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Recent clarifications of naturalness in supersymmetry robustly require the presence of four light higgsinos with mass ~100-300 GeV while gluinos and (top)-squarks may lie in the multi-TeV range, possibly out of LHC reach. We project the high luminosity (300-3000 fb^{-1}) reach of LHC14 via gluino cascade decays and via same-sign diboson production. We compare these to the reach for neutralino pair production tz_1tz_2 followed by tz_2totz_1ell^+ell^- decay to soft dileptons which recoil against a hard jet. It appears that 3000 fb^{-1} is just about sufficient integrated luminosity to probe naturalness with up to 3% fine-tuning at the 5-sigma level, thus either discovering natural supersymmetry or else ruling it out.
Gluinos that result in classic large missing transverse momentum signatures at the LHC have been excluded by 2011 searches if they are lighter than around 800 GeV. This adds to the tension between experiment and supersymmetric solutions of the natura
Radiatively-driven natural supersymmetry (RNS) potentially reconciles the Z and Higgs boson masses close to 100 GeV with gluinos and squarks lying beyond the TeV scale. Requiring no large cancellations at the electroweak scale in constructing M_Z=91.
The electroweak fine-tuning measure Delta(EW) allows for correlated SUSY soft terms as are expected in any ultra-violet complete theory. Requiring no less than 3% electroweak fine-tuning implies upper bounds of about 360~GeV on all higgsinos, while t
We review the prospects for quarkonium-production studies in proton and nuclear collisions accessible during the upcoming phases of the CERN Large Hadron Collider operation after 2021, including the ultimate high-luminosity phase, with increased lumi
Motivated by the absence of any clear signal of physics beyond the Standard Model at the LHC after Run I, we discuss one possible slight hint of new physics and one non-minimal extension of the Standard Model. In the first part we provide a tentative