at $x^-=0$ which are gauge equivalent to the unit element.
• Figure 2: Diagrammatic notation for gluon emission at small $x$. Gluon lines carry an adjoint Wilson line $U_{\bm z}^{a b}$, the vertical gray lines indicate sums over vertex insertions at the black vertex dots.
• Figure 3: Cancellation patterns in the $\overline{\text{in}}$-out-overlap: Diagrams in the first two columns (full outlines) cancel against each other according to Eq. \ref{['eq:x^-cancellations']}. This guarantees that the JIMWLK Hamiltonian yields zero when acting on constant $U$-fields. Alternatively the diagrams in the first three lines cancel amongst each other in a prototypical final state cancellation (dashed outlines). The remaining diagrams in both cases reflect the leading order JIMWLK corrections to the total DIS cross-section.
• Figure 4: The corrections to the $\overline{\text{out}}$-out-overlap for exclusive vector-meson production. With both the initial- and final-states of projectile and target in both amplitudes projected onto color singlets, the final state emissions in the middle column are forced to zero by color conservation.