Radiatively-Driven Natural Supersymmetry

• RNS is a framework in the MSSM where RG evolution drives mₕᵤ² from a positive high-scale value to a small negative value, ensuring natural electroweak symmetry breaking.
• It features light higgsinos (100–300 GeV) with highly mixed stops and heavy colored sparticles, allowing a 125 GeV Higgs without severe fine-tuning.
• The model integrates a DFSZ axion sector to address the μ problem and yield mixed axion–higgsino dark matter, linking SUSY naturalness with cosmological observations.

Radiatively-Driven Natural Supersymmetry (RNS) is a class of MSSM scenarios, developed prominently in work by Baer and collaborators, in which electroweak symmetry breaking is natural at the weak scale because the up-type Higgs soft mass parameter $m_{H_u}^2$ is driven by renormalization-group evolution from a positive high-scale value to a small negative weak-scale value, while the supersymmetric higgsino mass parameter $\mu$ remains of order $100\text{–}300$ GeV. In this construction, the weak scale arises without large cancellations among independent weak-scale contributions, even though stops, gluinos, and other soft terms may lie in the TeV or multi-TeV regime. RNS is usually realized in non-universal Higgs mass frameworks such as NUHM2 and is characterized phenomenologically by light higgsinos, highly mixed stops, a $125$ GeV Higgs boson, and a dark-matter picture centered on mixed axion–higgsino relics rather than a pure thermal WIMP miracle (Baer, 2013).

1. Definition and electroweak naturalness

RNS is defined through the MSSM Higgs-potential minimization condition evaluated at the weak scale. For moderate or large $\tan\beta$, the relation is written as

$$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$

where $\mu$ is the supersymmetric higgsino mass parameter, $m_{H_u}^2(Q)$ is the running up-type Higgs soft mass at $Q\sim m_{\rm SUSY}$, and $\Sigma_u^u$ denotes radiative corrections dominated by top-stop loops. The central naturalness criterion is that no individual term on the right-hand side should be much larger than $\mu$0 if the observed weak scale is to emerge without substantial cancellation (Baer, 2013).

The corresponding weak-scale fine-tuning measure is the electroweak measure $\mu$1, defined by identifying each contribution $\mu$2 to the minimization condition and taking

$\mu$3

Typical contributions include $\mu$4, $\mu$5, and $\mu$6. In this framework, $\mu$7 corresponds to about $\mu$8 fine-tuning, while $\mu$9 is regarded as natural. A central property of $100\text{–}300$0 is that it depends only on the weak-scale spectrum: two high-scale models with the same low-energy spectrum have the same $100\text{–}300$1 (Baer et al., 2013).

RNS emerged partly as a critique of conventional large-log or naïve Barbieri–Giudice analyses. The usual large-log estimate,

$100\text{–}300$2

was argued to overstate fine-tuning if $100\text{–}300$3 and $100\text{–}300$4 are treated as independent. In the MSSM they are not independent, since changing the high-scale boundary condition changes the radiative correction itself. RNS therefore treats the combined weak-scale quantity $100\text{–}300$5 as the relevant object for naturalness (Baer, 2013).

A persistent misconception is that natural SUSY necessarily requires sub-TeV stops and gluinos. In the RNS formulation, that conclusion follows only from more restrictive tuning measures or from treating dependent parameters as independent. Under $100\text{–}300$6, multi-TeV stops and gluinos remain compatible with naturalness provided $100\text{–}300$7 is small, $100\text{–}300$8 is only slightly negative, and loop corrections are controlled (Tata, 2015).

2. Radiative mechanism and high-scale realization

The phrase “radiatively-driven” refers to the renormalization-group evolution of $100\text{–}300$9 from the GUT scale to the weak scale. At $125$0, $125$1 is typically positive and of order the scalar soft scale, while the large top Yukawa coupling drives it downward. Schematically,

$125$2

RNS selects high-scale boundary conditions such that the weak-scale result is not a large negative number, but rather

$125$3

which allows $125$4 to be reproduced without severe cancellation (Baer, 2013).

In practice, this is usually implemented in NUHM2-type models, where $125$5 and $125$6 are treated as weak-scale inputs and the GUT-scale Higgs soft masses are adjusted accordingly. A representative RNS benchmark used for collider studies takes

$125$7

yielding $125$8 GeV and $125$9 (Baer et al., 2013).

Large trilinear terms are structurally important. Low $\tan\beta$0 requires controlled $\tan\beta$1, and this is aided by substantial stop mixing. Large $\tan\beta$2 simultaneously raises the Higgs mass to $\tan\beta$3 GeV and suppresses the dominant stop-loop contributions to the EWSB condition. This is why RNS typically occupies regions with highly mixed stops rather than very light unmixed stops (Baer et al., 2013).

Several UV constructions have been proposed that reduce at low energies to RNS-like spectra. A 5D SU(5) orbifold GUT model with Scherk–Schwarz SUSY breaking generates large $\tan\beta$4, non-universal Higgs masses, and a low-energy regime identified as radiative natural SUSY; in that setup, only the radiative natural branch readily accommodates a $\tan\beta$5 GeV Higgs while maintaining $\tan\beta$6 in part of parameter space (Han et al., 2013). Later work also embedded RNS into a string-landscape setting, where soft terms are statistically pulled to large values while anthropic selection on the derived weak scale prefers $\tan\beta$7, yielding typical light higgsinos and a Higgs mass near $\tan\beta$8 GeV across multiple spectrum generators (Baer et al., 2021).

3. Spectrum and phenomenological profile

RNS predicts a distinctive mass hierarchy in which the higgsino sector is light while much of the colored sector is considerably heavier. The defining feature is $\tan\beta$9 GeV, so that $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$0, $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$1, and $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$2 are higgsino-like and nearly degenerate, with mass gaps often of order $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$3 GeV in unified gaugino scenarios (Baer et al., 2013).

The heavier part of the spectrum is not forced to track the weak scale. Typical RNS ranges quoted in the literature include gluinos at $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$4 TeV or $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$5 TeV, top and bottom squarks in the $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$6 TeV range, and first/second generation sfermions from $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$7 to $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$8 TeV. These heavy first/second generation states are phenomenologically useful because they suppress SUSY flavor and CP effects while contributing little to $$\frac{m_Z^2}{2} \simeq -\,\mu^2 - m_{H_u}^2(Q) - \Sigma_u^u(Q),$$9 (Baer et al., 2013).

Sector	Typical RNS feature	Representative scale
Higgsinos	$\mu$0 light and compressed	$\mu$1 GeV
Stops/sbottoms	heavy, highly mixed	$\mu$2 TeV
Gluino	beyond early LHC limits, often near future hadron-collider reach	$\mu$3 TeV
1st/2nd generation sfermions	decoupled, flavor-safe	$\mu$4 TeV

This spectrum differs sharply from older “natural SUSY” formulations that required $\mu$5 and $\mu$6 below a few hundred GeV. The RNS point is that naturalness is controlled by the weak-scale EWSB relation, not by insisting on uniformly light third-generation squarks (Bae et al., 2015).

The Higgs sector is usually near the decoupling limit. Heavy Higgs states $\mu$7, $\mu$8, and $\mu$9 can lie in the TeV range with little direct impact on $m_{H_u}^2(Q)$0, because $m_{H_u}^2(Q)$1 enters the minimization condition suppressed by $m_{H_u}^2(Q)$2. Consequently, the light CP-even Higgs is expected to remain very SM-like in most of the natural RNS region (Bae et al., 2015).

The robustness of this profile against spectrum-generator systematics has been studied explicitly. Using Isasugra, SOFTSUSY, SUSPECT, and SPHENO, one finds qualitatively similar RNS spectra: light higgsinos, multi-TeV stops and gluinos, and a Higgs mass peak in the $m_{H_u}^2(Q)$3 GeV range, even though numerical values of $m_{H_u}^2(Q)$4 and $m_{H_u}^2(Q)$5 vary at the few-GeV or order-one level between codes (Baer et al., 2021).

4. Dark matter, the DFSZ sector, and the $m_{H_u}^2(Q)$6 problem

In standard RNS, the higgsino-like LSP annihilates efficiently into $m_{H_u}^2(Q)$7, $m_{H_u}^2(Q)$8, and $m_{H_u}^2(Q)$9, with coannihilations among $Q\sim m_{\rm SUSY}$0, $Q\sim m_{\rm SUSY}$1, and $Q\sim m_{\rm SUSY}$2 further lowering the thermal relic density. As a result,

$Q\sim m_{\rm SUSY}$3

for the $Q\sim m_{\rm SUSY}$4 GeV higgsino masses characteristic of RNS, well below the observed cold dark matter abundance. Thermal higgsino dark matter is therefore underabundant rather than overabundant in the natural region (Baer, 2013).

This underabundance motivates the standard RNS extension to a supersymmetric DFSZ axion sector. In that construction the superpotential contains

$Q\sim m_{\rm SUSY}$5

so that when PQ symmetry breaks, the effective $Q\sim m_{\rm SUSY}$6 parameter becomes

$Q\sim m_{\rm SUSY}$7

This realizes the Kim–Nilles solution to the SUSY $Q\sim m_{\rm SUSY}$8 problem and links the small $Q\sim m_{\rm SUSY}$9 required by electroweak naturalness to a PQ scale $\Sigma_u^u$0 and the axion sector (Baer, 2013).

The cosmology is then governed not only by higgsinos and axions but also by the axino $\Sigma_u^u$1 and saxion $\Sigma_u^u$2. In the DFSZ case, axino and saxion production is dominated by couplings to the Higgs/higgsino sector and is independent of the reheating temperature, unlike in KSVZ models. Their decays can inject neutralinos, axions, entropy, and dark radiation, so relic densities are determined by coupled Boltzmann equations rather than by a single freeze-out calculation (Bae et al., 2015).

For $\Sigma_u^u$3 GeV, which the 2013 analysis identifies as the standard axion window, axinos and saxions usually decay before neutralino freeze-out, leaving the neutralino relic density near its standard thermal value. The remaining dark matter is provided by axions from vacuum misalignment. In this regime, neutralinos typically supply about $\Sigma_u^u$4 of the dark matter and axions about $\Sigma_u^u$5 (Baer, 2013).

The DFSZ-augmented RNS picture is therefore not a pure WIMP model. It predicts mixed axion–higgsino dark matter, with the axion usually dominant but a non-negligible higgsino fraction retained. This has two important experimental consequences. First, WIMP direct-detection rates must be rescaled by

$\Sigma_u^u$6

since higgsinos constitute only a fraction of the local halo density. Second, indirect-detection rates scale as $\Sigma_u^u$7, making them less promising than direct searches (Bae et al., 2015).

5. Collider tests and Higgs precision probes

At hadron colliders, RNS is challenging precisely because its most robust signal—light higgsinos—comes with compressed spectra and soft visible decay products. Standard jets$\Sigma_u^u$8 searches are primarily sensitive to the colored sector, but in RNS gluinos and stops can lie above the early-LHC reach and even beyond much of the HL-LHC coverage. Dedicated LHC14 analyses found gluino reach up to $\Sigma_u^u$9 TeV with $\mu$00, while wino-pair production can generate a same-sign diboson signature extending the reach to $\mu$01 TeV for $\mu$02 and $\mu$03 TeV for $\mu$04 under unified gaugino masses (Baer et al., 2013).

The same-sign diboson channel is especially characteristic of RNS. It arises from

$\mu$05

followed by decays of heavier electroweakinos into $\mu$06 bosons plus light higgsinos. Since the daughter higgsinos release little visible energy, the final state contains same-sign leptons with modest jet activity and missing energy. This mode was identified as the best LHC reach channel within the RNS framework (Baer et al., 2013).

Direct higgsino production at the LHC yields softer signatures. Soft trilepton analyses exploiting the small $\mu$07 mass gap can be viable only when the mass splitting is not too small, and monojet/mono-photon strategies were argued to be unpromising because signal and background shapes are too similar once the full electroweak structure is included (Baer et al., 2013).

By contrast, lepton colliders are exceptionally well matched to RNS. Since $\mu$08 GeV is obligatory for low $\mu$09, an $\mu$10 collider with

$\mu$11

must produce higgsino pairs if RNS is realized. The 2013 ILC benchmark study concluded that an $\mu$12 collider operating at $\mu$13 GeV should provide a thorough search for the predicted light higgsinos and effectively act as a higgsino factory (Baer et al., 2013).

Higgs precision observables provide a complementary but generally less decisive probe. In low-$\mu$14 RNS, the light Higgs is expected to look very SM-like: $\mu$15 deviations are tiny, $\mu$16 is near unity, and only $\mu$17, $\mu$18, $\mu$19, or $\mu$20 can deviate noticeably in restricted corners of parameter space. In generic natural RNS, the more promising route to discovery remains direct higgsino production rather than Higgs coupling profiling (Bae et al., 2015).

A recent precision-Higgs application is the rare decay $\mu$21. In an MSSM realization of RNS with non-universal Higgs masses, varying the RNS parameters can enhance the SM prediction by up to $\mu$22, reaching $\mu$23 keV, but only by pushing the model to $\mu$24, outside the most natural region. In the same parameter region, $\mu$25 remains close to the SM expectation, with deviations $\mu$26, while $\mu$27 can be moderately suppressed by about $\mu$28 (R. et al., 12 Jul 2025). This suggests that large Higgs-rate deviations are associated with moderately fine-tuned, rather than canonical, RNS.

6. Related developments, variants, and ongoing debates

RNS sits within a broader family of “radiative naturalness” ideas, but not all such constructions are identical. One variant is “dynamically reduced radiative correction” (DRRC), which imposes the weak-scale condition

$\mu$29

and uses non-universal gaugino masses at $\mu$30 to engineer cancellations in RG evolution. This shares RNS’s focus on radiatively obtaining a small weak-scale Higgs mass parameter, but it allows a much heavier superpartner spectrum overall and does not center the analysis on a small $\mu$31 in the same way (Han et al., 2015).

An even sharper contrast appears in “super-natural SUSY,” particularly in M-theory-inspired NMSSM constructions. There the main claim is that all soft parameters scale with a single high-scale quantity, so the high-scale EENZ/Barbieri–Giudice fine-tuning measure is order unity even if $\mu$32 and most of the sparticle spectrum are around the TeV scale or above. From the standpoint of standard RNS, such models do not realize radiatively-driven naturalness in the usual sense because they do not require light higgsinos or small $\mu$33, but they engage the same general debate over which fine-tuning measure is physically appropriate (Li et al., 2015).

A separate discussion concerns R-parity. Canonical RNS is usually formulated with conserved R-parity, a neutralino LSP, and mixed axion–higgsino dark matter. However, natural-SUSY-like spectra can be radically reshaped at colliders by baryon-number violating R-parity violation, in which case light stops may decay promptly to dijets and the usual missing-energy signals disappear. This does not define RNS itself, but it underscores a broader point emphasized in the natural-SUSY literature: collider exclusions are strongly assumption-dependent, and null results in standard missing-energy searches do not by themselves exclude all natural supersymmetric spectra (Brust et al., 2012).

Since 2021, RNS has also been tied explicitly to the string-landscape picture. In that framework, a statistical pull to large soft terms, combined with a log-uniform distribution for $\mu$34 and anthropic selection on the weak scale, favors radiatively-driven natural spectra over finely tuned alternatives such as CMSSM, split, mini-split, spread, or PeV SUSY. This suggests that RNS is not merely a phenomenological patch after LHC8, but potentially the statistically preferred low-energy realization of SUSY in a landscape-based toy multiverse (Baer et al., 2022).

Taken together, these developments frame the central controversy around RNS. One side emphasizes weak-scale naturalness via $\mu$35, radiatively small $\mu$36, and obligatory light higgsinos. The other stresses high-scale sensitivity measures or single-scale UV structures and is willing to accept much heavier higgsinos and spectra. The RNS program’s distinctive contribution is to insist that the directly relevant question is whether the actual weak-scale terms entering the $\mu$37-mass relation are large and mutually cancelling. Under that criterion, a substantial and still testable region of supersymmetric parameter space remains natural after the LHC and after the discovery of a $\mu$38 GeV Higgs (Baer, 2013).