We perform a forecast of the CMSSM for the LHC based in an improved Bayesian analysis taking into account the present theoretical and experimental wisdom about the model. In this way we obtain a map of the preferred regions of the CMSSM parameter space and show that fine-tuning penalization arises from the Bayesian analysis itself when the experimental value of Mz is considered. The results are remarkable stable when using different priors
Adopting a bottom-up point of view, we make a comparative study of the simplest extensions of the MSSM with extra tree level contributions to the lightest Higgs boson mass. We show to what extent a relatively heavy Higgs boson, up to 200-350 GeV, can be compatible with data and naturalness. The price to pay is that the theory undergoes some change of regime at a relatively low scale. Bounds on these models come from electroweak precision tests and naturalness, which often requires the scale at which the soft terms are generated to be relatively low.
The "top-down" approach to minimal supersymmetric standard model (MSSM) phenomenology provides model-dependent indications for a natural stop mass. The approach is based on specific assumptions about the supersymmetry-breaking energy scale and parameters degeneracies. In order to determine robust predictions we update the stop-mass prediction within the MSSM with 25 parameters (MSSM-25) by including electroweak fine-tuning as "naturalness data" during the Bayesian fits of the parameters to experimental data. The approximately prior-independent results show that imposing naturalness, taken here…
The experiments at the Large Hadron Collider (LHC) have pushed the limits on masses of supersymmetric particles beyond the $\sim$TeV scale. This compromises naturalness of the simplest supersymmetric extension of the Standard Model, the minimal supersymmetric Standard Model (MSSM). In this paper we advocate that perhaps the current experimental data are actually hinting towards the physics beyond MSSM. To illustrate this, we treat MSSM as a low energy limit of a more fundamental yet unspecified theory at a scale $Λ$, and compute the fine-tuning measure $Δ$ for generic boundary conditions on so…
With a bottom-up approach, we consider naturalness in the MSSM and NMSSM. Assuming the light stops, the LHC gluino search implies that the degree of fine tuning in both models is less than 2.5%. Taking the LHC hints for the SM-like Higgs boson mass m_h\sim125 GeV seriously, we find that naturalness will favor the NMSSM. We study the Higgs boson mass for several scenarios in the NMSSM: (1) A large λand the doublet-singlet Higgs boson mixing effect pushing upward or pulling downward m_h. The former case can readily give the di-photon excess of the Higgs boson decay whereas the latter case can no…
We analyse the naturalness of the Minimal Supersymmetric Standard Model (MSSM) in the light of recent LHC results from the ATLAS and CMS experiments. We study non-universal boundary conditions for the scalar and the gaugino sector, with fixed relations between some of the soft breaking parameters, and find a significant reduction of fine-tuning for non-universal gaugino masses. For a Higgs mass of about 125 GeV, as observed recently, we find parameter regions with a fine-tuning of O(10), taking into account experimental and theoretical uncertainties. These regions also survive after comparison…
Recent years have seen increased use of Bayesian model comparison to quantify notions such as naturalness, simplicity, and testability, especially in the area of supersymmetric model building. After demonstrating that Bayesian model comparison can resolve a paradox that has been raised in the literature concerning the naturalness of the proton mass, we apply Bayesian model comparison to GUTs, an area to which it has not been applied before. We find that the GUTs are substantially favored over the non-unifying puzzle model. Of the GUTs we consider, the $B-L$ MSSM GUT is the most favored, but th…
We investigate the question of electroweak naturalness within the deflected mirage mediation (DMM) framework for supersymmetry breaking in the minimal supersymmetric standard model (MSSM). The class of DMM models considered are nine-parameter theories that fall within the general classification of the 19-parameter phenomenological MSSM (pMSSM). Our results show that these DMM models have regions of parameter space with very low electroweak fine-tuning, at levels comparable to the pMSSM. These parameter regions should be probed extensively in the current LHC run.
In this report, we compare the naturalness and Dark Matter (DM) properties of the Minimal Supersymmetric Standard Model (MSSM) and the $B-L$ Supersymmetric Standard Model (BLSSM), with universality in both cases. We do this by adopting standard measures for the quantitative analysis of the Fine-Tuning (FT), at both low (i.e. supersymmetric (SUSY)) and high (i.e. unification) scales. We will see a similar level of FT for both models in these scenarios, with a slightly better FT for the BLSSM at SUSY scales and MSSM at Grand Unification Theory (GUT) scales. When including DM relic constraints, w…
In the Minimal Supersymmetric Extension of the Standard Model (MSSM) the higgsino mass parameter $μ$ appears both in the masses of the Higgs bosons and in the neutralino mass matrix. Electroweak finetuning therefore prefers small values of $|μ|$. On the other hand, bino--like neutralinos make a good dark matter candidate. We show that current direct search limits then impose a strong lower bound on $|μ|$, in particular for $μ> 0$ or if the masses of the heavy Higgs bosons of the MSSM are near their current limit from LHC searches. There is therefore some tension between finetuning and neutrali…
We study the contributions of supersymmetric models with a $U(1)$ horizontal symmetry and only spontaneous CP breaking to various lepton flavor observables, such as $μ\to eγ$ and the electron electric dipole moment. We show that both a horizontal symmetry and a lack of explicit CP violation can alleviate the existing bounds from such observables. The undetermined $\mathcal{O}(1)$ coefficients in such mass matrix models muddle the interpretation of the bounds from various flavor observables. To overcome this, we define a new fine-tuning measure for different observables in such setups. This all…
In supersymmetric models a large average stop mass $M_S$ is well known to both boost the lightest Higgs boson mass $m_{h}$ and also make radiative electroweak symmetry breaking unnaturally tuned. The case of `maximal mixing', where the stop trilinear mixing term $A_t$ is set to give $A_t^2/M_S^2 = 6$, allows the stops to be as light as possible for a given $m_h$. Here we make the distinction between minimal $M_S$ and optimal naturalness, showing that the latter occurs for less-than-maximal mixing. Lagrange constrained optimisation reveals that the two coincide closely in the Minimal Supersymme…
Weak scale supersymmetry (SUSY) remains a prime explanation for the radiative stability of the Higgs field. A natural account of the Higgs boson mass, however, strongly favors extensions of the Minimal Supersymmetric Standard Model (MSSM). A plausible option is to introduce a new supersymmetric sector coupled to the MSSM Higgs fields, whose associated states resolve the little hierarchy problem between the third generation squark masses and the weak scale. SUSY also accomodates a weakly interacting cold dark matter (DM) candidate in the form of a stable neutralino. In minimal realizations, the…
There exists a vast literature examining the electroweak (EW) fine-tuning problem in supersymmetric scenarios, but little concerned with the dark matter (DM) one, which should be combined with the former. In this paper, we study this problem in an, as much as possible, exhaustive and rigorous way. We have considered the MSSM framework, assuming that the LSP is the lightest neutralino, $χ_1^0$, and exploring the various possibilities for the mass and composition of $χ_1^0$, as well as different mechanisms for annihilation of the DM particles in the early Universe (well-tempered neutralinos, fun…
The absence of any signal of supersymmetry (SUSY) at the LHC has raised the SUSY particle mass scale compared to $Z$ boson mass $M_Z$. We investigate the naturalness of the electroweak symmetry breaking after considering radiative symmetry breaking along with 125 GeV Higgs mass. We find that the important quantity to measure the naturalness of the hierarchy between the SUSY scale and $M_Z$ is the separation between the radiative symmetry breaking scale, i.e., where $m_{H_u}^2+μ^2$ turns negative for large $\tanβ$ case ($μ$ is the Higgsino mass and $m_{H_u}$ is the SUSY breaking up-type Higgs b…
Within a two-loop leading-log approximation, we review the prediction for the lightest Higgs mass (m_h) in the framework of constrained MSSM (CMSSM), derived from the naturalness requirement of minimal fine-tuning (Delta) of the electroweak scale and dark matter consistency. As a result, the Higgs mass is predicted to be just above the LEP2 bound, m_h=115.9\pm 2 GeV, corresponding to a minimal Delta=17.8, value obtained from consistency with electroweak and WMAP (3σ) constraints, but without the LEP2 bound. Due to quantum corrections (largely QCD ones for m_h above LEP2 bound), Delta grows \ap…
In MSSM models with various boundary conditions for the soft breaking terms (m_{soft}) and for a higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning Delta\approx 800 to 1000 for the constrained MSSM and Delta\approx 500 for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector (\sqrt f) to few TeV, which we show to restore naturalness to more acceptable levels Delta\approx…
We study the naturalness properties of the $B-L$ Supersymmetric Standard Model (BLSSM) and compare them to those of the Minimal Supersymmetric Standard Model (MSSM) at both low (i.e., Large Hadron Collider) energies and high (i.e., unification) scales. By adopting standard measures of naturalness, we assess that, in presence of full unification of the additional gauge couplings and scalar/fermionic masses of the BLSSM, such a scenario reveals a somewhat higher degree of Fine-Tuning (FT) than the MSSM, when the latter is computed at the unification scale and all available theoretical and experi…
The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a $\mathbb{Z}_3$ conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable ins…
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.…
The recent discovery of the 125.5 GeV Higgs boson at the LHC has fueled interest in the next-to-minimal supersymmetric standard model (NMSSM) as it may require less fine-tuning than the minimal model to accommodate such a heavy Higgs. To this end we present Bayesian naturalness priors to quantify fine-tuning in the (N)MSSM. These priors arise automatically as Occam razors in Bayesian model comparison and generalize the conventional Barbieri-Giudice measure. In this paper we show that the naturalness priors capture features of both the Barbieri-Giudice fine-tuning measure and a simple ratio mea…
Light states associated with the hierarchy problem affect the Higgs LHC production and decays. We illustrate this within the MSSM and two simple extensions applying the latest bounds from LHC Higgs searches. Large deviations in the Higgs properties are expected in a natural SUSY spectrum. The discovery of a non-Standard-Model Higgs may signal the presence of light stops accessible at the LHC. Conversely, the more the Higgs is Standard-Model-like, the more tuned the theory becomes. Taking the ratio of different Higgs decay channels at the LHC cancels the leading QCD uncertainties and potentiall…
In a recent paper arXiv:1107.5048, we discussed the correlation between the elastic neutralino-nucleon scattering cross section, constrained by dark matter direct detection experiments, and fine-tuning at tree-level in the electroweak symmetry breaking sector of the Minimal Supersymmetric Standard Model (MSSM). Here, we show that the correlation persists in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), and its variant, lambda-SUSY. Both models are strongly motivated by the recent discovery of a 125 GeV Higgs-like particle. We also discuss the implications of the recently published…
We perform a forecast of the MSSM with universal soft terms (CMSSM) for the LHC, based on an improved Bayesian analysis. We do not incorporate ad hoc measures of the fine-tuning to penalize unnatural possibilities: such penalization arises from the Bayesian analysis itself when the experimental value of $M_Z$ is considered. This allows to scan the whole parameter space, allowing arbitrarily large soft terms. Still the low-energy region is statistically favoured (even before including dark matter or g-2 constraints). Contrary to other studies, the results are almost unaffected by changing the u…
We study the fine tuning in the parameter space of the semi-constrained NMSSM, where most soft Susy breaking parameters are universal at the GUT scale. We discuss the dependence of the fine tuning on the soft Susy breaking parameters M_1/2 and m0, and on the Higgs masses in NMSSM specific scenarios involving large singlet-doublet Higgs mixing or dominant Higgs-to-Higgs decays. Whereas these latter scenarios allow a priori for considerably less fine tuning than the constrained MSSM, the early LHC results rule out a large part of the parameter space of the semi-constrained NMSSM corresponding to…
We present a sensitivity study for the pair-production of supersymmetric particles which decay through R-parity violating channels. As the scope of possible RPV signatures is very broad, the reach of several selected signatures spanning a representative variety of possible final states is considered. Preference in representation is given to spectra motivated by naturalness, i.e. light higgsinos, stops and gluinos. The sensitivity studies are presented for proton-proton collisions at 14 TeV with an integrated luminosity of 300 and 3000 fb^-1, as well as at 33 TeV with an integrated luminosity o…
Direct LHC bounds on colored SUSY particles now corner naturalness more than the measured value of the Higgs mass does. Bounds on the gluino are of particular importance, since it radiatively "sucks" up the stop and Higgs-up soft masses. As a result, even models that easily accommodate a 125 GeV Higgs are almost as tuned as the simplest version of SUSY, the MSSM: at best at the percent level. In this paper, we further examine how current LHC results constrain naturalness in three classes of models that may relax LHC bounds on sparticles: split families, baryonic RPV, and Dirac gauginos. In mod…
Why is natural supersymmetry neither detected nor ruled-out to date? To answer this question we use the Bayesian approach where the emphasis on finding prior-independent features within broader and minimally biased frames is taken as the guiding principle. The 20-parameter minimal supersymmetric standard model (MSSM) fits to subjective naturalness indicate the existence of a prior-independent upper bound on the pseudoscalar Higgs boson mass $m_A$ as a function of $\tan β$, the ratio of the vacuum expectation values of the MSSM Higgs doublets. For a 30-parameter MSSM this implies that $m_A \les…
We analyse the current status of the dilaton domination scenario in the MSSM and its singlet extensions taking into account the measured value of the Higgs mass, the relic abundance of dark matter and constraints from SUSY searches at the LHC. We find that in the case of the MSSM the requirement of a dark matter relic abundance in accord with observation severely restricts the allowed parameter space, implying an upper bound on the superpartner masses which makes it fully testable at LHC-14. In singlet extensions with a large singlet-MSSM coupling $λ$ as favoured by naturalness arguments the c…
Spurred by the discovery of a boson resonance at the LHC as the result of the search for the Standard Model Higgs, we pursue our investigation of the properties and signatures of Higgses in an effective supersymmetric scenario that goes beyond the usual MSSM. Such scenarios were first introduced to alleviate the naturalness problem of the MSSM Higgs and are found to have a very rich phenomenology that allows departures from the Standard Model in the production rate of the Higgs in many of the search channels. We now include the constraints from flavour observables in particular the rare decays…
The search of the light Higgsino {in the Minimal Supersymmetric Standard Model (MSSM)} is a crucial test for the criteria of the naturalness in supersymmetry. On the other hand, the direct production of light Higgsino is also known as one of the most challenging SUSY searches at the current CERN Large Hadron collider (LHC). The lack of visible leptons due to the compressed spectrum and their small production rates limits their discovery potential in both mono-jet plus MET as well as the weak boson fusion (WBF) production. The signal $S/B$ ratio prediction is usually within the background syste…
We investigate the impact of direct LHC SUSY searches on the parameter space of three natural scenarios in the MSSM. In the first case the spectrum consists of light stops, sbottoms, and Higgsino-like neutralinos, while the other particles are assumed to be out of the experimental reach. In the second case we consider an additional light gluino. Finally we study a more complex spectrum comprising also light sleptons, a wino-like chargino, and a bino-like neutralino. We simulate in detail three LHC searches: stop production at ATLAS with 20.7/fb, CMS 11.7/fb inclusive search for squarks and glu…
We examine the sensitivity of recent LHC searches to signatures of supersymmetry with R-parity violation (RPV). Motivated by naturalness of the Higgs potential, which would favor light third-generation squarks, and the stringent LHC bounds on spectra in which the gluino or first and second generation squarks are light, we focus on scenarios dominated by the pair production of light stops. We consider the various possible direct and cascade decays of the stop that involve the trilinear RPV operators. We find that in many cases, the existing searches exclude stops in the natural mass range and b…
We investigate multi-lepton signals produced by ElectroWeakino (EWino) decays in the MSSM and the TMSSM scenarios with sfermions, gluinos and non Standard Model Higgses at the TeV scale, being the Bino electroweak-scale dark matter. We recast the present LHC constraints on EWinos for these models and we find that wide MSSM and TMSSM parameter regions prove to be allowed. We forecast the number of events expected in the signal regions of the experimental multi-lepton analyses in the next LHC runs. The correlations among these numbers will help to determine whether future deviations in multi-lep…
One of the early criterion proposed for naturalness was a relatively small Higgs mixing parameter $μ$ with $μ/M_Z$ order few. A relatively small $μ$ may lead to heavier Higgs masses ($H^0, A, H^{\pm}$ in MSSM) which are significantly lighter than other scalars such as squarks. Such a situation is realized on the hyperbolic branch of radiative breaking of the electroweak symmetry. In this analysis we construct supergravity unified models with relatively small $μ$ in the sense described above and discuss the search for the charged Higgs boson $H^{\pm}$ at HL-LHC and HE-LHC where we also carry ou…
Naturalness arguments suggest that the stop sector is within reach of the Large Hadron Collider (LHC). We investigate how the observation of a third generation squark signal could predict masses and discovery modes of other supersymmetric particles, or potentially test the Higgs boson mass relation and the validity of the Minimal Supersymmetric Standard Model (MSSM) at the high luminosity LHC. We illustrate these ideas in three distinct scenarios: discovery of a light stop, a sbottom signal in multileptons, and a signal of the second (heavier) stop in boosted dibosons.
We examine the possibility of a light (below 46 GeV) neutralino dark matter (DM) candidate within the 19-parameter phenomenological Minimal Supersymmetric Standard Model (pMSSM) in the light of various recent experimental results, especially from the LHC, XENON100, and Planck. We also study the extent of electroweak fine-tuning for such a light neutralino scenario in view of the null results from the searches for supersymmetry so far. Using a Markov Chain Monte Carlo likelihood analysis of the full pMSSM parameter space, we find that a neutralino DM with mass > 10 GeV can in principle still sa…
We present an efficient method of reconstructing the parameters of the Constrained MSSM from assumed future LHC data, applied both on their own right and in combination with the cosmological determination of the relic dark matter abundance. Focusing on the ATLAS SU3 benchmark point, we demonstrate that our simple Gaussian approximation can recover the values of its parameters remarkably well. We examine two popular non-informative priors and obtain very similar results, although when we use an informative, naturalness-motivated prior, we find some sizeable differences. We show that a further s…
