[Paper Review] kt-factorization for Hard Processes in Nuclei

Fabio Domínguez, Xiao, Bo-Wen+1 more|PubMed|Sep 11, 2010

High-Energy Particle Collisions Research3 citations

TL;DR

This paper establishes an effective $k_t$-factorization framework for hard processes in nuclei at small $x$, demonstrating that dijet correlations in $pA$ collisions and quark-antiquark jet correlations in DIS probe distinct $k_t$-dependent gluon distributions—specifically, the Weizsäcker-Williams gluon distribution and the unintegrated gluon distribution (UGD) derived from the Fourier transform of the color-dipole cross section. The key result is that although naive $k_t$-factorization fails, a modified factorization holds by constructing non-universal parton distributions from universal building blocks, validated through power-counting and consistency checks with inclusive limits and the CGC formalism.

ABSTRACT

Two widely proposed k(t)-dependent gluon distributions in the small-x saturation regime are investigated using two-particle back-to-back correlations in high energy scattering processes. The Weizsäcker-Williams gluon distribution, interpreted as the number density of gluon inside nucleus, is studied in the quark-antiquark jet correlation in deep inelastic scattering. On the other hand, the unintegrated gluon distribution, defined as the Fourier transform of the color-dipole cross section, is probed in the direct photon-jet correlation in pA collisions.

Motivation & Objective

• To address the breakdown of naive $k_t$-factorization in two-particle production in $pA$ collisions at small $x$.
• To establish a consistent factorization framework for hard processes in nuclei by modifying parton distributions to account for multiple interactions in the small-$x$ saturation regime.
• To distinguish and probe two distinct $k_t$-dependent gluon distributions—Weizsäcker-Williams and unintegrated gluon distributions—using different high-energy scattering processes.
• To validate the effective factorization through consistency checks with inclusive cross sections and the collinear limit.
• To provide a foundation for interpreting experimental data from RHIC and the future Electron-Ion Collider (EIC) using a unified framework of non-universal but constructible parton distributions.

Proposed method

• Uses back-to-back two-particle correlations in high-energy $pA$ and $\gamma^*A$ collisions to probe $k_t$-dependent gluon distributions in the small-$x$ regime.
• Applies power-counting methods in the back-to-back limit ($q_\perp \ll P_\perp$) to isolate leading-order $q_\perp/P_\perp$ contributions dependent on unintegrated gluon distributions (UGDs).
• Defines two key UGDs: the Weizsäcker-Williams distribution as the number density of gluons in the CGC formalism, and the UGD as the Fourier transform of the color-dipole cross section.
• Constructs effective parton distributions in nuclei from universal building blocks, allowing factorization despite non-universality of the distributions.
• Derives the differential cross section for dijet production in $pA$ collisions as a combination of convolutions involving both UGDs, with explicit expressions for hard partonic cross sections in $qg\to qg$, $gg\to q\bar{q}$, and $gg\to gg$ channels.
• Validates the framework by recovering the inclusive dijet cross section upon integration over $q_\perp$, reproducing the collinear factorization result at large $q_\perp$, and confirming consistency with the CGC formalism.

Experimental results

Research questions

• RQ1 Can an effective $k_t$-factorization be established for hard processes in nuclei when naive $k_t$-factorization fails due to multiple interactions at small $x$?
• RQ2 How do different two-particle correlation processes—such as quark-antiquark jet production in DIS and direct photon-jet production in $pA$ collisions—probe distinct $k_t$-dependent gluon distributions?
• RQ3 What is the relationship between the Weizsäcker-Williams gluon distribution and the unintegrated gluon distribution defined via the Fourier transform of the dipole cross section in the context of high-energy scattering?
• RQ4 How can non-universal parton distributions in nuclei be systematically constructed from universal building blocks in the small-$x$ saturation regime?
• RQ5 To what extent do the theoretical predictions for dijet correlations in $pA$ collisions agree with experimental data from RHIC, particularly in the forward rapidity region?

Key findings

• The differential cross section for dijet production in $pA$ collisions depends on both the Weizsäcker-Williams and the Fourier-transformed dipole cross section-based UGDs through complex combinations and convolutions, invalidating naive $k_t$-factorization.
• Quark-antiquark jet correlations in deep inelastic scattering directly probe the Weizsäcker-Williams gluon distribution, providing a clean experimental access to this distribution at the future Electron-Ion Collider (EIC).
• Direct photon-jet correlations in $pA$ collisions probe the unintegrated gluon distribution defined as the Fourier transform of the color-dipole cross section, offering a complementary probe to the WW distribution.
• The effective factorization framework successfully recovers the inclusive dijet cross section upon integration over the transverse momentum imbalance $q_\perp$, confirming consistency with known results.
• The framework reproduces the collinear factorization limit at large $q_\perp$ ($P_\perp \gg q_\perp \gg Q_S, \Lambda_{\text{QCD}}$), validating its correctness in the perturbative regime.
• The CGC formalism is found to be fully consistent with the derived expressions, confirming the theoretical robustness of the framework across different energy regimes.