Perturbative QCD at high density

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Title: Perturbative QCD at high density
Author: Paalanen, Ilkka
Contributor: University of Helsinki, Faculty of Science
Publisher: Helsingin yliopisto
Date: 2020
Language: eng
Thesis level: master's thesis
Discipline: Teoreettinen fysiikka
Abstract: Cold quark matter is matter consisting of free quarks in high energy density, and it can be formed when the energy density of ordinary hadronic matter increases to a region of 1 GeV/fm3. At such high energies, hadronic matter undergoes a phase transition and quarks that would normally be in color confinement break free to form a new phase. It is assumed that similar process happened in the very early universe, but in the opposite direction, when high temperature quark-gluon plasma cooled down significantly. With the cooling, the quark and gluon degrees of freedom switched to hadrons and ordinary matter began to form. Opposed to the hot quark-gluon plasma, there are no direct observations of cold quark matter and its existence is still speculative. Still, it is suspected that cold quark matter can be found in dense neutron star cores or even as stable quark matter in strange quark stars. Theoretically, cold quark matter and quark-gluon plasma can be studied in finite-temperature field theory. Finite-temperature field theory combines the field formalism of quantum field theory and the thermodynamical and statistical methods utilized in quantum statistics. The asymptotic freedom of the theory of strong interactions, quantum chromodynamics (QCD), provides an opportunity to expand the equation of state of high-energy quark matter in the limit of weak coupling, and thus opens a door to implement the tools of finite-temperature field theory perturbatively. Along with the perturbative analysis, it is useful to look at the possibilities offered by effective theories. Two of which are important in the study of finite-temperature QCD, dimensional reduction and hard thermal loop effective theory. Both effective theories address the issue of infrared divergences that arise in finite-temperature field theory efficiently compared to the naïve loop expansion. In dimensional reduction, scales that are defined as hard by the scale hierarchy are integrated out of the theory, after which the infrared problems of gluonic Matsubara zero-modes can be studied in a simpler three-dimensional setting. Hard thermal loop effective theory, on the other hand, examines the infrared divergences that appear in loop-level corrections of soft gluons. When the magnitude of the loop-momentum corresponds to the hard scale, the correction that contains the loop becomes proportional to a tree-level amplitude and breaks the perturbative expansion. The effective theory answers this problem by resumming the propagators and vertex functions and using the new quantities in place of the ordinary ones. With perturbation theory and the effective descriptions, the equation of state of cold quark matter and the pressure extracted from it, have been solved partially up to and including order g6ln2g2 in coupling. The meaning of this thesis is to present the methods of finite-temperature field theory and the supporting effective theories and their implementation to study the equation of state of cold quark matter. The results for QCD pressure will be presented to the last known order in coupling. Also, the effect of a massive strange quark and the role of cold quark matter in solving the neutron star equation of state will be discussed briefly.
Subject: Thermal field theory
perturbation theory
strong interaction
quark matter
neutron star
hard thermal loops

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