Electroweak phase transition in theories beyond the Standard Model

Non-perturbative analysis provides the most accurate information about the properties of the electroweak phase transition in the Standard Model of particle physics. In this thesis, we initiate similar non-perturbative studies for three theories of physics beyond the Standard Model. Properties of the phase transition are important for both obtaining reliable predictions for potential gravitational wave background produced by this phase transition, and for viability of electroweak baryogenesis, that attempts to solve the problem of observed matter/antimatter asymmetry of the universe. In particular, we study three models with an extended Higgs sector: the Two-Higgs-Doublet Model, the real singlet and the real triplet extensions of the Standard Model. In all these models we have derived three-dimensional effective theories by using a method of high temperature dimensional reduction. The main result of this thesis is a set of dimensional reduction matching relations between parameters of effective theories and physical quantities in the aforementioned extensions of the Standard Model. In certain regions of parameter space for each model, we are able to perform a non-perturbative analysis simply by recycling lattice results obtained in the past. For a full analysis, new simulations are required, which goes beyond the scope of this thesis. In this thesis, we provide a brief introduction to the electroweak phase transition and electroweak baryogenesis. We then discuss both perturbative and non-perturbative approaches to the problem in greater detail. Finally, we summarise and discuss the results obtained so far, and outline future directions for research.Vuonna 2012 havaitun Higgsin bosonin löytymisen jälkeen uusien hiukkasten kokeellinen etsintä jatkuu ja hiukkasfysiikan standardimallin ns. Higgsin sektorin laajennukset ovat aktiivinen teoreettinen tutkimuskohde. Perustana olevan hiukkasfysiikan teorian tarkka rakenne on merkittävässä osassa varhaisessa maailmankaikkeudessa tapahtuneen sähköheikon faasimuunnoksen tutkimusta. Sähköheikon faasimuunnoksen ominaisuuksien tunteminen mahdollistaa tarkkojen kvantitatiivisten ennusteiden tekemisen faasimuunnoksessa mahdollisesti syntyneille gravitaatioaalloille, sekä sähköheikon baryogeneesin tutkimuksen. Viimeksi mainittu mekanismi pyrkii selittämään maailmankaikkeudessa havaitun aine-antiaine-epätasapainon, joka on yksi kosmologian suurista ratkaisemattomista ongelmista. Hilasimulaatioihin perustuva analyysi tarjoaa tarkimman informaation sähköheikön faasitransition ominaisuuksista. Osa tätä analyysiä on ns. dimensionaalinen reduktio, jossa täydelle hiukkasfysiikan mallille johdetaan korkean lämpötilan efektiivinen teoria. Tässä väitöskirjassa dimensionaalinen reduktio suoritetaan kolmelle eri hiukkasfysiikan standardimallin laajennukselle. Tutkielman päätulos ovat relaatiot efektiivisten teorioiden ja täyden teorian fysikaalisten suureiden välillä näissä malleissa. Nämä relaatiot muodostavat perustan tulevalle tutkimukselle, jossa faasimuunnoksen ominaisuuksia tutkitaan uusien hilasimulaatioiden avulla. Lisäksi tässä tutkielmassa annetaan lyhyt johdatus Sähköheikkoon faasimuunnokseen ja perehdytään tarkemmin sen tutkimuksessa käytettäviin eri metodeihin

Perturbative effective field theory expansions for cosmological phase transitions

Guided by previous non-perturbative lattice simulations of a two-step electroweak phase transition, we reformulate the perturbative analysis of equilibrium thermodynamics for generic cosmological phase transitions in terms of effective field theory (EFT) expansions. Based on thermal scale hierarchies, we argue that the scale of many interesting phase transitions is in-between the soft and ultrasoft energy scales, which have been the focus of studies utilising high-temperature dimensional reduction. The corresponding EFT expansions provide a handle to control the perturbative expansion, and allow us to avoid spurious infrared divergences, imaginary parts, gauge dependence and renormalisation scale dependence that have plagued previous studies. As a direct application, we present a novel approach to two-step electroweak phase transitions, by constructing separate effective descriptions for two consecutive transitions. Our approach provides simple expressions for effective potentials separately in different phases, a numerically inexpensive method to determine thermodynamics, and significantly improves agreement with the non-perturbative lattice simulations.Comment: 58 pages, 14 figure

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

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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

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

Perturbative effective field theory expansions for cosmological phase transitions

Guided by previous non-perturbative lattice simulations of a two-step electroweak phase transition, we reformulate the perturbative analysis of equilibrium thermodynamics for generic cosmological phase transitions in terms of effective field theory (EFT) expansions. Based on thermal scale hierarchies, we argue that the scale of many interesting phase transitions is in-between the soft and ultrasoft energy scales, which have been the focus of studies utilising high-temperature dimensional reduction. The corresponding EFT expansions provide a handle to control the perturbative expansion, and allow us to avoid spurious infrared divergences, imaginary parts, gauge dependence and renormalisation scale dependence that have plagued previous studies. As a direct application, we present a novel approach to two-step electroweak phase transitions, by constructing separate effective descriptions for two consecutive transitions. Our approach provides simple expressions for effective potentials separately in different phases, a numerically inexpensive method to determine thermodynamics, and significantly improves agreement with the non-perturbative lattice simulations

Dimensional reduction of the Standard Model coupled to a new singlet scalar field

We derive an effective dimensionally reduced theory for the Standard Model augmented by a real singlet scalar. We treat the singlet as a superheavy field and integrate it out, leaving an effective theory involving only the Higgs and SU(2)(L) x U(1)(y) gauge fields, identical to the one studied previously for the Standard Model. This opens up the possibility of efficiently computing the order and strength of the electroweak phase transition, numerically and nonperturbatively, in this extension of the Standard Model. Understanding the phase diagram is crucial for models of electroweak baryogenesis and for studying the production of gravitational waves at thermal phase transitions.Peer reviewe