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Explaining the baryon asymmetry of the Universe has been a long-standing problem of particle physics, with the consensus being that new physics is required as the Standard Model (SM) cannot resolve this issue. Beyond the Standard Model (BSM) scenarios would need to incorporate new sources of \(CP\) violation and either introduce new departures from thermal equilibrium or modify the existing electroweak phase transition. In this thesis, we explore two approaches to baryogenesis, i.e. the generation of this asymmetry.
In the first approach, we study the two-particle irreducible (2PI) formalism as a means to investigate non-equilibrium phenomena. After arriving at the renormalised equations of motions (EOMs) to describe the dynamics of a phase transition, we discuss the techniques required to obtain the various counterterms in an on-shell scheme. To this end, we consider three truncations up to two-loop order of the 2PI effective action: the Hartree approximation, the scalar sunset approximation and the fermionic sunset approximation. We then reconsider the renormalisation procedure in an \(\overline{\text{MS}}\) scheme to evaluate the 2PI effective potential for the aforementioned truncations. In the Hartree and the scalar sunset approximations, we obtain analytic expressions for the various counterterms and subsequently calculate the effective potential by piecing together the finite contributions. For the fermionic sunset approximation, we obtain similar equations for the counterterms in terms of divergent parts of loop integrals. However, these integrals cannot be expressed in an analytic form, making it impossible to evaluate the 2PI effective potential with the fermionic contribution. Our main results are thus related to the renormalisation programme in the 2PI formalism: \( (i) \)the procedure to obtain the renormalised EOMs, now including fermions, which serve as the starting point for the transport equations for electroweak baryogenesis and \( (ii) \) the method to obtain the 2PI effective potential in a transparent manner.
In the second approach, we study baryogenesis via leptogenesis. Here, an asymmetry in the lepton sector is generated, which is then converted into the baryon asymmetry via the sphaleron process in the SM. We proceed to consider an extension of the SM along the lines of a scotogenic framework. The newly introduced particles are charged odd under a \(\mathbb{Z}_2\) symmetry, and masses for the SM neutrinos are generated radiatively. The \(\mathbb{Z}_2\) symmetry results in the lightest BSM particle being stable, allowing for a suitable dark matter (DM) candidate. Furthermore, the newly introduced heavy Majorana fermionic singlets provide the necessary sources of \(CP\) violation through their Yukawa interactions and their out-of-equilibrium decays produce a lepton asymmetry. This model is constrained from a wide range of observables, such as consistency with neutrino oscillation data, limits on branching ratios of charged lepton flavour violating decays, electroweak observables and obtaining the observed DM relic density. We study leptogenesis in this model in light of the results of a Markov chain Monte Carlo scan, implemented in consideration of the aforementioned constraints. Successful leptogenesis in this model, to account for the baryon asymmetry, then severely constrains the available parameter space.
One of the most popular extensions of the SM is Supersymmetry (SUSY). It is a symmetry relating fermions and bosons and also the only feasible extension to the symmetries of spacetime. With SUSY it is then possible to explain some of the open questions left by the SM while at the same time opening the possibility of gauge unification at a high scale. SUSY theories require the addition of new particles, in particular an extra Higgs doublet and at least as many new scalars as fermions in the SM. Much in the same way that the Higgs boson breaks SU (2)L symmetry, these new scalars can break any symmetry for which they carry a charge through spontaneous symmetry breaking.
Let us assume there is a local minimum of the potential that reproduces the correct phenomenol- ogy for a parameter point of a given model. By exploring whether there are other deeper minima with VEVs that break symmetries we want to conserve, like SU (3)C or U (1)EM , it is possible to exclude regions of parameter space where that happens. The local minimum with the correct phenomenology might still be metastable, so it is also necessary to calculate the probability of tunneling between minima.
In this work we propose and apply a framework to constrain the parameter space of models with many scalars through the minimization of the one-loop eff e potential and the calculation of tunneling times at zero and non zero temperature.After a brief discussion about the shortcomings of the SM and an introduction of the basics of SUSY, we introduce the theory and numerical methods needed for a successful vacuum stability analysis. We then present Vevacious, a public code where we have implemented our proposed framework. Afterwards we go on to analyze three interesting examples.
For the constrained MSSM (CMSSM) we explore the existence of charge- and color- breaking (CCB) minima and see how it constraints the phenomenological relevant region of its parameter space at T = 0. We show that the regions reproducing the correct Higgs mass and the correct relic density for dark matter all overlap with regions suffering from deeper CCB minima.
Inspired by the results for the CMSSM, we then consider the natural MSSM and check the region of parameter space consistent with the correct Higgs mass against CCB minima at T /= 0. We find that regions of parameter space with CCB minima overlap significantly with that reproducing the correct Higgs mass. When thermal eff are considered the majority of such points are then found to have a desired symmetry breaking minimum with very low survival probability. In both these studies we find that analytical conditions presented in the literature fail in dis- criminating regions of parameter space with CCB minima. We also present a way of adapting our framework so that it runs quickly enough for use with parameter fit studies.
Lastly we show a different example of using vacuum stability in a phenomenological study. For the BLSSM we investigate the violation of R-parity through sneutrino VEVs and where in parameter space does this happen. We find that previous analyses in literature fail to identify regions with R-parity conservation by comparing their results to our full numerical analysis.
It is generally agreed upon the fact that the Standard Model of particle physics can only be viewed as an effective theory that needs to be extended as it leaves some essential questions unanswered. The exact realization of the necessary extension is subject to discussion. Supersymmetry is among the most promising approaches to physics beyond the Standard Model as it can simultaneously solve the hierarchy problem and provide an explanation for the dark matter abundance in the universe. Despite further virtues like gauge coupling unification and radiative electroweak symmetry breaking, minimal supersymmetric models cannot be the ultimate answer to the open questions of the Standard Model as they still do not incorporate neutrino masses and are besides heavily constrained by LHC data. This does, however, not derogate the beauty of the concept of supersymmetry. It is therefore time to explore non-minimal supersymmetric models which are able to close these gaps, review their consistency, test them against experimental data and provide prospects for future experiments.
The goal of this thesis is to contribute to this process by exploring an extraordinarily well motivated class of models which bases upon a left-right symmetric gauge group. While relaxing the tension with LHC data, those models automatically include the ingredients for neutrino masses.
We start with a left-right supersymmetric model at the TeV scale in which scalar \(SU(2)_R\) triplets are responsible for the breaking of left-right symmetry as well as for the generation of neutrino masses. Although a tachyonic doubly-charged scalar is present at tree-level in this kind of models, we show by performing the first complete one-loop evaluation that it gains a real mass at the loop level. The constraints on the predicted additional charged gauge bosons are then evaluated using LHC data, and we find that we can explain small excesses in the data of which the current LHC run will reveal if they are actual new physics signals or just background fluctuations. In a careful evaluation of the loop-corrected scalar potential we then identify parameter regions in which the vacuum with the phenomenologically correct symmetry-breaking properties is stable. Conveniently, those regions favour low left-right symmetry breaking scales which are accessible at the LHC.
In a slightly modified version of this model where a \(U(1)_R × U(1)_{B−L}\) gauge symmetry survives down to the TeV scale, we implement a minimal gauge-mediated supersymmetry breaking mechanism for which we calculate the boundary conditions in the presence of gauge kinetic mixing. We show how the presence of the extended gauge group raises the tree-level Higgs mass considerably so that the need for heavy supersymmetric spectra is relaxed. Taking the constraints from the Higgs sector into account, we then explore the LHC phenomenology of this model and point out where the expected collider signatures can be distinguished from standard scenarios.
In particular if neutrino masses are explained by low-scale seesaw mechanisms as is done throughout this work, there are potentially spectacular signals at low-energy experiments which search for charged lepton flavour violation. The last part of this thesis is dedicated to the detailed exploration of processes like μ → e γ, μ → 3 e or μ−e conversion in nuclei in a supersymmetric framework with an inverse seesaw mechanism. In particular, we disprove claims about a non-decoupling effect in Z-mediated three-body decays and study the prospects for discovering and distinguishing signals at near-future experiments. In this context we identify the possibility to deduce from ratios like BR(\(τ → 3 μ\))/BR(\(τ → μ e^+ e^−\)) whether the contributions from ν − W loops dominate over supersymmetric contributions or vice versa.
Testing Models with Higher Dimensional Effective Interactions at the LHC and Dark Matter Experiments
(2013)
Dark matter and non-zero neutrino masses are possible hints for new physics beyond the Standard Model of particle physics. Such potential consequences of new physics can be described by effective field theories in a model independent way. It is possible that the dominant contribution to low-energy effects of new physics is generated by operators of dimension d>5, e.g., due to an additional symmetry. Since these are more suppressed than the usually discussed lower dimensional operators, they can lead to extremly weak interactions even if new physics appears at comparatively low scales. Thus neutrino mass models can be connected to TeV scale physics, for instance. The possible existence of TeV scale particles is interesting, since they can be potentially observed at collider experiments, such as the Large Hadron Collider. Hence, we first recapitulate the generation of neutrino masses by higher dimensional effective operators in a supersymmetric framework. In addition, we discuss processes that can be used to test these models at the Large Hadron Collider. The introduction of new particles can affect the running of gauge couplings. Hence, we study the compatibilty of these models with Grand Unified Theories. The required extension of these models can imply the existence of new heavy quarks, which requires the consideration of cosmological constraints. Finally, higher dimensional effective operators can not only generate small neutrino masses. They also can be used to discuss the interactions relevant for dark matter detection experiments. Thus we apply the methods established for the study of neutrino mass models to the systematic discussion of higher dimensional effective operators generating dark matter interactions.
The thesis deals with the automated generation and efficient evaluation of scattering amplitudes in general relativistic quantum field theories at one-loop order in perturbation theory. At the
present time we lack signals beyond the Standard Model which, in the past, have guided the
high-energy physics community, and ultimately led to the discovery of new physics phenomena.
In the future, precision tests could acquire this guiding role by systematically probing the Standard Model and constraining Beyond the Standard Model theories. As current experimental
constraints strongly favour Standard Model-like theories, only small deviations with respect to the Standard Model are expected which need to be studied in detail. The required precision
demands one-loop corrections in all future analyses, ideally in a fully automated way, allowing
to test a variety of observables in different models and in an effective field theory approach.
In the process of achieving this goal we have developed an enhanced version of the tool
Recola and on this basis the generalization Recola2. These tools represent fully automated
tree- and one-loop-amplitude providers for the Standard Model, or in the case of Recola2
for general models. Concerning the algorithm, we use a purely numerical and fully recursive
approach allowing for extreme calculations of yet unmatched complexity. Recola has led to the first computation involving 9-point functions. Beyond the Standard Model theories and Effective Field theories are integrated into the Recola2 framework as model files. Renormalized model files are produced with the newly developed tool Rept1l, which can perform the renormalization in a fully automated way, starting from nothing but Feynman rules. In view of validation, we have extended Recola2 to new gauges such as the Background-Field Method and the class of Rxi gauges. In particular, the Background-Field Method formulation for new theories serves as an automated validation, and is very useful in practical calculations and the formulation of renormalization conditions. We have applied the system to produce the first results for Higgs-boson production in Higgs strahlung and vector-boson fusion in the Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model. All in all, we have laid the foundation for an automated generation and computation of one-loop amplitudes within a large class of phenomenologically interesting theories. Furthermore, we enable the use of our system via a very flexible and dynamic control which does not require any intermediate intervention.