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This is the written version of a talk given by S.K. at the $10^{th}$ International Conference on High Energy and Astroparticle, Constantine, Algeria. We briefly review the Standard Model (SM) and the major evidences and main direction of physics beyond the SM (BSM). We introduce supersymmetry, as one of the well-motivated BSM. Basic introduction to Minimal Supersymmetric Standard Model (MSSM) is given. We analyze the thermal relic abundance of lightest neutralino, which is the Lightest Supersymmetric Particle (LSP) in the MSSM. We show that the combined Large Hadron Collider (LHC) and relic abundance constraints rule out most of the MSSM parameter space except a very narrow region. We also review non-minimal SUSY model, based on the gauge group $SU(3)_C times SU(2)_L times U(1)_Y times U(1)_{B-L}$ (BLSSM), where an Inverse Seesaw mechanism of light neutrino mass generation is naturally implemented. The phenomenological implications of this type of model at the Large Hadron Collider (LHC) are analyzed.
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We derive the latest constraints on various simplified models of natural SUSY with light higgsinos, stops and gluinos, using a detailed and comprehensive reinterpretation of the most recent 13 TeV ATLAS and CMS searches with $sim 15$ fb$^{-1}$ of dat
We review the current strategies to search for generic SUSY models with R-parity conservation in the ATLAS and CMS detectors at the LHC. The discovery reach in early data will be presented for the different search channels based on missing transverse
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