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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.
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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 thus-far null results of direct DM searches, along with the DM relic abundance constraint, introduce a level of fine-tuning as severe as the one due to the SUSY little hierarchy problem. We analyse the generic implications of new SUSY sectors parametrically heavier than the minimal SUSY spectrum, devised to increase the Higgs boson mass, on this little neutralino DM problem. We focus on the SUSY operator of smallest scaling dimension in an effective field theory description, which modifies the Higgs and DM sectors in a correlated manner. Within this framework, we show that recent null results from the LUX experiment imply a tree-level fine-tuning for gaugino DM which is parametrically at least a few times larger than that of the MSSM. Higgsino DM whose relic abundance is generated through a thermal freeze-out mechanism remains also severely fine-tuned, unless the DM lies below the weak boson pair-production threshold. As in the MSSM, well-tempered gaugino-Higgsino DM is strongly disfavored by present direct detection results.
In this paper we study a new class of supersymmetric models that can explain a 125 GeV Higgs without fine-tuning. These models contain additional `auxiliary Higgs fields with large tree-level quartic interaction terms but no Yukawa couplings. These have electroweak-breaking vacuum expectation values, and contribute to the VEVs of the MSSM Higgs fields either through an induced quartic or through an induced tadpole. The quartic interactions for the auxiliary Higgs fields can arise from either D-terms or F-terms. The tadpole mechanism has been previously studied in strongly-coupled models with large D-terms, referred to as `superconformal technicolor. The perturbative models studied here preserve gauge coupling unification in the simplest possible way, namely that all new fields are in complete SU(5) multiplets. The models are consistent with the observed properties of the 125 GeV Higgs-like boson as well as precision electroweak constraints, and predict a rich phenomenology of new Higgs states at the weak scale. The tuning is less than 10% in almost all of the phenomenologically allowed parameter space. If electroweak symmetry is broken by an induced tadpole, the cubic and quartic Higgs self-couplings are significantly smaller than in the standard model.
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 b-> s gamma and Bs -> mu+ mu- including the recent measurement from LHCb. We also address the issue of Dark Matter and its impact on Higgs physics. In particular, we incorporate the latest data from XENON100 on the spin independent direct detection rates. These turn out to be powerful constraints, especially if one also imposes that the observed thermal relic density is obtained. We also study models with a low abundance that can more easily evade the direct detection rates. We study the impact of the flavour and Dark Matter observables on the production rates of the Higgs at the LHC, and their correlations in the diphoton, diphoton+jets and 4 leptons. We also comment on the other channels.
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.
In the absence of universality the naturalness upper limits on supersymmetric particle masses increase significantly. The superpartners of the two light generations can be much heavier than the weak scale without extreme fine-tunings; they can weigh up to about 900 GeV --- or even up to 5 TeV, if SU(5) universality is invoked. This supresses sparticle-mediated rare processes and consequently ameliorates the problem of supersymmetric flavor violations. On the other hand, even without universality, the gluino and stop remain below about 400 GeV while the charginos and neutralinos are likely to be accessible at LEP2.
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