While it is often stated that the notion of electroweak (EW) naturalness in supersymmetric models is subjective, fuzzy and model-dependent, here we argue the contrary: electroweak naturalness can be elevated to a principle which is both objective and predictive. We demonstrate visually when too much fine-tuning sets in at the electroweak scale which corresponds numerically to the measure ∆ BG ∼ ∆ EW > ∼ 30. While many constrained SUSY models are already excluded by this value, we derive updated upper bounds on sparticle masses within the two-extra parameter non-universal Higgs model (NUHM2). We confirm the classic Barbieri-Giudice (BG) result that ∆ BG < 30 implies µ < 350 GeV. However, by combining dependent soft terms which appear as multiples of m 3/2 in supergravity models, then we obtain mg < ∼ 4 TeV as opposed to the BG result that mg < ∼ 350 GeV. We compare the NUHM2 results to a similar scan in the pMSSM with 19 weak scale parameters. In the pMSSM with complete one-loop scalar potential plus dominant two-loop terms, then a mg < 7 TeV bound is found. Our tabulation of upper bounds provides a target for experimenters seeking to discover or else falsify the existence of weak scale supersymmetry. In an Appendix, we show contributions to the naturalness measure from one-loop contributions to the weak scale scalar potential. *

In supersymmetric models where the superpotential mu term is generated with mu<< m_{soft} (e.g. from radiative Peccei-Quinn symmetry breaking or compactified string models with sequestration and stabilized moduli), and where the string landscape 1. favors soft supersymmetry (SUSY) breaking terms as large as possible and 2. where the anthropic condition that electroweak symmetry is properly broken with a weak scale m_{W,Z,h}~100 GeV ({\it i.e.} not too weak of weak interactions), then these combined landscape/anthropic requirements act as an attractor pulling the soft SUSY breaking terms towards values required by models with radiatively-driven naturalness: near the line of criticality where electroweak symmetry is barely broken and the Higgs mass is ~125 GeV. The pull on the soft terms serves to ameliorate the SUSY flavor and CP problems. The resulting sparticle mass spectrum may barely be accessible at high-luminosity LHC while the required light higgsinos should be visible at a linear e^+e^- collider with \sqrt{s}>2m(higgsino).Comment: 5 pages plus 3 figures; version 2 coincides with published version, some references adde

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.

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 Z1 Z2 followed by Z2 → Z1 + − 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 5σ level, thus either discovering natural supersymmetry or else ruling it out.

By insisting on naturalness in both the electroweak and quantum chromodynamics (QCD) sectors of the minimal supersymmetric standard model (MSSM), the portrait for dark matter production is seriously modified from the usual weakly interacting massive particle (WIMP) miracle picture. In supersymmetry (SUSY) models with radiatively-driven naturalness (radiative natural SUSY or radiative natural SUSY (RNS)) which include a Dine-Fischler-Srednicki-Zhitnitsky (DFSZ)-like solution to the strong charge-conjugation-parity (CP) and SUSY µ problems, dark matter is expected to be an admixture of both axions and higgsino-like WIMPs. The WIMP/axion abundance calculation requires simultaneous solution of a set of coupled Boltzmann equations which describe quasi-stable axinos and saxions. In most of parameter space, axions make up the dominant contribution of dark matter although regions of WIMP dominance also occur. We show the allowed range of Peccei-Quinn (PQ) scale f a and compare to the values expected to be probed by the axion dark matter search experiment (ADMX) axion detector in the near future. We also show WIMP detection rates, which are suppressed from usual expectations, because now WIMPs comprise only a fraction of the total dark matter. Nonetheless, ton-scale noble liquid detectors should be able to probe the entirety of RNS parameter space. Indirect WIMP detection rates are less propitious since they are reduced by the square of the depleted WIMP abundance.