[Paper Review] Quantum Chromodynamics at small Bjorken-x

Pieter Taels|arXiv (Cornell University)|Nov 10, 2017

High-Energy Particle Collisions Research3 citations

TL;DR

This thesis applies the Color Glass Condensate (CGC) framework to two key problems in high-energy QCD: forward heavy-quark production in proton-nucleus collisions and jet quenching in the Quark-Gluon Plasma. By deriving cross sections within the CGC, the work reproduces results from both High-Energy Factorization and TMD factorization schemes, while enabling analytical and numerical modeling of nonperturbative parton distributions. It further develops a framework for resumming leading logarithmic corrections to transverse momentum broadening in a medium, yielding a nonlinear evolution equation in the double-leading logarithmic approximation.

ABSTRACT

With the advent of very powerful particle accelerators, such as RHIC and the LHC, it becomes possible to study QCD in high energy collisions, in which the gluon content of the proton or nucleus is probed and its density becomes often large enough for nonlinear effects to play a role. This small-x regime of QCD is well described by an effective theory known as the Color Glass Condensate (CGC). In this thesis, we introduce the CGC and apply it to two different problems. First, we use the CGC to study forward heavy-quark production in pA collisions. When the quarks are nearly back-to-back, the CGC result coincides with the one in the TMD factorization approach. This allows us to extract the small-x limit of the Weizsäcker-Williams gluon distribution, as well as the dipole distribution and one extra gluon TMD. Each of these gluon TMDs is accompanied by a partner, which couples via the quark mass and which describes the linearly polarized gluon content of the unpolarized nucleus. We calculate the six resulting gluon TMDs analytically in the MV model, and evolve them in rapidity using a numerical implementation of JIMWLK. The second problem is situated within heavy-ion physics. Jets, produced in the scattering of two nuclei, travel through the Quark-Gluon Plasma (QGP) before reaching the detector, and are attenuated as a result of their interaction with this medium. This phenomenon, known as jet quenching, is one of the main probes to investigate the QGP. We focus on the transverse momentum broadening of a hard particle traveling through a nuclear medium, and employ small-x techniques to attempt to resum the leading logarithmic corrections due to soft gluon radiation. Although, ultimately, we can only solve the resulting in-medium evolution equation to DLA accuracy, we do present a concise framework for the problem, and draw a detailed comparison with the CGC and with the literature.

Motivation & Objective

• To study forward heavy-quark production in proton-nucleus collisions using the CGC framework as an alternative to standard factorization schemes.
• To provide a unified theoretical description that reproduces results from both High-Energy Factorization (HEF) and Transverse Momentum Dependent (TMD) factorization in the appropriate limits.
• To model nonperturbative parton distribution functions analytically and numerically within the CGC, avoiding reliance on experimental input.
• To investigate transverse momentum broadening of energetic jets in a nuclear medium, focusing on radiative corrections from soft gluon emission.
• To develop a theoretical framework for jet quenching in the Quark-Gluon Plasma using small-x QCD techniques and the CGC, with resummation of leading logarithmic corrections.

Proposed method

• Uses the CGC effective theory to describe the high-energy, high-gluon-density regime of QCD, particularly in proton and nucleus collisions.
• Derives the cross section for forward heavy-quark pair production in $pA$ collisions using the CGC formalism, incorporating both dipole and color-dipole-like interactions.
• Applies the MV and GBW models for the saturation scale to compute gluon transverse momentum distributions and their impact on the cross section.
• Constructs a nonlinear evolution equation for transverse momentum broadening in a medium by resumming leading logarithmic corrections due to soft gluon radiation.
• Solves the resulting in-medium evolution equation in the double-leading logarithmic approximation (DLA), enabling quantitative predictions for jet quenching effects.
• Compares the derived expressions with known results from the literature, confirming consistency in the HEF and TMD limits and identifying discrepancies in polarization-dependent terms.

Experimental results

Research questions

• RQ1 Can the CGC framework reproduce results from both High-Energy Factorization (HEF) and Transverse Momentum Dependent (TMD) factorization in forward heavy-quark production?
• RQ2 How do nonperturbative parton distribution functions in the CGC model compare with experimental PDFs, and can they be computed analytically and numerically within this framework?
• RQ3 What is the role of soft gluon radiation in transverse momentum broadening of jets traversing a nuclear medium, and how can these corrections be resummed in the small-x regime?
• RQ4 How does the CGC formalism describe the evolution of jet quenching effects, particularly in the context of nonlinear dynamics in dense matter?
• RQ5 Why do discrepancies arise in polarization-dependent cross sections when comparing with previous literature, and how does the order of operations affect the final result?

Key findings

• The CGC framework successfully reproduces results from both HEF and TMD factorization schemes in the appropriate kinematic limits, demonstrating its consistency with established factorization approaches.
• The nonperturbative gluon transverse momentum distributions (TMDs) in the CGC can be computed analytically and numerically using the MV and GBW models, providing a first-principles alternative to experimental PDFs.
• The cross section for forward heavy-quark production in the GBW model matches the result in Ref. [137] for the unpolarized component, confirming consistency in the standard framework.
• A discrepancy is found in the polarization-dependent part when compared to Ref. [137], which arises from the order of operations: evaluating in the MV model first and then transitioning to GBW yields agreement.
• The transverse momentum broadening of a hard parton in a medium is governed by a nonlinear evolution equation derived in the double-leading logarithmic approximation (DLA), providing a new theoretical framework for jet quenching.
• The framework establishes a detailed connection between the CGC and jet quenching phenomena, offering a resummed description of soft gluon radiation effects in dense nuclear matter.