Unveiling the sea: universality of the transverse momentum dependent quark distributions at small $x$

TL;DR

This paper establishes sea-quark TMD factorisation at small $x$ within the Color Glass Condensate framework for back-to-back dijets in both $eA$ DIS and $pA$ collisions. A universal structure emerges: sea-quark TMDs constructed from a SIDIS/Drell–Yan-type operator convolved with the quark–antiquark dipole S-matrix, with evolution governed by BK/JIMWLK. The authors define generalized sea-quark TMDs $xq^{(n)}(x,oldsymbol{K})$ (with $n=1,2,3$) that encode increasing color-dipole complexity and initial/final-state interactions; explicit, process-dependent cross-sections are provided, showing how these TMDs enter $qg$ and $ar{q}g$ final states with corresponding gauge-link structures. Numerical MV-model studies illustrate the universal large-$K_ot$ tails and the impact of saturation on the nucleus vs. proton, highlighting Cronin-like behavior for higher $n$ and setting the stage for quantitative phenomenology at the EIC and in forward $pA$ collisions, including the need for Sudakov resummation.

Abstract

Within the Colour Glass Condensate effective theory, we demonstrate that back-to-back dijet correlations in dilute-dense collisions involving a small-$x$ quark from the nuclear target can be factorised in terms of universal transverse momentum dependent distributions (TMDs) for the sea quarks. Two building blocks are needed to construct all these TMDs at the operator level: the sea quark TMD operator which appears in semi-inclusive Deep-Inelastic Scattering (SIDIS) or in the Drell-Yan process and the elastic $S$-matrix for a quark-antiquark dipole. Compared to SIDIS, the saturation effects are stronger for dijet production in forward proton-nucleus collisions, due to additional scattering in the initial and final state, effectively resulting in a larger value for the nuclear saturation momentum.

Figures (7)

• Figure 1: Example of graphs contributing to quark-gluon production in DIS at small $x$ and to leading order in $\alpha_s$. Left: target picture (the photon is absorbed by a sea quark, which then decays into a quark-gluon pair). Right: CGC picture (a quark-antiquark-gluon fluctuation of the photon scatters off the shockwave target field; the soft ($z\ll 1$) antiquark is not measured).
• Figure 2: The correspondence between the CGC and the target picture diagrams for $qg$ production in DIS. On each row, the first two diagrams provide the set of diagrams with same topology. The third column shows the associated diagrams in the target picture. For more clarity, we show in black the part of a target-picture graph which encodes the hard partonic subprocess, and in red the part representing the formation of the sea quark via a gluon decay.
• Figure 3: Left: target picture graph (topology B) for back-to-back quark-gluon dijets in $\gamma^*A$ collisions. Right: the associated colour flow at large $N_c$.
• Figure 4: The three CGC diagrams contributing to the photon emission after gluon topology for $\gamma g$ production in pA collisions.
• Figure 5: Left: one of the two target picture diagrams for $\gamma g$ jets in $pA$ collisions. Right: the associated colour flow at large $N_c$.