[Paper Review] Minijet initial state of heavy-ion collisions from next-to-leading order perturbative QCD

Risto Paatelainen|arXiv (Cornell University)|Sep 11, 2014

High-Energy Particle Collisions Research15 references3 citations

TL;DR

This paper presents a next-to-leading order (NLO) perturbative QCD framework for computing minijet initial conditions in heavy-ion collisions, incorporating improved parton distribution functions and infrared/collinear-safe measurement functions. The NLO-improved EKRT model successfully reproduces bulk observables at both RHIC and LHC energies, enabling a constrained determination of the temperature-dependent shear viscosity of QCD matter.

ABSTRACT

The aim of this thesis is to calculate field-theoretically as rigorously as possible the initial state of partonic matter produced in ultrarelativistic heavy-ion collisions at CERN-LHC and BNL-RHIC colliders. The computed minijet initial conditions are then used in the initialization of the relativistic hydrodynamical modeling of these collisions. In the theoretical introduction part the computation of parton production cross section at next-to-leading order (NLO) perturbative QCD (pQCD) is discussed. Furthermore, the full analytical calculation for the squared quark-quark scattering matrix element including the systematic ultraviolet renormalization is presented. Finally, the subtraction method allowing for the cancellation of the infrared and collinear singularities in the partonic QCD cross section at NLO is discussed. In the more phenomenological part of the thesis the original EKRT model, which combines collinearly factorized leading-order pQCD minijet production with gluon saturation, is introduced. Next, the minijet production is generalized rigorously to NLO. In particular, a new set of measurement functions is introduced to define the produced infrared- and collinear-safe minijet transverse energy, in terms of which the saturation is now formulated. Finally, the framework is updated with the latest knowledge of nuclear parton distribution functions. Using the NLO-improved EKRT model with hydrodynamics we obtained a good agreement with the measured centrality dependence of the low-transverse-momentum bulk observables, simultaneously at the LHC and RHIC. In particular, aiming at a determination of the QCD matter properties from these measurements, we were able to constrain the temperature dependence of the QCD matter shear viscosity, which is an important result.

Motivation & Objective

• To develop a field-theoretically rigorous NLO pQCD framework for minijet production in ultrarelativistic heavy-ion collisions.
• To address infrared and collinear singularities in partonic cross sections using the subtraction method and ultraviolet renormalization.
• To generalize the EKRT model by incorporating NLO corrections and updated nuclear parton distribution functions.
• To improve the description of initial energy density and saturation effects using infrared- and collinear-safe measurement functions for minijet transverse energy.
• To constrain the temperature dependence of QCD matter shear viscosity by comparing hydrodynamic simulations with experimental data at RHIC and LHC.

Proposed method

• Perform full analytical calculation of the squared quark-quark scattering amplitude at NLO, including one-loop virtual corrections and real emission contributions.
• Implement systematic ultraviolet renormalization using QCD counterterms for self-energy, vertex, and box diagrams.
• Apply the subtraction method to cancel infrared and collinear divergences in the NLO cross sections.
• Introduce a new set of measurement functions to define infrared- and collinear-safe minijet transverse energy, enabling consistent saturation modeling.
• Update the EKRT model with NLO-improved minijet production and modern nuclear PDFs, including nuclear modification factors.
• Combine the NLO minijet initial conditions with relativistic viscous hydrodynamics to simulate bulk observables in heavy-ion collisions.

Experimental results

Research questions

• RQ1 How can NLO pQCD be systematically applied to compute minijet initial conditions in heavy-ion collisions with field-theoretic rigor?
• RQ2 What is the impact of NLO corrections and improved parton distribution functions on the saturation scale and initial energy density?
• RQ3 Can the NLO-improved EKRT model simultaneously describe centrality-dependent bulk observables at both RHIC and LHC energies?
• RQ4 How does the inclusion of viscous hydrodynamics and NLO initial conditions affect the extraction of QCD matter shear viscosity?
• RQ5 What constraints can be placed on the temperature dependence of the shear viscosity-to-entropy density ratio from comparison with experimental data?

Key findings

• The NLO-improved EKRT model achieves good agreement with measured centrality dependence of low-transverse-momentum bulk observables at both RHIC and LHC energies.
• The inclusion of NLO corrections and updated nuclear PDFs significantly improves the description of minijet production and initial energy density.
• The framework enables a consistent and infrared- and collinear-safe definition of minijet transverse energy through new measurement functions.
• The model successfully constrains the temperature dependence of the QCD matter shear viscosity, providing a key physical insight into the nature of the quark-gluon plasma.
• The numerical implementation of the NLO minijet program, including full renormalization and subtraction, was validated and used to produce all results in the thesis.
• The NLO-improved hydrodynamic simulations reproduce experimental data for charged-hadron $p_T$ spectra and nuclear suppression factors across a wide energy range.