Search

We consider a low-energy effective theory of the next-to-minimal supersymmetric Standard Model by decoupling all scalar states except one Higgs doublet and the complex gauge singlet. The mass spectrum of the resulting singlet-extended Standard Model is calculated from two different perspectives: 1) using a matching of the scalar sectors at next-to-leading order; 2) using the simplified-model approach of calculating the masses in the effective theory at fixed order at the weak scale ignoring any connection to the full theory. Significant deviations between the two methods are found not only in the scalar sector, but also properties of the additional fermions can be very different. Thus, only a small part of the parameter space of the simplified model can be embedded in a well motivated SUSY framework., Comment: 11 pages, 9 figures

xBIT is a tool for performing parameter scans in beyond the Standard Model theories. It's written in Python and fully open source. The main purpose of xBIT is to provide an easy to use tool to help phenomenologists with their daily task: exploring the parameter space of new models. It was developed under the impression of the SARAH/SPheno framework, but should be use-able with other tools as well that use the SLHA format to transfer data. It also supports by default MicrOmegas for dark matter calculations, HiggsBounds and HiggsSignals for checking the Higgs properties, and Vevacious for testing the vacuum stability. Classes for other tools can be added if necessary. In order to improve the efficiency of the parameter scans, the recently proposed 'Machine Learning Scan' approach is included. For this purpose, xBIT uses pyTorch to deal with artificial neural networks., Comment: 16 pages, 5 figures. GitHub page: https://github.com/fstaub/xBIT

Several ideas exist how the stringent mass limits from LHC on new coloured particles can be avoided. One idea are the so-called `stealth' scenarios in which missing transversal energy (MET) is avoided due a peculiar mass configuration. It is usually assumed that the cascade decay of the dominantly-produced coloured particle finishes in a two-body decay, where this mass configuration leads to a very small amount of MET. We discuss here the potential impact of other decay channels, either loop-induced or via off-shell mediators. It is shown that those channels already become important even for moderate branching ratios of 10%. Larger branching ratios in particular into a photon can completely wash out all benefits of the stealth setup. We discuss this in a model-independent form, but also at the simplest SUSY stealth scenario which can be realised in the NMSSM., Comment: 12 pages, 8 figures, 2 tables

We demonstrate that in a recently proposed unified leptoquark model based on the gauge group $SU(4)_C\times SU(2)_L \times U(1)_R$ significant deviations from the Standard Model values of $R_K$ and $R_{K^*}$ can be accommodated without any need of extra heavy fermions. Low energy data, in particular lepton flavour violating $\mu$ decays and $K_L\to e \mu$, severely constrain the available parameter space. We show that in the allowed part of the parameter space (i) some of the lepton-flavour-violating tau decay branching ratios are predicted to be close to their current experimental limits. (ii) The underlying scalar leptoquarks can be probed at the LHC via their dominant decay modes into tau-leptons and electrons and the third generation quarks. (iii) The constraints from meson oscillations imply that the masses of scalar gluons, another pair of coloured multiplets around, have to be bigger than around 15 TeV and, thus, they can be probed only at a future 100 TeV collider. In both neutral and charged variants, these scalars decay predominantly into third generation quarks, with up to $O$(10\%) branching ratios into family-mixed final states. Besides that, we comment on the phenomenology of the scalar gluons in the current scenarios in the case that the $B$-decay anomalies eventually disappear.

The format defined by the SUSY Les Houches Accord (SLHA) is widely used in high energy physics to store and exchange information. It is no longer applied only to a few supersymmetric models, but the general structure is adapted to all kind of models. Therefore, it is helpful to have parsers at hand which can import files in the SLHA format into high-level languages as Python and Mathematica in order to further process the data. The focus of the xSLHA package, which exists now for Python and Mathematica, was on a fast read-in of large data samples. Moreover, also some blocks used by different tools, as HiggsBounds for instance, deviate from the standard conventions. These are also supported by xSLHA., Comment: 10 pages, no figures

We have reached a new era of particle physics in which the properties of the Higgs boson, in particular its mass, turned into precision observables. Therefore, it is necessary to have accurate predictions of these properties in models for new physics. I give an overview of available tools for supersymmetric and non-supersymmetric models which are publically available. Afterwards, the main idea behind generic tools to study a large variety of models is summarised. Also some remarks about the validity of checks for perturbative unitarity, which are often applied for non-supersymmetric models, are given., Comment: Prepared for proceedings for Charged2018

There are nowadays strong experimental constraints on supersymmetric theories from the Higgs measurements as well as from the null results in Sparticle searches. However, even the parameter spaces which are in agreement with experimental data can be further constrained by using theoretical considerations. Here, we discuss for the MSSM and NMSSM the impact of perturbative unitarity as well as of the stability of the one-loop effective potential. We find in the case of the MSSM, that vacuum stability is always the stronger constraint. On the other side, the situation is more diverse in the NMSSM and one should always check both kind of constraints., Comment: 8 pages, 8 figures

Nowadays, one needs to consider seriously the possibility that a large separation between the scale of new physics and the electroweak scale exists. Nevertheless, there are still observables in this scenario, in particular the Higgs mass, which are sensitive to the properties of the UV theory. In order to obtain reliable predictions for a model which involves very heavy degrees of freedom, the precise matching to an effective theory is necessary. While this has been so far only studied for a few selected examples, we present an extension of the ${\tt Mathematica}$ package ${\tt SARAH}$ to perform automatically the matching between two scalar sectors at the full one-loop level for general models. We show that we can reproduce all important results for commonly studied models like split- or high-scale supersymmetry. One can now easily go beyond that and study new ideas involving very heavy states, where the effective model can either be just the standard model or an extension of it. Also scenarios with several matching scales can be easily considered. We provide model files for the MSSM with seven different mass hierarchies as well as two high-scale versions of the NMSSM. Moreover, it is explained how new models are implemented.

We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the $\beta$-functions of the dimensionful Lagrangian parameters (the fermion mass, the bilinear and trilinear scalar couplings) as well as the dimensionless quartic scalar couplings. There are two sources for these discrepancies. Firstly, the known expressions for the scalar couplings assume a diagonal wave-function renormalisation which is not appropriate for models with mixing in the scalar sector. Secondly, the dimensionful parameters have been derived in the literature using a dummy field method which we critically re-examine, obtaining revised expressions for the $\beta$-function of the fermion mass. We perform an independent cross-check using well-tested supersymmetric RGEs which confirms our results. The numerical impact of the changes in the $\beta$-function for the fermion mass terms is illustrated using a toy model with a heavy vector-like fermion pair coupled to a scalar gauge singlet. Unsurprisingly, the correction to the running of the fermion mass becomes sizeable for large Yukawa couplings of the order of O(1). Furthermore, we demonstrate the importance of the correction to the $\beta$-functions of the scalar quartic couplings using a general type-III Two-Higgs-Doublet-Model. All the corrected expressions have been implemented in updated versions of the Mathematica package SARAH and the Python package PyR@TE., Comment: Changes to Eq.(5.12) due to a literature error which has propagated also to Eqs.(5.45),(7.7),(7.9). Changes to Fig.2 are hardly visible. The diagrams in App.(A.3), (A.5),(A.6) have been corrected. Without affecting the overall conclusion, a few typographical errors as well as the changed Eq.(5.12) lead to a modification of Eqs.(B.6),(B.14),(B.16),(B.18),(B.20),(B.40). Erratum submitted to NPB

The anomalies in the $B$-meson sector, in particular $R_{K^{(*)}}$ and $R_{D^{(*)}}$, are often interpreted as hints for physics beyond the Standard Model. To this end, leptoquarks or a heavy $Z'$ represent the most popular SM extensions which can explain the observations. However, adding these fields by hand is not very satisfactory as it does not address the big questions like a possible embedding into a unified gauge theory. On the other hand, light leptoquarks within a unified framework are challenging due to additional constraints such as lepton flavor violation. The existing accounts typically deal with this issue by providing estimates on the relevant couplings. In this letter we consider a complete model based on the $SU(4)_{\rm C}\otimes SU(2)_{\rm L}\otimes U(1)_{\rm R}$ gauge symmetry, a subgroup of $SO(10)$, featuring both scalar and vector leptoquarks. We demonstrate that this setup has, in principle, all the potential to accommodate $R_{K^{(*)}}$ and $R_{D^{(*)}}$ while respecting bounds from other sectors usually checked in this context. However, it turns out that $K_L \to e^{\pm} \mu^{\mp}$ severely constraints not only the vector but also the scalar leptoquarks and, consequently, also the room for any sizeable deviations of $R_{K^{(*)}}$ from 1. We briefly comment on the options for extending the model in order to conform this constraint. Moreover, we present a simple criterion for all-orders proton stability within this class of models., Comment: 9 pages, 7 figures, 2 tables

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 figures

Triplet extensions are attractive alternatives to the standard model (SM) of particle physics. While models with only one triplet are highly constrained by electroweak precision observables, this is not necessarily the case once several triplets are present as in the Georgi-Machacek model. As in all other BSM models, the parameter space of triplet extensions is constrained by the condition that perturbative unitarity is not violated. For this purpose, limits on the eigenvalues of the scalar $2 \to 2$ scattering matrix are set. It is very common in the BSM literature that the scattering matrix is calculated under one crucial assumption: the scattering energy s is so large that only point interactions involving quartic couplings provide non-negligible contributions. However, it is not given that this approximation is always valid - in fact, diagrams involving propagators can play an important role. We discuss at the examples of (i) the SM model extended by a real triplet, (ii) the Y = 1 triplet extension of the SM, and (iii) the Georgi-Machacek model, how the tree-level unitarity constraints are affected once the large s approximation is given up. For all models we find that the impact of (effective) cubic couplings can be crucial., Comment: 12 pages, 9 figures

Two-Higgs-Doublet-Models (THDMs) are among the simplest extensions of the standard model and are intensively studied in the literature. Using on-shell parameters such as the masses of the additional scalars as input, corresponds often to large quartic couplings in the underlying Lagrangian. Therefore, it is important to check if these couplings are for instance in agreement with perturbative unitarity. The common approach for doing this check is to consider the two-particle scattering matrix of scalars in the large centre-of-mass energy limit where only point interactions contribute. We show that this is not always a valid approximation: the full calculation including all tree-level contributions at finite energy can lead to much more stringent constraints. We show how the allowed regions in the parameter space are affected. In particular, the light Higgs window with a second Higgs below 125 GeV completely closes for large values of the $Z_2$ breaking parameter $|M_{12}|$. We also compare against the loop corrected constraints, which use also the large $\sqrt{s}$ approximation, and find that (effective) cubic couplings are often more important than radiative corrections., Comment: 8 pages, 6 figures

We present an update of the Mathematica package SARAH to calculate unitarity constraints in BSM models. The new functions can perform an analytical and numerical calculation of the two-particle scattering matrix of (uncoloured) scalars. We do not make use of the simplifying assumption of a very large scattering energy, but include all contributions which could become important at small energies above the weak scale. This allows us to constrain trilinear scalar couplings. However, it can also modify (weakening or strengthening) the constraints on quartic couplings, which we show via the example of a singlet extended Standard Model., Comment: 17 pages, 3 figures

We define a data exchange format for numerical values of Wilson coefficients of local operators parameterising low-energy effects of physics beyond the Standard Model. The format facilitates interfacing model-specific Wilson coefficient calculators, renormalisation group (RG) runners, and observable calculators. It is designed to be unambiguous (defining a non-redundant set of operators with fixed normalisation in each basis), extensible (allowing the addition of new EFTs or bases by the user), and robust (being based on industry standard file formats with parsers implemented in many programming languages). We have implemented the format for the Standard Model EFT (SMEFT) and for the weak effective theory (WET) below the electroweak scale and have added interfaces to a number of public codes dealing with SMEFT or WET. We also provide command-line utilities and a Python module for convenient manipulation of WCxf files, including translation between different bases and matching from SMEFT to WET., Comment: 22 pages. Additional documentation can be found at https://wcxf.github.io/. v2: Discussion of wilson package added, discussion of EOS, flavio, and SMEFTsim updated. Matches version published in Computer Physics Communications

We investigate the high-scale behaviour of Higgs sectors beyond the Standard Model, pointing out that the proper matching of the quartic couplings before applying the renormalisation group equations (RGEs) is of crucial importance for reliable predictions at larger energy scales. In particular, the common practice of leading-order parameters in the RGE evolution is insufficient to make precise statements on a given model's UV behaviour, typically resulting in uncertainties of many orders of magnitude. We argue that, before applying N-loop RGEs, a matching should even be performed at N-loop order in contrast to common lore. We show both analytical and numerical results where the impact is sizeable for three minimal extensions of the Standard Model: a singlet extension, a second Higgs doublet and finally vector-like quarks. We highlight that the known two-loop RGEs tend to moderate the running of their one-loop counterparts, typically delaying the appearance of Landau poles. For the addition of vector-like quarks we show that the complete two-loop matching and RGE evolution hints at a stabilisation of the electroweak vacuum at high energies, in contrast to results in the literature., Comment: 16 pages, 11 figures; v2: title changed, accepted for publication in PRD

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 figures

Models with a light, additional gauge boson are attractive extensions of the standard model. Often these models are only considered as effective low energy theory without any assumption about an UV completion. This leaves not only the hierarchy problem of the SM unsolved, but introduces a copy of it because of the new fundamental scalars responsible for breaking the new gauge group. A possible solution is to embed these models into a supersymmetric framework. However, this gives rise to an additional source of fine-tuning compared to the MSSM and poses the question how natural such a setup is. One might expect that the additional fine-tuning is huge, namely, $O(M^2_{\rm SUSY}/m^2_{Z'})$. In this paper we point out that this is not necessarily the case. We show that it is possible to find a focus point behaviour also in the new sector in co-existence to the MSSM focus point. We call this 'Double Focus Point Supersymmetry'. Moreover, we stress the need for a proper inclusion of radiative corrections in the fine-tuning calculation: a tree-level estimate would lead to predictions for the tuning which can be wrong by many orders of magnitude. As showcase, we use the $U(1)_{B-L}$ extended MSSM and discuss possible consequence of the observed $^8\textrm{Be}$ anomaly. However, similar features are expected for other models with an extended gauge group which involve potentially large Yukawa-like interactions of the new scalars., Comment: 11 pages, 4 figures, two column format, reference updated

The calculation of the Higgs mass in general renormalisable field theories has been plagued by the so-called "Goldstone Boson Catastrophe", where light (would-be) Goldstone bosons give infra-red divergent loop integrals. In supersymmetric models, previous approaches included a workaround that ameliorated the problem for most, but not all, parameter space regions; while giving divergent results everywhere for non-supersymmetric models! We present an implementation of a general solution to the problem in the public code SARAH, along with new calculations of some necessary loop integrals and generic expressions. We discuss the validation of our code in the Standard Model, where we find remarkable agreement with the known results. We then show new applications in Split SUSY, the NMSSM, the Two-Higgs-Doublet Model, and the Georgi-Machacek model. In particular, we take some first steps to exploring where the habit of using tree-level mass relations in non-supersymmetric models breaks down, and show that the loop corrections usually become very large well before naive perturbativity bounds are reached., Comment: 45 pages, 12 figures

The stability of the electroweak potential is a very important constraint for models of new physics. At the moment, it is standard for Two-Higgs doublet models (THDM), singlet or triplet extensions of the standard model to perform these checks at tree-level. However, these models are often studied in the presence of very large couplings. Therefore, it can be expected that radiative corrections to the potential are important. We study these effects at the example of the THDM type-II and find that loop corrections can revive more than 50% of the phenomenological viable points which are ruled out by the tree-level vacuum stability checks. Similar effects are expected for other extension of the standard model., Comment: 6 pages, 5 figures; added few explanations and fixed typos in eqs. (8)-(9), matches version accepted for publication by PLB

We describe a fully generic implementation of two-body partial decay widths at the full one-loop level in the SARAH and SPheno framework compatible with most supported models. It incorporates fermionic decays to a fermion and a scalar or a gauge boson as well as scalar decays into two fermions, two gauge bosons, two scalars or a scalar and a gauge boson. We present the relevant generic expressions for virtual and real corrections. Whereas wavefunction corrections are determined from on-shell conditions, the parameters of the underlying model are by default renormalised in a DR (or MS) scheme. However, the user can also define model-specific counter-terms. As an example we discuss the renormalisation of the electric charge in the Thomson limit for top-quark decays in the standard model. One-loop induced decays are also supported. The framework additionally allows the addition of mass and mixing corrections induced at higher orders for the involved external states. We explain our procedure to cancel infra-red divergences for such cases, which is achieved through an infra-red counter-term taking into account corrected Goldstone boson vertices. We compare our results for sfermion, gluino and Higgs decays in the minimal supersymmetric standard model (MSSM) against the public codes SFOLD, FVSFOLD and HFOLD and explain observed differences. Radiative induced gluino and neutralino decays are compared against the original implementation in SPheno in the MSSM. We exactly reproduce the results of the code CNNDecays for decays of neutralinos and charginos in R-parity violating models. The new version SARAH 4.11.0 by default includes the calculation of two-body decay widths at the full one-loop level. Current limitations for certain model classes are described., Comment: 76 pages, 11 figures; v2: some clarifications added. Matches version accepted for publication by EPJC

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 figures

For a long time, the minimal supersymmetric standard model (MSSM) with light masses for the supersymmetric states was considered as the most natural extension of the Standard Model of particle physics. Consequently, a valid approximation was to match the MSSM to the precision measurement directly at the electroweak scale. This approach was also utilized by all dedicated spectrum generators for the MSSM. However, the higher the supersymmetric (SUSY) scale is, the bigger the uncertainties which are introduced by this matching. We point out important consequences of a two-scale matching, where the running parameters within the SM are calculated at $M_Z$ and evaluated up to the SUSY scale, where they are matched to the full model. We show the impact on gauge coupling unification as well as the SUSY mass spectrum. Also the Higgs mass prediction for large supersymmetric masses has been improved by performing the calculation within an effective SM. The approach presented here is now also available in the spectrum generator SPheno. Moreover, also SARAH was extended accordingly and gives the possibility to study these effects now in many different supersymmetric models., Comment: 24 pages, 13 figures; v2) A few clarifications added, matches published version

We evaluate the amount of fine-tuning in constrained versions of the minimal supersymmetric standard model (MSSM), with different boundary conditions at the GUT scale. Specifically we study the fully constrained version as well as the cases of non-universal Higgs and gaugino masses. We allow for the presence of additional non-holomorphic soft-terms which we show further relax the fine-tuning. Of particular importance is the possibility of a Higgsino mass term and we discuss possible origins for such a term in UV complete models. We point out that loop corrections typically lead to a reduction in the fine-tuning by a factor of about two compared to the estimate at tree-level, which has been overlooked in many recent works. Taking these loop corrections into account, we discuss the impact of current limits from SUSY searches and dark matter on the fine-tuning. Contrary to common lore, we find that the MSSM fine-tuning can be as small as 10 while remaining consistent with all experimental constraints. If, in addition, the dark matter abundance is fully explained by the neutralino LSP, the fine-tuning can still be as low as $\sim$ 20 in the presence of additional non-holomorphic soft-terms. We also discuss future prospects of these models and find that the MSSM will remain natural even in the case of a non-discovery in the foreseeable future., Comment: 23 pages, 10 figures; v2: added references, matches published version

It has been proposed that the observed diphoton excess at 750 GeV could be explained within the constrained minimal supersymmetric standard model via resonantly produced stop bound states. We reanalyze this scenario critically and extend previous work to include the constraints from the stability of the electroweak vacuum and from the decays of the stoponium into a pair of Higgs bosons. It is shown that the interesting regions of parameter space with a light stop and Higgs of the desired mass are ruled out by these constraints. This conclusion is not affected by the presence of the bound states because the binding energy is usually very small in the regions of parameter space which can explain the Higgs mass. Thus, this also leads to strong constraints on the diphoton production cross section which is in general too small., Comment: 8 pages, 5 figures; v2: added Fig. 5, matches published version

We propose an explanation of the galactic center gamma ray excess by supersymmetric WIMPs as heavy as 500 GeV. The lightest neutralino annihilates into vector-like leptons or quarks which cascade decay through intermediate Higgs bosons. Due to the long decay chains, the gamma ray spectrum is much softer than naively expected and peaks at GeV energies. The model predicts correlated diboson and dijet signatures to be tested at the LHC., Comment: 8 pages, 8 figures; v2: focus on gamma ray excess, matches published version

We discuss the automatised calculation of the Higgs mass in renormalisable supersymmetric models with complex parameters at the two-loop level. Our setup is based on the public codes SARAH and SPheno, which can now compute the two-loop corrections to masses of all neutral scalars in such theories. The generic ansatz for these calculations and the handling of the `Goldstone Boson catastrophe' is described. It is shown that we find perfect agreement with other existing two-loop calculations performed in the DR-bar scheme. We also use the functionality to derive results for the MSSM and NMSSM not available before: the Higgs mass in the constrained version of the complex MSSM, and the impact of CP phases in the two-loop corrections beyond order alpha-strong alpha-top for the scale invariant NMSSM are briefly analysed., Comment: 19 pages, 14 figures

It is often argued that low fine tuning in the MSSM necessarily requires a rather light Higgsino. In this note we show that this need not be the case when a more complete set of soft SUSY breaking mass terms are included. In particular an Higgsino mass term, that correlates the $\mu-$term contribution with the soft SUSY-breaking Higgsino masses, significantly reduces the fine tuning even for Higgsinos in the TeV mass range where its relic abundance means it can make up all the dark matter., Comment: 5 pages, 2 figures

I give in this brief tutorial a short practical introduction to the Mathematica package SARAH. First, it is shown how an existing model file can be changed to implement a new model in SARAH. In the second part, masses, vertices and renormalisation group equations are calculated with SARAH. Finally, the main commands to generate model files and output for other tools are summarised., Comment: 8 pages, 1 figure; Tutorial (based on lecture arXiv:1509.07061) given at "School and Workshops on Elementary Particle Physics and Gravity", Corfu Summer Institute, September 2015

Non-Decoupling D-Terms are an attractive possibility to enhance the tree-level mass of the standard model like Higgs boson in supersymmetric models. We discuss here for the case of a new Abelian gauge group two effects usually neglected in literature: (i) the size of the additional radiative corrections to the Higgs mass due to the presence of the new gauge coupling, and (ii) the impact of gauge kinetic mixing. It is shown that both effects reduce to some extent the positive effect of the non-decoupling D-terms on the Higgs mass., Comment: 7 pages, 6 figures; v2: small clarifications, matches version accepted for publication by PLB

The hints for a new resonance at 750 GeV from ATLAS and CMS have triggered a significant amount of attention. Since the simplest extensions of the standard model cannot accommodate the observation, many alternatives have been considered to explain the excess. Here we focus on several proposed renormalisable weakly-coupled models and revisit results given in the literature. We point out that physically important subtleties are often missed or neglected. To facilitate the study of the excess we have created a collection of 40 model files, selected from recent literature, for the Mathematica package SARAH. With SARAH one can generate files to perform numerical studies using the tailor-made spectrum generators FlexibleSUSY and SPheno. These have been extended to automatically include crucial higher order corrections to the diphoton and digluon decay rates for both CP-even and CP-odd scalars. Additionally, we have extended the UFO and CalcHep interfaces of SARAH, to pass the precise information about the effective vertices from the spectrum generator to a Monte-Carlo tool. Finally, as an example to demonstrate the power of the entire setup, we present a new supersymmetric model that accommodates the diphoton excess, explicitly demonstrating how a large width can be obtained. We explicitly show several steps in detail to elucidate the use of these public tools in the precision study of this model., Comment: 184 pages, 24 figures; model files available at http://sarah.hepforge.org/Diphoton_Models.tar.gz; v2: added a few clarifications and references

Motivated by the 750 GeV diphoton excess found at LHC, we compute the maximal width into $\gamma\gamma$ that a neutral scalar can acquire through a loop of charged fermions or scalars as function of the maximal scale at which the theory holds, taking into account vacuum (meta)stability bounds. We show how an extra gauge symmetry can qualitatively weaken such bounds, and explore collider probes and connections with Dark Matter., Comment: 16 pages, 6 figures

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 version

Soft supersymmetry-breaking terms provide a wealth of new potential sources of flavour violation, which are tightly constrained by precision experiments. This has posed a challenge to construct flavour models which both explain the structure of the Standard Model Yukawa couplings and also predict soft-breaking patterns that are compatible with these constraints. While such models have been studied in great detail, the impact of flavour violating soft terms on the Higgs mass at the two-loop level has been assumed to be small or negligible. In this letter, we show that large flavour violation in the up-squark sector can give a positive or negative mass shift to the SM-like Higgs of several GeV, without being in conflict with other observations. We investigate in which regions of the parameter space these effects can be expected., Comment: 8 pages, 9 figures

Supersymmetric Standard Models (SSMs) with Dirac gauginos have the appealing supersoft property that they only cause finite contributions to scalar masses. Considering gauge mediated SUSY breaking with conformal sequestering and assuming there is one and only one fundamental parameter with dimension mass arising from supersymmetry breaking, we find a cancellation between the dominant terms that contribute to the EWFT. The resulting EWFT measure can be of order one even for supersymmetric particle masses and $\mu$-terms in the TeV range., Comment: 6 pages, 1 figure; v2: title and abstract changed, small rephrasing of the text, conclusions unchanged. Matches version accepted for publication by PRD

I give in this lecture an overview of the features of the Mathematica package SARAH, and explain how it can be used together with other codes to study all aspects of a BSM model. The focus will be on the description of the analytical calculations which SARAH can perform and how this information is used to generate automatically a spectrum generator based on SPheno. I also summarize the main aspects of the other interfaces to public codes like HiggsBounds/HiggsSignals, FeynArts/FormCalc, CalcHep, MicrOmegas, WHIZARD, Vevacious or MadGraph. The appendix contains a short tutorial about the implementation and usage of a new model., Comment: 16 pages, Lecture given at "Summer School and Workshop on the Standard Model and Beyond", Corfu Summer Institute 2015; v2: moved to PoS style

An unidentified 3.5 keV line from X-ray observations of galaxy clusters has been reported recently. Although still under scrutiny, decaying dark matter could be responsible for this signal. We investigate whether an axino with a mass of 7 keV could explain the line, keeping the discussion as model independent as possible. We point out several obstacles, which were overlooked in the literature, and which make the axino an unlikely candidate. The only viable scenario predicts a light metastable neutralino, with a mass between 0.1 and 10 GeV and a lifetime between $10^{-3}$ and $10^4$ s., Comment: 5 pages; v2 matches the one published in PLB

The publicly available spectrum generators for the NMSSM often lead to different predictions for the mass of the standard model-like Higgs boson even if using the same renormalization scheme and two-loop accuracy. Depending on the parameter point, the differences can exceed 5 GeV, and even reach 8 GeV for moderate superparticle masses of up to 2 TeV. It is shown here that these differences can be traced back to the calculation of the running standard model parameters entering all calculations, to the approximations used in the two-loop corrections included in the different codes, and to different choices for the renormalization conditions and scales. In particular, the importance of the calculation of the top Yukawa coupling is pointed out., Comment: 24 pages, no figures; v2: slightly extended discussion, matches version accepted for publication by CPC

We perform the first analysis of Dark Matter scenarios in a constrained model with Dirac Gauginos. The model under investigation is the Constrained Minimal Dirac Gaugino Supersymmetric Standard model (CMDGSSM) where the Majorana mass terms of gauginos vanish. However, $R$-symmetry is broken in the Higgs sector by an explicit and/or effective $B_\mu$-term. This causes a mass splitting between Dirac states in the fermion sector and the neutralinos, which provide the dark matter candidate, become pseudo-Dirac states. We discuss two scenarios: the universal case with all scalar masses unified at the GUT scale, and the case with non-universal Higgs soft-terms. We identify different regions in the parameter space which fullfil all constraints from the dark matter abundance, the limits from SUSY and direct dark matter searches and the Higgs mass. Most of these points can be tested with the next generation of direct dark matter detection experiments., Comment: 28 pages, 11 figures; v2: minor changes, title modified; matches published version

We present a precise analysis of the Higgs mass corrections stemming from vectorlike top partners in supersymmetric models. We reduce the theoretical uncertainty compared to previous studies in the following aspects: (i) including the one-loop threshold corrections to SM gauge and Yukawa couplings due to the presence of the new states to obtain the $\bar{\text{DR}}$ parameters entering all loop calculations, (ii) including the full momentum dependence at one-loop, and (iii) including all two-loop corrections but the ones involving $g_1$ and $g_2$. We find that the additional threshold corrections are very important and can give the largest effect on the Higgs mass. However, we identify also parameter regions where the new two-loop effects can be more important than the ones of the MSSM and change the Higgs mass prediction by up to 10 GeV. This is for instance the case in the low $\tan\beta$, small $M_A$ regime. We use these results to calculate the electroweak fine-tuning of an UV complete variant of this model. For this purpose, we add a complete $\textbf{10}$ and $\bar{\textbf{10}}$ representation of $SU(5)$ to the MSSM particle content. We embed this model in minimal Gauge Mediated Supersymmetry Breaking and calculate the electroweak fine-tuning with respect to all important parameters. It turns out that the limit on the gluino mass becomes more important for the fine-tuning than the Higgs mass measurements which is easily to satisfy in this setup., Comment: 64 pages, 17 figures

This paper describes the physics case for a new fixed target facility at CERN SPS. The SHiP (Search for Hidden Particles) experiment is intended to hunt for new physics in the largely unexplored domain of very weakly interacting particles with masses below the Fermi scale, inaccessible to the LHC experiments, and to study tau neutrino physics. The same proton beam setup can be used later to look for decays of tau-leptons with lepton flavour number non-conservation, $\tau\to 3\mu$ and to search for weakly-interacting sub-GeV dark matter candidates. We discuss the evidence for physics beyond the Standard Model and describe interactions between new particles and four different portals - scalars, vectors, fermions or axion-like particles. We discuss motivations for different models, manifesting themselves via these interactions, and how they can be probed with the SHiP experiment and present several case studies. The prospects to search for relatively light SUSY and composite particles at SHiP are also discussed. We demonstrate that the SHiP experiment has a unique potential to discover new physics and can directly probe a number of solutions of beyond the Standard Model puzzles, such as neutrino masses, baryon asymmetry of the Universe, dark matter, and inflation, Comment: 200 pages + appendices/references

The LHCb collaboration has recently reported on some anomalies in $b\to s$ transitions. In addition to discrepancies with the Standard Model (SM) predictions in some angular observables and branching ratios, an intriguing hint for lepton universality violation was found. Here we propose a simple model that extends the SM with a dark sector charged under an additional $U(1)$ gauge symmetry. The spontaneous breaking of this symmetry gives rise to a massive $Z^\prime$ boson, which communicates the SM particles with a valid dark matter candidate, while solving the $b\to s$ anomalies with contributions to the relevant observables., Comment: 9 pages, 4 figures. Few typos corrected, references added

I give an overview about the features the Mathematica package SARAH provides to study new models. In general, SARAH can handle a wide range of models beyond the MSSM coming with additional chiral superfields, extra gauge groups, or distinctive features like Dirac gaugino masses. All of these models can be implemented in a compact form in SARAH and are easy to use: SARAH extracts all analytical properties of the given model like two-loop renormalization group equations, tadpole equations, mass matrices and vertices. Also one- and two-loop corrections to tadpoles and self-energies can be obtained. For numerical calculations SARAH can be interfaced to other tools to get the mass spectrum, to check flavour or dark matter constraints, and to test the vacuum stability, or to perform collider studies. In particular, the interface to SPheno allows a precise prediction of the Higgs mass in a given model comparable to MSSM precision by incorporating the important two-loop corrections. I show in great detail at the example of the B-L-SSM how SARAH together with SPheno, HiggsBounds/HiggsSignals, FlavorKit, Vevacious, CalcHep, MicrOmegas, WHIZARD, and MadGraph can be used to study all phenomenological aspects of a model. Even if I concentrate in this manuscript on the analysis of supersymmetric models most features are also available in the non-supersymmetric case., Comment: 169 pages, 14 figures; pedagogical summary of 0806.0538, 0909.2863, 1002.0840, 1109.5147, 1207.0906, 1307.1477, 1309.7223, 1405.1434, 1411.0675 and 1503.03098 prepared for "Supersymmetry, Supergravity, and Superstring Phenomenology"

We propose the Supersymmetric Standard Models (SSMs) with a pseudo-Dirac gluino from hybrid $F-$ and $D-$term supersymmetry (SUSY) breakings. Similar to the SSMs before the LHC, all the supersymmetric particles in the Minimal SSM (MSSM) obtain the SUSY breaking soft terms from the traditional gravity mediation and have masses within about 1 TeV except gluino. To evade the LHC SUSY search constraints, the gluino also has a heavy Dirac mass above 3 TeV from $D-$term SUSY breaking. Interestingly, such a heavy Dirac gluino mass will not induce the electroweak fine-tuning problem. We realize such SUSY breakings via an anomalous $U(1)_X$ gauge symmetry inspired from string models. To maintain the gauge coupling unification and increase the Higgs boson mass, we introduce extra vector-like particles. We study the viable parameter space which satisfies all the current experimental constraints, and present a concrete benchmark point. This kind of models not only preserves the merits of pre-LHC SSMs such as naturalness, dark matter, etc, but also solves the possible problems in the SSMs with Dirac gauginos due to the $F$-term gravity mediation., Comment: 6 pages,3 figures,revised version

We discuss the impact of the two-loop corrections to the Higgs mass in the NMSSM beyond $O(\alpha_S(\alpha_b + \alpha_t))$. For this purpose we use the combination of the public tools SARAH and SPheno to include all contributions stemming from superpotential parameters. We show that the corrections in the case of a heavy singlet are often MSSM-like and reduce the predicted mass of the SM-like state by about 1 GeV as long as $\lambda$ is moderately large. For larger values of $\lambda$ the additional corrections can increase the SM-like Higgs mass. If a light singlet is present the additional corrections become more important even for smaller values of $\lambda$ and can even dominate the ones involving the strong interaction. In this context we point out that important effects are not reproduced quantitatively when only including $O((\alpha_b+\alpha_t+\alpha_\tau)^2)$ corrections known from the MSSM., Comment: 23 pages, 11 figures

We study the impact of large trilinear R-parity violating couplings on the lightest CP-even Higgs boson mass in supersymmetric models. We use the publicly available computer codes SARAH and SPheno to compute the leading two-loop corrections. We use the effective potential approach. For not too heavy third generation squarks (< 1 TeV) and couplings close to the unitarity bound we find positive corrections up to a few GeV in the Higgs mass., Comment: 6 pages, 5 figures

We present an extension to the Mathematica package SARAH which allows for Higgs mass calculations at the two-loop level in a wide range of supersymmetric models beyond the MSSM. These calculations are based on the effective potential approach and include all two-loop corrections which are independent of electroweak gauge couplings. For the numerical evaluation Fortran code for SPheno is generated by SARAH. This allows the prediction of the Higgs mass in more complicated SUSY models with the same precision that most state-of-the-art spectrum generators provide for the MSSM., Comment: 23 pages, 4 figures; v2: matches published version up to updated references

This is a compact overview of Higgs sectors in extensions of the MSSM. The focus is on the summary of the main features of models with additional singlets and triplets as well as of models with Dirac gauginos. In addition, also important aspects of models with an extended gauge sector are shown. Finally, I comment on available tools which can be used for an adequate study of non-minimal SUSY models., Comment: Invited talk given at Prospects for Charged Higgs Discovery at Colliders - CHARGED 2014, 16-18 September 2014, Uppsala. 9+6 pages; 4 Figures; v2: updated/extended references

We present a new kit for the study of flavor observables in models beyond the standard model. The setup is based on the public codes SARAH and SPheno and allows for an easy implementation of new observables. The Wilson coefficients of the corresponding operators in the effective Lagrangian are computed by SPheno modules written by SARAH. New operators can also be added by the user in a modular way. For this purpose a handy Mathematica package called PreSARAH has been developed. This uses FeynArts and FormCalc to derive the generic form factors at tree- and 1-loop levels and to generate the necessary input files for SARAH. This framework has been used to implement BR($\ell_\alpha\to \ell_\beta \gamma$), BR($\ell_\alpha \to 3\, \ell_\beta$), CR($\mu-e,A$), BR($\tau \to P \, \ell$), BR($h\to \ell_\alpha \ell_\beta$), BR($Z\to \ell_\alpha \ell_\beta$), BR($B_{s,d}^0 \to \ell \bar{\ell}$), BR($\bar B \to X_s\gamma$), BR($\bar B \to X_s \ell \bar{\ell}$), BR($\bar B \to X_{d,s} \nu \bar \nu$), BR($K^+ \to \pi^+ \nu \bar \nu$), BR($K_L \to \pi^0 \nu \bar \nu$), $\Delta M_{B_s,B_d}$, $\Delta M_K$, $\varepsilon_K$, BR($B \to K \mu \bar{\mu}$), BR($B\to \ell \nu$), BR($D_s \to \ell \nu$) and BR($K \to \ell \nu$) in SARAH. Predictions for these observables can now be obtained in a wide range of SUSY and non-SUSY models. Finally, the user can use the same approach to easily compute additional observables., Comment: 68 pages; PreSARAH and FlavorKit (included in SARAH 4.2.0) can be downloaded at http://sarah.hepforge.org/FlavorKit.html; v2: minor extensions, matches published version; v3: unifying layout in the appendix

The distinguishing feature of the Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) axion is that it couples to the electroweak Higgs fields. There is thus an immediate connection between the Peccei-Quinn (PQ) scale and the weak scale. We wish to incorporate the DFSZ axion in a complete supersymmetric model, valid at all scales, and then to implement it in a numerical code connecting the high scale and the low scale physics on a quantitative level. We find that the simplest supersymmetric DFSZ model, as proposed by Rajagopal et al. in 1990, is inconsistent when we consider the minimization of the scalar potential. The problem is that we obtain a negative squared mass for the saxion, the scalar partner of the axion, at the minimum. We then consider the minimal extension in order to get a consistent model for all scales: one has to include an additional explicit sector to spontaneously break the PQ symmetry. In the complete model we can determine the mass of the axino, the fermionic partner of the axion. It is useful to distinguish two cases: (1) the supersymmetry (SUSY) breaking scale is lower than the PQ breaking scale, and (2) the scales are comparable. We find that the axino is very light in (1), while its mass is generically of the order of the other soft SUSY breaking masses in (2). We have implemented SUSY breaking via generic soft breaking terms, and thus make no explicit statement about the form and mediation of SUSY breaking. This complete model can then be incorporated in a numerical code connecting the two scales. We briefly discuss the renormalization group equations and the couplings of the axion to gluons and photons., Comment: v3: 11 pages, double-column format; added sections on RGEs and on couplings of axion/axino to gauge fields; expanded the discussion on the axino mass. This version matches the one to appear in PRD