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Supersymmetry, a new symmetry that relates bosons and fermions in particle physics, still escapes observation. Search for supersymmetry is one of the main aims of the Large Hadron Collider. The other possible manifestation of supersymmetry is the Dark Matter in the Universe. The present lectures contain a brief introduction to supersymmetry in particle physics. The main notions of supersymmetry are introduced. The supersymmetric extension of the Standard Model -- the Minimal Supersymmetric Standard Model -- is considered in more detail. Phenomenological features of the Minimal Supersymmetric Standard Model as well as possible experimental signatures of supersymmetry at the Large Hadron Collider are described. The present limits on supersymmetric particles are presented and the allowed region of parameter space of the MSSM is shown.
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The direct searches for Superymmetry at colliders can be complemented by direct searches for dark matter (DM) in underground experiments, if one assumes the Lightest Supersymmetric Particle (LSP) provides the dark matter of the universe. It will be shown that within the Constrained minimal Supersymmetric Model (CMSSM) the direct searches for DM are complementary to direct LHC searches for SUSY and Higgs particles using analytical formulae. A combined excluded region from LHC, WMAP and XENON100 will be provided, showing that within the CMSSM gluinos below 1 TeV and LSP masses below 160 GeV are excluded (m_{1/2} > 400 GeV) independent of the squark masses.
Prospective searches for lepton flavor violation (LFV) in rare kaon decays at the existing and future intermediate-energy accelerators are considered. The proposed studies are complementary to LFV searches in muon-decay experiments and offer a unique opportunity to probe models with approximately conserved fermion-generation quantum number with sensitivity superior to that in other processes. Consequently, new searches for LFV in kaon decays are an important and independent part of the general program of searches for lepton flavor violation in the final states with charged leptons.
In this article we review the case for a light ($< m_{h_{125}}/2$) neutralino and sneutrino being a viable Dark Matter (DM) candidate in Supersymmetry(SUSY). To that end we recapitulate, very briefly, three issues related to the DM which impact the discussions : calculation of DM relic density, detection of the DM in Direct and Indirect experiments and creation /detection at the Colliders. In case of SUSY, the results from Higgs and SUSY searches at the colliders also have implications for the DM mass and couplings. In view of the constraints coming from all these sources, the possibility of a light neutralino is all but ruled out for the constrained MSSM : cMSSM. The pMSSM, where the gaugino masses are not related at high scale, is also quite constrained and under tension in case of thermal DM and will be put to very stern test in the near future in Direct Detection (DD) experiments as well as by the LHC analyses. However in the pMSSM with modified cosmology and hence non-thermal DM or in the NMSSM, a light neutralino is much more easily accommodated. A light RH sneutrino is also still a viable DM candidate although it requires extending the MSSM with additional singlet neutrino superfields. All of these possibilities can be indeed tested jointly in the upcoming SUSY-electroweakino and Higgs searches at the HL/HE luminosity LHC, the upcoming experiments for the Direct Detection (DD) and indirect detection for the DM as well as the high precision electron-positron colliders under planning.
In previous work, we have established that for any 2-to-2 process in MSSM, only the helicity conserving (HC) amplitudes survive asymptotically. Studying a large number of such processes, at the 1loop Electroweak (EW) order, it is now found that their high energy HC amplitudes are determined by just three forms: a log-squared function of the ratio of two of the (s,t,u) variables, to which a pi^2 is added; and two Sudakov-like ln- and ln^2-terms accompanied by respective mass-dependent constants. Apart from an additional residual constant, all high energy HC amplitudes, may be expressed as linear combinations of the above three forms, with coefficients being rational functions of the $(s,t,u)$ variables. We call this fact supersimplicity. Applying to the $ugto dW$ amplitudes, for which the complete 1loop expressions are available, we find that supersimplicity may be a very good approximation at LHC energies, provided the SUSY scale is not too high. SM processes are also discussed, and their differences are explored.
The low energy $J/psi$ photoproduction cross-section has been studied on the basis of the Pomeron model. To incorporate the discrepancy between experimental data and the predictionns by the conventional models, i.e. the sum of the soft Pomeron with intercept 1.08 and the hard Pomeron with intercept 1.418, a Regge trajectory associated with a scalar meson (f,a) exchange which we call supersoft Pomeron, is introduced additionally. To distinguish between the conventional model and this new additional Pomeron, observations related to other polarization observables in upcoming polarized experiments are discussed.
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