Treading on the cut: Semi inclusive observables at high energy

TL;DR

The work develops a comprehensive framework to compute semi-inclusive observables in high-energy QCD using the JIMWLK/KLWMIJ formalism, extending beyond total cross sections to diffraction, momentum transfer, and gluon production. It derives evolution equations for a broad class of observables, including elastic, diffractive, and diffractive-with-gap processes, and presents explicit dipole-model limits that reduce to simple differential equations like BK/Kovchegov when appropriate. A key finding is that full JIMWLK/KLWMIJ dynamics allow target diffraction and diffractive effects suppressed by $1/N_c^2$, while the dipole model confines diffraction to the valence rapidity interval, consistent with fan diagrams; this highlights significant qualitative differences arising from Pomeron loops and higher multipoles. The results provide a unified, perturbative saturation-based approach to semi-inclusive phenomena relevant for DIS on nuclei at preasymptotic energies, with practical implications for predicting diffractive and gluon-production observables in high-energy collisions.

Abstract

We develop the formalizm for calculating semi inclusive observables at high energy in the JIMWLK/KLWMIJ approach. We consider several examples including diffractive processes, elastic and inclusive over the target degrees of freedom, scattering with fixed total transverse momentum transfer and inclusive gluon production. We discuss evolution of these observables with respect to various rapidity variables involved in their definitions (total rapidity, rapidity gap, width of diffractive interval etc.). We also discuss the dipole model limit of these observables and derive closed simple (as opposed to functional) differential equations in this approximation. We point out that there are some interesting differences between the full JIMWLK/KLWMIJ evolution and the dipole model evolution of diffractive cross section. In particular we show that in the dipole approximation the target does not diffract beyond the valence rapidity interval, consistently with the intuition suggested by the Pomeron fan diagramms. On the other hand such diffractive processes do exist in the full JIMWLK/KLWMIJ approach, albeit suppressed by the factor 1/N_c^2.

Figures (3)

• Figure 1: Elastic scattering: (a) total elastic: the final states on the cut are the same as the initial ones both on the projectile (P) and target (T) sides; (b)projectile elastic, target inclusive - all final states on the target side $T'$ are summed over; (c) target eslastic, projectile inclusive: all projectile final states $P'$ are summed over; (d) double inclusive with maximal gap. Horizontal lines denote final state gluons.
• Figure 2: Diffraction: (a) Projectile diffraction; (b) Target diffraction; (c) Double diffraction; (d) Central diffraction. Notations are the same as in Fig.1.
• Figure 3: Fan diagrams for diffraction: (a) Projectile diffraction with target scattered elastically; (b) Projectile diffraction with target diffracting in a small rapidity interval; (c) Projectile scatters elastically. Notations are the same as in Fig.1.