Universality of Unintegrated Gluon Distributions at small x (1101.0715v2)

Abstract: We systematically study dijet production in various processes in the small-$x$ limit and establish an effective $k_t$-factorization for hard processes in a system with dilute probes scattering on a dense target. We find that the well-known Weizs\"{a}cker-Williams gluon distribution can be directly probed in the quark-antiquark jet correlation in deep inelastic scattering and the dipole gluon distribution can be directly measured in the direct photon-jet correlation in $pA$ collisions. In the large-$N_c$ limit, the unintegrated gluon distributions involved in other different dijet channels in pA collisions are shown to be related to two widely proposed ones: the Weizs\"{a}cker-Williams gluon distribution and the dipole gluon distribution.

• The paper establishes an effective kt-factorization framework that describes hard dijet production in dilute-dense scattering systems at small x.
• The paper identifies two primary unintegrated gluon distributions—the WW and dipole distributions—that underpin various TMD gluon channels.
• The study validates its approach using both CGC and TMD-factorization methods, offering prospects for probing saturation physics in future experiments.

Overview of "Universality of Unintegrated Gluon Distributions at small x"

This paper presents a systematic paper of dijet production processes in the small-x regime, focusing on an effective $k_t$-factorization for hard scatterings involving dilute probes and dense targets. The key result is the identification of two fundamental unintegrated gluon distributions (UGDs): the Weizsäcker-Williams (WW) gluon distribution and the dipole gluon distribution. These UGDs are shown to be the building blocks of other transverse momentum dependent (TMD) gluon distributions in various dijet channels, particularly in the large-N_c limit.

Key Contributions

1. $k_t$-Factorization for Hard Processes: The authors successfully establish an effective TMD factorization for certain hard processes in a dilute-dense scattering system. This involves developing theoretical tools to describe such processes in the small-x limit where saturation and nonlinear effects in QCD become essential.
2. Identification of Two Distinct UGDs: The paper identifies two primary UGDs at small-x:
   • Weizsäcker-Williams Gluon Distribution: This distribution can be directly probed by quark-antiquark jet correlations in deep inelastic scattering (DIS).
   • Dipole Gluon Distribution: It is directly accessible through direct photon-jet correlations in proton-nucleus (pA) collisions.
3. Relation of UGDs to Experimental Processes: The paper highlights the WW and dipole gluon distributions as the underlying factors of the TMD gluon distributions observable in hard scattering processes. For instance, the WW gluon distribution relates to dijet production in DIS and the dipole gluon distribution to direct photon-jet correlations in $pA$ collisions.
4. Universality and Building Blocks: The combination of colliding particle channels and the UGDs illustrates how various gluon distributions can be reconstructed using these two fundamental components. Theoretical implications include potential new experimental avenues for directly probing these distributions.
5. Validation through CGC and TMD Approaches: The paper cross-validates its theoretical framework using both the Color Glass Condensate (CGC) approach and the TMD-factorization approach. This ensures consistency and robust interpretation of results.

Implications and Future Speculation

The developed framework for understanding UGDs and their role in small-x physics offers significant opportunities for future developments in both theoretical and experimental high energy physics. By providing explicit prescriptions for the UGDs, this work opens paths for more accurate and direct experimental validation of saturation physics, particularly in future experimental setups like the Electron-Ion Collider (EIC). Such studies could refine our understanding of the saturation scale and its role in high-density QCD environments.

In the longer term, these insights may pave the way for more nuanced models of parton distributions, enhancing our predictions for particle production in high-energy collisions, and refining the broader theoretical groundwork concerning non-linear dynamics in QCD.

In summary, the paper's detailed examination and effective theoretical approach not only contribute to our understanding of small-x physics and gluon distributions in dense matter but also lay groundwork for better experimental strategies and future theoretical explorations.