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We stress that the lack of direct evidence for supersymmetry forces the soft mass parameters to lie very close to the critical line separating the broken and unbroken phases of the electroweak gauge symmetry. We argue that the level of criticality, or fine-tuning, that is needed to escape the present collider bounds can be quantitatively accounted for by assuming that the overall scale of the soft terms is an environmental quantity. Under fairly general assumptions, vacuum-selection considerations force a little hierarchy in the ratio between m_Z^2 and the supersymmetric particle square masses, with a most probable value equal to a one-loop factor.
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A recent cosmological bound on the gravitino mass, $m_{3/2}<4.7$ eV, together with LHC results on the Higgs mass and direct searches, excludes minimal gauge mediation with high reheating temperatures. We discuss a minimal, vector-mediated model which incorporates the seesaw mechanism for neutrino masses, allows for thermal leptogenesis, ameliorates the $mu$ problem, and achieves the observed Higgs mass and a gravitino as light as $1$-$2$ eV.
An introduction to the minimal supersymmetric Standard Model (MSSM) is given. The motivation for ``low-energy supersymmetry is reviewed, and the structure of the MSSM is outlined. In its most general form, the MSSM can be viewed as a low-energy effective theory parametrized by a set of arbitrary soft-supersymmetry-breaking parameters. A variety of techniques for reducing the parameter freedom of the MSSM are surveyed. The search for supersymmetry below and above the threshold for supersymmetric particle production presents a challenging task for experimentalists at present and future colliders.
A supersymmetric model with four generations is proposed, in which the top quark is approximately degenerate in mass with the $W^{pm}$ gauge boson, $m_tsimeq m_W$, leading to values of $R_b$ in better agreement with the present experimental data than in the Standard Model. The model shares many of the good features of the minimal supersymmetric extension of the Standard Model (MSSM), such as the unification of gauge and Yukawa couplings at a common high-energy scale. The model differs from the MSSM by re-interpreting the Tevatron ``top-quark events as the production of the fourth generation quark $tpri$, which decays dominantly to $bW^+$. The top quark decays primarily into supersymmetric particles, $trtawidetilde twidetildechi^0_1$, with $widetilde trta cwidetildechi^0_1$, thereby evading previous searches. Light supersymmetric particles are predicted to lie in the mass range between 25 and 70 GeV, which together with the fourth generation leptons provide a rich spectrum of new physics which can be probed at LEP-2 and the Tevatron.
In models of low-energy gauge mediation, the observed Higgs mass is in tension with the cosmological limit on the gravitino mass $m_{3/2} lesssim 16$ eV. We present an alternative mediation mechanism of supersymmetry breaking via a $U(1)$ $D$-term with an $E_6$-inspired particle content, which we call vector mediation. The gravitino mass can be in the eV range. The sfermion masses are at the 10 TeV scale, while gauginos around a TeV. This mechanism also greatly ameliorates the $mu$-problem.
We discuss physical implications of the four-dimensional effective supergravity, that describes low-energy physics of the Randall--Sundrum model with moduli fields in the bulk and charged chiral matter living on the branes. Cosmological constant can be cancelled through the introduction of a brane Polonyi field and a brane superpotential for the 4d dilaton. We deduce a generalization of the effective 4d action to the case of a general, not necessarily exponential, warp factor. We note, that breakdown of supersymmetry in generic warped models may lead to the stabilization of the interbrane distance.
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