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Register a new userNaturalness in low-scale SUSY models and non-linear MSSM
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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 Deltaapprox 800 to 1000 for the constrained MSSM and Deltaapprox 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 Deltaapprox 80 for the most conservative case of low tan_beta and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce Delta. In the present case Delta is reduced due to additional (effective) quartic higgs couplings proportional to the ratio m_{soft}/(sqrt f) of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale sqrt f one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.
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In N=1 supergravity the scalar potential may have supersymmetric (SUSY) and non-supersymmetric Minkowski vacua (associated with supersymmetric and physical phases) with vanishing energy density. In the supersymmetric Minkowski (second) phase some breakdown of SUSY may be induced by non-perturbative effects in the observable sector that give rise to a tiny positive vacuum energy density. Postulating the exact degeneracy of the physical and second vacua as well as assuming that at high energies the couplings in both phases are almost identical, one can estimate the dark energy density in these vacua. It is mostly determined by the SUSY breaking scale M_S in the physical phase. Exploring the two-loop renormalization group (RG) flow of couplings in these vacua we find that the measured value of the cosmological constant can be reproduced if M_S varies from 20 TeV to 400 TeV. We also argue that this prediction for the SUSY breaking scale is consistent with the upper bound on M_S in the higgsino dark matter scenario.
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 $Lambda$, and compute the fine-tuning measure $Delta$ for generic boundary conditions on soft SUSY breaking parameters and various cut-off scales. As a general trend we observe reduction in fine-tuning together with lowering $Lambda$. In particular, perfectly natural [$Delta lesssim mathcal{O}(10)$] theories with a multi-TeV spectrum of supersymmetric particles and consistent with all current observations can be obtained for $Lambda sim mathcal{O}(100)$TeV. The lowering of the fine-tuning for large cut-off scales can also be observed in theories exhibiting special quasi-fixed point behaviours of parameters. Our observations call for a more throughout exploration of possible alternative ultraviolet completions of MSSM.
We show that when supersymmetry is broken at the TeV scale by strong dynamics, the Higgs sector of the MSSM can be drastically modified. This arises from possible sizeable mixings of the Higgs with the resonances of the strong sector. In particular the mass of the lightest Higgs boson can be significantly above the MSSM bound (~130 GeV). Furthermore only one Higgs doublet is strictly necessary, because the Yukawa couplings can have a very different structure compared to the MSSM. Using the AdS/CFT correspondence electroweak precision observables can be calculated and shown to be below experimental bounds. The most natural way to generate sparticle masses is through mixing with the composite states. This causes the gauginos and Higgsinos to easily obtain Dirac masses around 200 GeV, while scalar masses can be generated either from extra D-terms or also through mixing with the strongly-coupled states. Finally one of the most interesting predictions of these scenarios is the sizeable decay width of the Higgs boson into a very light gravitino (~ 10^{-4} eV) and a Higgsino.
We interpret within the phenomenological MSSM (pMSSM) the results of SUSY searches published by the CMS collaboration based on the first ~1 fb^-1 of data taken during the 2011 LHC run at 7 TeV. The pMSSM is a 19-dimensional parametrization of the MSSM that captures most of its phenomenological features. It encompasses, and goes beyond, a broad range of more constrained SUSY models. Performing a global Bayesian analysis, we obtain posterior probability densities of parameters, masses and derived observables. In contrast to constraints derived for particular SUSY breaking schemes, such as the CMSSM, our results provide more generic conclusions on how the current data constrain the MSSM.
For a 4D N=1 supersymmetric model with a low SUSY breaking scale (f) and general Kahler potential K(Phi^i,Phi_j^*) and superpotential W(Phi^i) we study, in an effective theory approach, the relation of the goldstino superfield to the (Ferrara-Zumino) superconformal symmetry breaking chiral superfield X. In the presence of more sources of supersymmetry breaking, we verify the conjecture that the goldstino superfield is the (infrared) limit of X for zero-momentum and Lambda->infty. (Lambda is the effective cut-off scale). We then study the constraint X^2=0, which in the one-field case is known to decouple a massive sgoldstino and thus provide an effective superfield description of the Akulov-Volkov action for the goldstino. In the presence of additional fields that contribute to SUSY breaking we identify conditions for which X^2=0 remains valid, in the effective theory below a large but finite sgoldstino mass. The conditions ensure that the effective expansion (in 1/Lambda) of the initial Lagrangian is not in conflict with the decoupling limit of the sgoldstino (1/m_sgoldstinosim Lambda/f, f<Lambda^2).
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