Perturbativity Constraints in BSM Models

Phenomenological studies performed for non-supersymmetric extensions of the Standard Model usually use tree-level parameters as input to define the scalar sector of the model. This implicitly assumes that a full on-shell calculation of the scalar sector is possible - and meaningful. However, this doesn't have to be the case as we show explicitly at the example of the Georgi-Machacek model. This model comes with an appealing custodial symmetry to explain the smallness of the $\rho$ parameter. However, the model cannot be renormalised on-shell without breaking the custodial symmetry. Moreover, we find that it can often happen that the radiative corrections are so large that any consideration based on a perturbative expansion appears to be meaningless: counter-terms to quartic couplings can become much larger than $4\pi$ and/or two-loop mass corrections can become larger than the one-loop ones. Therefore, conditions are necessary to single out parameter regions which cannot be treated perturbatively. We propose and discuss different sets of such perturbativity conditions and show their impact on the parameter space of the Georgi-Machacek model. Moreover, the proposed conditions are general enough that they can be applied to other models as well. We also point out that the vacuum stability constraints in the Georgi-Machacek model, which have so far only been applied at the tree level, receive crucial radiative corrections. We show that large regions of the parameter space which feature a stable electroweak vacuum at the loop level would have been - wrongly - ruled out by the tree-level conditions.Comment: 64 pages, 20 figure

Spontaneous Charge Breaking in the NMSSM - Dangerous or not?

We investigate the impact of charge-breaking minima on the vacuum stability of the NMSSM. We find that, in contrast to Two-Higgs-Doublet Models like the MSSM, at both tree- and loop-level there exists global charge-breaking minima. Consequently, many regions of parameter space are rendered metastable, which otherwise would have been considered stable if these charge-breaking minima were neglected. However, the inclusion of these new scalar field directions has little impact on otherwise metastable vacuum configurations.Comment: 7 pages, 4 figure

The Ultraviolet Landscape of Two-Higgs Doublet Models

We study the predictions of generic ultraviolet completions of two-Higgs doublet models. We assume that at the matching scale between the two-Higgs doublet model and a ultraviolet complete theory -- which can be anywhere between the TeV and the Planck scale -- arbitrary but perturbative values for the quartic couplings are present. We evaluate the couplings down from the matching scale to the weak scale and study the predictions for the scalar mass spectrum. In particular, we show the importance of radiative corrections which are essential for both an accurate Higgs mass calculation as well as determining the stability of the electroweak vacuum. We study the relation between the mass splitting of the heavy Higgs states and the size of the quartic couplings at the matching scale, finding that only a small class of models exhibit a sizeable mass splitting between the heavy scalars at the weak scale. Moreover, we find a clear correlation between the maximal size of the couplings and the considered matching scale.Comment: 16 pages, 10 figure

A constrained supersymmetric left-right model

We present a supersymmetric left-right model which predicts gauge coupling unification close to the string scale and extra vector bosons at the TeV scale. The subtleties in constructing a model which is in agreement with the measured quark masses and mixing for such a low left-right breaking scale are discussed. It is shown that in the constrained version of this model radiative breaking of the gauge symmetries is possible and a SM-like Higgs is obtained. Additional CP-even scalars of a similar mass or even much lighter are possible. The expected mass hierarchies for the supersymmetric states differ clearly from those of the constrained MSSM. In particular, the lightest down-type squark, which is a mixture of the sbottom and extra vector-like states, is always lighter than the stop. We also comment on the model's capability to explain current anomalies observed at the LHC.Comment: 21 pages, 5 figures; v2: references added, matches published versio

R-Parity Violation at the LHC

We investigate the phenomenology of the MSSM extended by a single R-parity violating coupling at the unification scale. For all R-parity violating couplings, we discuss the evolution of the particle spectra through the renormalization group equations and the nature of the lightest supersymmetric particle (LSP) within the CMSSM, as an example of a specific complete supersymmetric model. We use the nature of the LSP to classify the possible signatures. For each possible scenario we present in detail the current LHC bounds on the supersymmetric particle masses, typically obtained using simplified models. From this we determine the present coverage of R-parity violating models at the LHC. We find several gaps, in particular for a stau-LSP, which is easily obtained in R-parity violating models. Using the program CheckMATE we recast existing LHC searches to set limits on the parameters of all R-parity violating CMSSMs. We find that virtually all of them are either more strongly constrained or similarly constrained in comparison to the R-parity conserving CMSSM, including the $\bar U\bar D\bar D$ models. For each R-parity violating CMSSM we then give the explicit lower mass bounds on all relevant supersymmetric particles.Comment: 43 pages, 13 tables, 17 figures; updated Figs. 11-17 and Tab. 12 including NLO corrections; version accepted for publication in EPJ