Multi-loop investigations of strong interactions at high temperatures

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

Integrating by parts at finite density

Both nonzero temperature and chemical potentials break the Lorentz symmetry present in vacuum quantum field theory by singling out the rest frame of the heat bath. This leads to complications in the application of thermal perturbation theory, including the appearance of novel infrared divergences in loop integrals and an apparent absence of four-dimensional integration-by-parts (IBP) identities, vital for high-order computations. Here, we propose a new strategy that enables the use of IBP techniques in the evaluation of vacuum, or bubble, diagrams in the limit of vanishing temperature $T$ but nonzero chemical potentials $\mu$. The central elements of the new setup include a contour representation for the temporal momentum integrals, the use of a small but nonzero $T$ as a regulator, and the systematic application of both temporal and spatial differential operators in the generation of IBP relations. The relations we derive contain novel inhomogeneous terms featuring differentiated Fermi-Dirac distribution functions, which severely complicate calculations at nonzero temperature, but are shown to reduce to solvable lower-dimensional objects as $T$ tends to zero. Pedagogical example computations are kept at the one- and two-loop levels, but the application of the new method to higher-order calculations is discussed in some detail.Comment: 48 pages, 1 figure, minor changes in text and references added (v2

Singlet-assisted electroweak phase transition at two loops

We investigate the electroweak phase transition in the real-singlet extension of the Standard Model at two-loop level, building upon existing one-loop studies. We calculate the effective potential in the high-temperature approximation and detail the required resummations at two-loop order. In typical strongtransition scenarios, we find deviations of order 20%-50% from one-loop results in transition strength and critical temperature for both one- and two-step phase transitions. For extremely strong transitions, the discrepancy with one-loop predictions is even larger, presumably due to sizable scalar couplings in the tree-level potential. Along the way, we obtain a dimensionally reduced effective theory applicable for nonperturbative lattice studies of the model.Peer reviewe

Combining thermal resummation and gauge invariance for electroweak phase transition

For computing thermodynamics of the electroweak phase transition, we discuss a minimal approach that reconciles both gauge invariance and thermal resummation. Such a minimal setup consists of a two-loop dimensional reduction to three-dimensional effective theory, a one-loop computation of the effective potential and its expansion around the leading-order minima within the effective theory. This approach is tractable and provides formulae for resummation that are arguably no more complicated than those that appear in standard techniques ubiquitous in the literature. In particular, we implement renormalisation group improvement related to the hard thermal scale. Despite its generic nature, we present this approach for the complex singlet extension of the Standard Model which has interesting prospects for high energy collider phenomenology and dark matter predictions. The presented expressions can be used in future studies of phase transition thermodynamics and gravitational wave production in this model.Peer reviewe

The force-force-correlator in hot QCD perturbatively and from the lattice

High-energy particles traversing a medium experience modified dispersion. In the Quark-Gluon Plasma, such dispersion affects jet propagation and transport properties and should be determined better. Above similar to 2T(c) we expect strongly coupled infrared behavior and perturbative ultraviolet behavior, allowing a perturbative matching to an effective theory called EQCD, which can be studied non-perturbatively. We study the relevant non-local operator in EQCD at next-to-leading order which allows for a complete EQCD-to-lattice match and prepares the groundwork for a matching between EQCD and full QCD. Our results in EQCD show remarkable agreement between perturbation theory and the lattice in the expected regime.Peer reviewe

Robust approach to thermal resummation : Standard Model meets a singlet

Perturbation theory alone fails to describe thermodynamics of the electroweak phase transition. We review a technique combining perturbative and non-perturbative methods to overcome this challenge. Accordingly, the principal theme is a tutorial of high-temperature dimensional reduction. We present an explicit derivation with a real singlet scalar and compute the thermal effective potential at two-loop order. In particular, we detail the dimensional reduction for a real-singlet extended Standard Model. The resulting effective theory will impact future non-perturbative studies based on lattice simulations as well as purely perturbative investigations.Peer reviewe

Hard parton dispersion in the quark-gluon plasma, non-perturbatively

The in-medium dispersion of hard partons, encoded in their so-called asymptotic mass, receives large non-perturbative contributions from classical gluons, i.e. soft gluons with large occupation numbers. Here, we discuss how the analytical properties of thermal amplitudes allow for a non-perturbative determination of the infrared classical contribution through lattice determinations in the dimensionally-reduced effective theory of hot QCD, EQCD. We show how these lattice determinations need to be complemented by perturbative two-loop matching calculations between EQCD and QCD, so that the unphysical (classical) ultraviolet behavior of EQCD is replaced by its proper quantum QCD counterpart. We show how lattice and perturbative EQCD are in good agreement in the UV and present an outlook on the two-loop quantum QCD contribution.Comment: 6 pages, to appear in the proceedings of Hard Probes 202

Emphysematous cystitis: mortality, risk factors, and pathogens of a rare disease

Although high mortality rates have been reported for emphysematous pyelonephritis (EP), information on emphysematous cystitis (EC), which is less common, is sparse. Here, we report one new case of severe EC and 136 cases of EC that occurred between 2007 and 2016, and review information about the characteristics, diagnosis, treatment and mortality of these patients, and the pathogens found in these patients. The mean age of the 136 patients was 67.9±14.2 years. Concurrent emphysematous infections of other organs were found in 21 patients (15.4%), with emphysematous pyelonephritis being the most common of these infections. The primary pathogen identified was Escherichia coli (54.4%). Patients were mainly treated by conservative management that included antibiotics (n=105; 77.2%). Ten of the 136 patients with EC died, yielding a mortality rate of 7.4%. Despite the relatively low mortality rate of EC compared with that of EP, a high degree of suspicion must be maintained to facilitate successful and conservative management

Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory

A gauge-invariant framework for computing bubble nucleation rates at finite temperature in the presence of radiative barriers was presented and advocated for model-building and phenomenological studies in an accompanying article [1]. Here, we detail this computation using the Abelian Higgs Model as an illustrative example. Subsequently, we recast this approach in the dimensionally-reduced high-temperature effective field theory for nucleation. This allows for including several higher order thermal resummations and furthermore delineate clearly the approach's limits of validity. This approach provides for robust perturbative treatments of bubble nucleation during possible first-order cosmic phase transitions, with implications for electroweak baryogenesis and production of a stochastic gravitational wave background. Furthermore, it yields a sound comparison between results of perturbative and non-perturbative computations.Peer reviewe

Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory

A gauge-invariant framework for computing bubble nucleation rates at finite temperature in the presence of radiative barriers was presented and advocated for model-building and phenomenological studies in an accompanying article [1]. Here, we detail this computation using the Abelian Higgs Model as an illustrative example. Subsequently, we recast this approach in the dimensionally-reduced high-temperature effective field theory for nucleation. This allows for including several higher order thermal resummations and furthermore delineate clearly the approach's limits of validity. This approach provides for robust perturbative treatments of bubble nucleation during possible first-order cosmic phase transitions, with implications for electroweak baryogenesis and production of a stochastic gravitational wave background. Furthermore, it yields a sound comparison between results of perturbative and non-perturbative computations.Peer reviewe