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The electroweak fine-tuning measure ∆ 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 top squarks are lighter than ∼ 3 TeV and gluinos are bounded by ∼ 6 − 9 TeV. We examine the reach for SUSY of the planned high luminosity (HL: 3 ab −1 at 14 TeV) and the proposed high energy (HE: 15 ab −1 at 27 TeV) upgrades of the LHC via four LHC collider search channels relevant for natural SUSY: 1. gluino pair production followed by gluino decay to third generation (s)quarks, 2. top-squark pair production followed by decay to third generation quarks and light higgsinos, 3. neutral higgsino pair production with QCD jet radiation (resulting in monojet events with soft dileptons), and 4. wino pair production followed by decay to light higgsinos leading to same-sign diboson production. We confront our reach results with upper limits on superpartner masses in four natural SUSY models: natural gravity-mediation via the 1. two-and 2. three-extra-parameter non-universal Higgs models, 3. natural mini-landscape models with generalized mirage mediation and 4. natural anomaly-mediation We find that while the HL-LHC can probe considerable portions of natural SUSY parameter space in all these models, the HE-LHC will decisively cover the entire natural SUSY parameter space with better than 3% fine-tuning. *

The requirement of electroweak naturalness in supersymmetric (SUSY) models of particle physics necessitates light higgsinos not too far from the weak scale characterized by m weak ∼ m W,Z,h ∼ 100 GeV. On the other hand, LHC Higgs mass measurements and sparticle mass limits point to a SUSY breaking scale in the multi-TeV regime. Under such conditions, the lightest SUSY particle is expected to be a mainly higgsino-like neutralino with non-negligible gaugino components (required by naturalness). The computed thermal WIMP abundance in natural SUSY models is then found to be typically a factor 5-20 below its measured value. To gain concordance with observations, either an additional DM particle (the axion is a well-motivated possibility) must be present or additional non-thermal mechanisms must augment the neutralino abundance. We compare present direct and indirect WIMP detection limits to three natural SUSY models based on gravity-, anomaly-and mirage-mediation. We show that the case of natural higgsinoonly dark matter where non-thermal production mechanisms augment its relic density, is essentially excluded by a combination of direct detection constraints from PandaX-II, LUX and Xenon-1t experiments, and by bounds from Fermi-LAT/MAGIC observations of gamma rays from dwarf spheroidal galaxies. *

Radiatively-driven natural SUSY (RNS) models enjoy electroweak naturalness at the 10% level while respecting LHC sparticle and Higgs mass constraints. Gluino and top-squark masses can range up to several TeV (with other squarks even heavier) but a set of light Higgsinos are required with mass not too far above m h ∼ 125 GeV. Within the RNS framework, gluinos dominantly decay viãwhere the decay products of the higgsino-like W 1 and Z 2 are very soft. Gluino pair production is, therefore, signaled by events with up to four hard b-jets and large E T . We devise a set of cuts to isolate a relatively pure gluino sample at the (high-luminosity) LHC and show that in the RNS model with very heavy squarks, the gluino signal will be accessible for mg < 2400 (2800) GeV for an integrated luminosity of 300 (3000) fb −1 . We also show that the measurement of the rate of gluino events in the clean sample mentioned above allows for a determination of mg with a statistical precision of 2-5% (depending on the integrated luminosity and the gluino mass) over the range of gluino masses where a 5σ discovery is possible at the LHC.

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