Models of natural supersymmetry seek to solve the little hierarchy problem by positing a spectrum of light higgsinos 200 − 300 GeV and light top squarks 600 GeV along with very heavy squarks and TeV-scale gluinos. Such models have low electroweak fine-tuning and satisfy the LHC constraints. However, in the context of the MSSM, they predict too low a value of m h , are frequently in conflict with the measured b → sγ branching fraction and the relic density of thermally produced higgsino-like WIMPs falls well below dark matter (DM) measurements. We propose a framework dubbed radiative natural SUSY (RNS) which can be realized within the MSSM (avoiding the addition of extra exotic matter) and which maintains features such as gauge coupling unification and radiative electroweak symmetry breaking. The RNS model can be generated from SUSY GUT type models with nonuniversal Higgs masses (NUHM). Allowing for high scale soft SUSY breaking Higgs mass m Hu > m 0 leads to automatic cancellations during renormalization group (RG) running, and to radiatively-induced low fine-tuning at the electroweak scale. Coupled with large mixing in the top squark sector, RNS allows for fine-tuning at the 3-10% level with TeV-scale top squarks and a 125 GeV light Higgs scalar h. The model allows for at least a partial solution to the SUSY flavor, CP and gravitino problems since first/second generation scalars (and the gravitino) may exist in the 10-30 TeV regime. We outline some possible signatures for RNS at the LHC such as the appearance of low invariant mass opposite-sign isolated dileptons from gluino cascade decays. The smoking gun signature for RNS is the appearance of light higgsinos at a linear e + e − collider. If the strong CP problem is solved by the Peccei-Quinn mechanism, then RNS naturally accommodates mixed axion-higgsino cold dark matter, where the light higgsino-like WIMPS -which in this case make up only a fraction of the measured relic abundance -should be detectable at upcoming WIMP detectors.

The lack of evidence for superparticles at the CERN LHC, along with the rather high value of the Higgs boson mass, has sharpened the perception that what remains of supersymmetric model parameter space suffers a high degree of electroweak fine-tuning (EWFT). We compare three different measures of fine-tuning in supersymmetric models. 1. ∆ HS measures a subset of terms containing large log contributions to m Z (and m h ) that are inevitable in models defined at scales much higher than the electroweak scale. 2. The traditional ∆ BG measures fractional variation in m Z against fractional variation of model parameters and allows for correlations among high scale parameters which are not included in ∆ HS . 3. The model-independent ∆ EW measures how naturally a model can generate the measured value of m Z = 91.2 GeV (or m h ) in terms of weak scale parameters alone. We hypothesize an overarching Ultimate Theory (UTH) wherein the high scale soft terms are all correlated. The UTH might be contained within the more general effective SUSY theories which are popular in the literature. In the case of ∆ HS , EWFT can be grossly overestimated by neglecting additional non-independent terms which lead to large cancellations. In the case of ∆ BG , EWFT can be overestimated by applying the measure to the effective theories instead of to the UTH. The measure ∆ EW allows for the possibility of parameter correlations which should be present in the UTH and, since it is model-independent, provides the same value of EWFT for the effective theories as should occur for the UTH. We find that the well-known mSUGRA/CMSSM model is fine-tuned under all three measures so that it is unlikely to contain the UTH. The non-universal Higgs model NUHM2 appears fine-tuned with ∆ HS,BG 10 3 . But since ∆ EW can be as small as 7 (corresponding to 14% fine-tuning), it may contain the UTH for parameter ranges which allow for low true EWFT. *

Recent null results from LHC8 SUSY searches along with the discovery of a SM-like Higgs boson with mass m(h) ~ 125.5 GeV indicates sparticle masses in the TeV range, causing tension with conventional measures of electroweak fine-tuning. We propose a simple Fine-tuning Rule which should be followed under any credible evaluation of fine-tuning. We believe that overestimates of electroweak fine-tuning by conventional measures all arise from violations of this rule. We show that to gain accord with the Fine-tuning Rule, then both Higgs mass and the traditional \Delta_{BG} fine-tuning measures reduce to the model-independent electroweak fine-tuning measure \Delta_{EW}. This occurs by combining dependent contributions to m(Z) or m(h) into independent units. Then, using \Delta_{EW}, we evaluate EW fine-tuning for a variety of SUSY models including mSUGRA, NUHM1, NUHM2, mGMSB, mAMSB, hyper-charged AMSB and nine cases of mixed moduli-anomaly (mirage) mediated SUSY breaking models (MMAMSB) whilst respecting LHC Higgs mass and B-decay constraints (we do not impose LHC8 sparticle mass constraints due to the possibility of compressed spectra within many of these models). We find mSUGRA, mGMSB, mAMSB and MMAMSB models all to be highly fine-tuned. The NUHM1 model is moderately fine-tuned while NUHM2 which allows for radiatively-driven naturalness (RNS) allows for fine-tuning at a meager 10% level in the case where m(higgsinos) ~ 100-200 GeV and the TeV-scale top squarks are well-mixed. Models with RNS may or may not be detect at LHC14. A \sqrt{s} ~ 500 GeV e^+e^- collider will be required to make a definitive search for the requisite light higgsinos.Comment: 30 pages and 12 figures; revised version includes additional references and several typo fixe

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 = 91.2 GeV while maintaining a light Higgs scalar with m h ≃ 125 GeV implies a sparticle mass spectrum including light higgsinos with mass ∼ 100 − 300 GeV, electroweak gauginos in the 300 − 1200 GeV range, gluinos at 1 − 4 TeV and top/bottom squarks in the 1-4 TeV range (probably beyond LHC reach), while first/second generation matter scalars can exist in the 5-30 TeV range (far beyond LHC reach). We investigate several characteristic signals for RNS at LHC14. Gluino pair production yields a reach up to mg ∼ 1.7 TeV for 300 fb −1 . Wino pair production -pp → W 2 Z 4 and W 2 W 2 -leads to a unique same-sign diboson (SSdB) signature accompanied by modest jet activity from daughter higgsino decays; this signature provides the best reach up to mg ∼ 2.1 TeV within this framework. Wino pair production also leads to final states with (W Z → 3ℓ) + E miss T as well as 4ℓ + E miss T which give confirmatory signals up to mg ∼ 1.4 TeV. Directly produced light higgsinos yield a clean, soft trilepton signature (due to very low visible energy release) which can be visible, but only for a not-too-small a Z 2 − Z 1 mass gap. The clean SSdB signal -as well as the distinctive mass shape of the dilepton mass distribution from Z 2,3 → Z 1 ℓℓ decays if this is accessible -will mark the presence of light higgsinos which are necessary for natural SUSY. While an e + e − collider operating with √ s ∼ 600 GeV should unequivocally reveal the predicted light higgsinos, the RNS model with m 1/2 1 TeV may elude all LHC14 search strategies even while maintaining a high degree of electroweak naturalness.-1 -

Naturalness arguments applied to supersymmetric theories imply a spectrum containing four light higgsinos Z 1,2 and W ± 1 with masses ∼ 100 − 300 GeV (the closer to M Z , the more natural). The compressed mass spectrum and associated low energy release from W 1 and Z 2 three-body decay makes higgsinos difficult to detect at LHC14, while the other sparticles might be heavy, and possibly even beyond LHC14 reach. In contrast, the International Linear e + e − Collider (ILC) with √ s > 2m(higgsino) would be a higgsino factory in addition to a Higgs boson factory and would serve as a discovery machine for natural SUSY! In this case, both chargino and neutralino production occur at comparable rates, and lead to observable signals above SM backgrounds. We examine two benchmark cases, one just beyond the LHC8 reach with W 1 ( Z 2 ) − Z 1 mass gap of 15 (21) GeV, and a second more difficult case beyond even the LHC14 reach, where the mass gap is just 10 GeV, close to its minimum in models with no worse than 3% finetuning. The signal is characterized by low visible energy events together with E T in the one or two jets +1ℓ channel from chargino production, and in the opposite sign, sameflavour, acoplanar dilepton channel from Z 1 Z 2 production. For both cases, we find that the signal is observable above backgrounds from the usual 2 → 2 SM events and from γγ collisions with just a few fb −1 of integrated luminosity. We also show that with an integrated luminosity of 100 fb −1 , it should be possible to extract W 1 and Z 1 masses at 2-3% level from chargino events if the mass gap is ≥ 15 GeV, and neutralino masses at the sub-percent level from neutralino events. The latter should also allow a determination of m Z 2 − m Z 1 at the 200 MeV level. These measurements would point to higgsinos as the origin of new physics and strongly suggest a link to a natural origin for W , Z and h masses.