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Browsing by Subject "QCD"

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  • Vihko, Sami Vihko (2022)
    We will review techniques of perturbative thermal quantum chromodynamics (QCD) in the imaginary-time formalism (ITF). The Infrared (IR)-problems arising from the perturbative treatment of equilibrium thermodynamics of QCD and their phenomenological causes will be investigated in detail. We will also discuss the construction of two effective field theory (EFT) frameworks most often used in modern high precision calculations to overcome these. The EFTs are the dimensionally reduced theories EQCD and MQCD and Hard thermal loop effective theory (HTL). EQCD is three-dimensional Euclidean Yang-Mills theory coupled to an adjoint scalar field and MQCD is three-dimensional Euclidean pure Yang-Mills theory. The effective parameters in these theories are determined through matching calculations. HTL is based on resummation of hard thermal loops and uses effective propagators and vertex functions. We will also discuss the determination of the pressure of QCD perturbatively. In general, this thesis details calculations and the methodology.
  • Paalanen, Ilkka (2020)
    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.
  • Nummi, Vilhelmiina (2024)
    Quantum Chromodynamics (QCD) is the quantum field theory of strong interaction and therefore describes one of the fundamental forces in the universe. Quarks and gluons, together called partons, interact via strong force, and their interactions can be observed in high-energy collisions involving hadrons. Hadrons always contain some composition of quarks. The simplest way to obtain a partonic outgoing state in a collision, is through an electron-positron annihilation that produces a photon, which scatters, forming a combination of partons. Partons, unlike leptons, have properties known as color and flavor. There are six different types of quarks, all of which can be produced in a collision at sufficiently high energies. The energy involved in a hard collision of an electron and a positron is carried through the entire process. Generally, the partons’ binding to each other, known as color confinement, is so strong that they are observed as hadrons. Hadrons are color-neutral, meaning that the colored quarks are arranged such that they result in a color-neutral particle. This thesis focuses on calculating partonic collision outcomes on a small scale using perturbative QCD. At high energies and short distances, quarks are weakly coupled, allowing them to be considered relatively free from parton-parton interactions. By comparing the outcomes of electron-positron collisions, namely the electromagnetic and strong force (leptonic and partonic) outcomes, we can receive information on their differences when interacting. By constructing the process of leptonic annihilation, we can observe probabilities of charged particle outcomes that scatter from a photon. Furthermore, we calculate the cross-sections of the processes resulting in several partonic configurations. One of the results of this thesis is the ratio between the hadronic and leptonic outcomes stemming from the same initial collision. With partonic outcome cross-section calculated up to next-to-leading order, the ratio exhibits the impact of color factors as well as the running coupling of the parton-parton interaction.