Multi-loop investigations of strong interactions at high temperatures

Abstract

Matter alters its properties remarkably when confronted with extreme conditions such astemperatures as high as in the early universe. The emergenceof the Quark-Gluon Plasma andrestoration of electroweak symmetry through phase transitions are but the most prominentphenomena to invigorate studies of gauge theories at finite temperatures. If the temperatureis sufficiently high, static observables are effectively described in a reduced dimension by aframework known as Dimensional Reduction.The computer algebraic multi-loop treatment of perturbation theory for finite-temperaturetheories is at the core of this thesis. It adopts sophisticated tools from zero temperature todecimate typically vast numbers of Feynman integrals with the objective to automate thedimensional reduction. To accomplish this, integration-by-parts identities pertinent to bothmassless and massive loops at finite temperature are illuminated. Additionally, an inclusionof 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] inchapter 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 magnetostaticcoupling in dimensionally reduced hot Yang-Mills theory [1]. By including dimension-sixoperators the result is found to be infrared finite and influenced by all scales in the QCDhierarchy. Incorporating also electrostatic effects indicates a non-perturbative ultrasoft gaugecoupling atO(α3/2s).Based on its relevance in cosmology, we determine another low-energy coefficient in elec-trostatic QCD, the Debye mass. By including effects from massive fermions up to twoloops [2], energy ranges of (1 GeV–10 TeV) are scanned to showthe smooth crossing ofquark mass thresholds.