Multi-loop investigations of strong interactions at high temperatures
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Abstract
Matter alters its properties remarkably when confronted with extreme conditions such as temperatures as high as in the early universe. The emergence of the Quark-Gluon Plasma and restoration of electroweak symmetry through phase transitions are but the most prominent phenomena to invigorate studies of gauge theories at finite temperatures. If the temperature is sufficiently high, static observables are effectively described in a reduced dimension by a framework known as Dimensional Reduction.
The computer algebraic multi-loop treatment of perturbation theory for finite-temperature theories is at the core of this thesis. It adopts sophisticated tools from zero temperature to decimate typically vast numbers of Feynman integrals with the objective to automate the dimensional reduction. To accomplish this, integration-by-parts identities pertinent to both massless and massive loops at finite temperature are illuminated. Additionally, an inclusion of higher-dimensional operators in these theories is first motivated and then generalised.
The developed tools are applied to review the advancements of [1] in chapter 4 and [2] in chapter 5. There, we analyse the dimensionally reduced theories of high-temperature QCD, namely electrostatic and magnetostatic QCD.
We inspect three-loop contributions stemming from non-static modes to the magnetostatic coupling in dimensionally reduced hot Yang-Mills theory [1]. By including dimension-six operators the result is found to be infrared finite and influenced by all scales in the QCD hierarchy. Incorporating also electrostatic effects indicates a non-perturbative ultrasoft gauge coupling at O(as^3/2).
Based on its relevance in cosmology, we determine another low-energy coefficient in electrostatic QCD, the Debye mass. By including effects from massive fermions up to two loops [2], energy ranges of (1 GeV–10 TeV) are scanned to show the smooth crossing of quark mass thresholds.
The computer algebraic multi-loop treatment of perturbation theory for finite-temperature theories is at the core of this thesis. It adopts sophisticated tools from zero temperature to decimate typically vast numbers of Feynman integrals with the objective to automate the dimensional reduction. To accomplish this, integration-by-parts identities pertinent to both massless and massive loops at finite temperature are illuminated. Additionally, an inclusion of higher-dimensional operators in these theories is first motivated and then generalised.
The developed tools are applied to review the advancements of [1] in chapter 4 and [2] in chapter 5. There, we analyse the dimensionally reduced theories of high-temperature QCD, namely electrostatic and magnetostatic QCD.
We inspect three-loop contributions stemming from non-static modes to the magnetostatic coupling in dimensionally reduced hot Yang-Mills theory [1]. By including dimension-six operators the result is found to be infrared finite and influenced by all scales in the QCD hierarchy. Incorporating also electrostatic effects indicates a non-perturbative ultrasoft gauge coupling at O(as^3/2).
Based on its relevance in cosmology, we determine another low-energy coefficient in electrostatic QCD, the Debye mass. By including effects from massive fermions up to two loops [2], energy ranges of (1 GeV–10 TeV) are scanned to show the smooth crossing of quark mass thresholds.
Date of Publication
2020
Year of graduation
2020
Theses Type
dissertation
Subject(s)
Language(s)
en
Author(s)
Schicho, Philipp Maximilian |
Faculty/Graduate School
Access(Rights)
open.access
Primary OA Publication
true