Weak-Scale Supersymmetry (SUSY)

• Weak-scale SUSY is a framework that achieves technical naturalness by pairing bosons with fermions to cancel large radiative corrections in the Higgs sector.
• It predicts a spectrum with light Higgsinos (~350 GeV), TeV-scale stops and gluinos, and multi-TeV sfermions, aligning with current LHC constraints.
• Radiatively-driven models and NUHM extensions leverage landscape statistics and anthropic selection to naturally reproduce the observed electroweak scale and a 125 GeV Higgs.

Weak-scale supersymmetry (SUSY) is a technically natural solution to the gauge hierarchy problem in particle physics, positing a symmetry between bosons and fermions that cancels quadratic divergences in the Higgs mass. The framework employs softly broken supersymmetry with characteristic mass scales: $m_{\text{weak}}\simeq\mathcal{O}(100~\text{GeV})$ for weakly interacting particles (Higgs, $Z$, Higgsinos), and $m_{\text{soft}}\gtrsim1~\text{TeV}$ for squarks, gluinos, and heavy Higgses. Modern collider searches define stringent constraints on superpartner masses, sharpening the so-called "Little Hierarchy Problem" ($m_{\text{weak}} \ll m_{\text{soft}}$). Contemporary analyses emphasize low-scale, model-independent measures of electroweak naturalness and incorporate statistical and anthropic selection from the string landscape, leading to distinctive predictions for the spectrum and phenomenology of SUSY at current and future collider experiments (Zhang, 3 Jan 2026, Baer et al., 2024, Baer et al., 15 Feb 2025).

1. Theoretical Motivation and Technical Naturalness

The Standard Model (SM) Higgs sector exhibits quadratic sensitivity to ultraviolet scales, $\delta m^2_H \sim (g^2/16\pi^2)\Lambda^2$, leading to severe fine-tuning for any large $\Lambda$. Weak-scale SUSY resolves this instability by pairing each SM fermion with a bosonic superpartner (and vice versa), ensuring exact cancellation of divergent terms in radiative corrections. In softly broken SUSY, the superpartner masses are parametrized by $m_{\rm soft}\gtrsim 1~$TeV, distinct from the weak scale $m_{\rm weak}\sim m_Z,\mu,m_h\lesssim 100$–$350$ GeV (Zhang, 3 Jan 2026, Nevzorov, 2011). This property—dubbed technical naturalness—renders SUSY a minimal, renormalizable extension of the SM capable of explaining the smallness of $m_Z$.

2. LHC Constraints and the Little Hierarchy Problem

After Run 2 at the LHC, ATLAS and CMS have set exclusion limits:

• Gluinos: $m_{\tilde g}\gtrsim 2.2$ TeV
• Stops: $m_{\tilde t_1}\gtrsim 1.2$ TeV
• Wino-like electroweakinos: up to $\sim 700$ GeV
• Higgsino-like electroweakinos: up to $200$–$300$ GeV for appreciable mass splittings

These experimental results imply $m_{\rm soft}\gg m_{\rm weak}$, driving the little hierarchy problem: "Why is $m_Z\sim 91~\text{GeV}$ and $\mu\sim 100$–$300~\text{GeV}$ so much smaller than $m_{\text{soft}}\gtrsim1~$TeV?" Traditional models necessitate fine-tuning unless protected by symmetry or environmental (anthropic) selection (Zhang, 3 Jan 2026, Baer et al., 2020, Baer et al., 15 Feb 2025).

3. Weak-Scale Electroweak Naturalness: The $\Delta_{EW}$ Measure

Electroweak naturalness is quantified by the model-independent, low-scale measure $\Delta_{EW}$, derived from the MSSM Higgs potential minimization:

$$\frac{m_Z^2}{2} = \frac{m_{H_d}^2+\Sigma_d^d - (m_{H_u}^2+\Sigma_u^u)\tan^2\beta}{\tan^2\beta-1} - \mu^2$$

with radiative corrections $\Sigma_{u,d}^{u,d}$ included. The measure is:

$$\Delta_{EW} = \max_i\left| \frac{C_i}{m_Z^2/2} \right|$$

where $C_i$ are weak-scale contributions. Avoiding fine-tuning at the $3\%$ level requires $\Delta_{EW}\lesssim30$, which constrains phenomenologically viable spectra:

• $\mu\lesssim350~\text{GeV}$ (light higgsinos)
• $m_{\tilde t_{1,2}}\lesssim2$–$3~\text{TeV}$ (with large $A_t$ for maximal mixing)
• $m_{\tilde g}\lesssim6~\text{TeV}$
• First/second-generation sfermions up to $\sim 40~\text{TeV}$ This approach avoids ambiguities stemming from high-scale parameter choices and is independent of mediation details (Zhang, 3 Jan 2026, Baer et al., 2023, Baer et al., 2015, Baer et al., 2021).

4. String Landscape and "Stringy Naturalness"

The string landscape, most concretely realized in flux compactifications (e.g., IIB on Calabi–Yau orientifolds), provides a statistical ensemble of vacua characterized by a power-law preference for large SUSY-breaking soft terms: $f_{\rm SUSY}(m_{\rm soft}) \sim m_{\rm soft}^n$ with $n=2n_F + n_D - 1$. However, anthropic selection—enforced via the atomic principle—requires the weak scale in each pocket universe to remain within a factor $2$–$5$ of the observed value ($m_Z\sim91$ GeV) to allow complex chemistry (Baer et al., 2024, Baer et al., 2021, Baer et al., 15 Feb 2025). The result is a concentration of vacua at the highest $m_{\rm soft}$ consistent with $m_Z$; this provides an environmental rationale for radiatively-driven naturalness:

• Typical spectrum: First/second-generation scalars at tens of TeV (ameliorating CP/flavor problems), third-generation squarks at few TeV with large mixing (yielding $m_h\simeq125$ GeV automatically), gluinos at the TeV scale, and low $\mu$ parameter, i.e., light higgsinos.
• Models with large fine-tuning (split/high-scale SUSY) occupy negligible landscape volume and are not favored.

5. Non-Universal Higgs Mass Models (NUHM2–4) and Spectral Realization

Non-Universal Higgs Mass (NUHM2–4) models generalize supersymmetric boundary conditions by allowing independent GUT-scale values for $m_{H_u}^2$ and $m_{H_d}^2$, separated from universal matter scalars $m_0$. Maximizing stop mixing via $A_0$ and tuning $m_{H_u}^2$ yields $|\mu|\sim100$–$350$ GeV and a SM-like Higgs in the correct mass range:

• $m_h \sim 125$ GeV
• $\Delta_{EW} \lesssim 30$
• $m_{\tilde q,\tilde\ell}(1,2) \sim 10$–$40$ TeV
• $m_{\tilde t_{1,2}} \sim 2$–$4$ TeV
• $m_{\tilde g} \sim 2$–$6$ TeV

This configuration, termed "radiatively-driven natural SUSY," is both statistically favored in the landscape and phenomenologically consistent with current collider constraints (Zhang, 3 Jan 2026, Baer et al., 15 Feb 2025, Baer et al., 2021, Baer et al., 2015).

6. Collider Phenomenology at High Luminosity LHC (HL-LHC)

For $\sqrt{s}=14$ TeV, $3~\mathrm{ab}^{-1}$:

• Higgsino production ($pp \to \tilde\chi_1^+\tilde\chi_2^0$): discover $m_{\tilde\chi_2^0}\lesssim300$ GeV for $\Delta m \gtrsim10$ GeV via ISR jet plus soft dilepton.
• Stop production ($pp\to\tilde t_1\tilde t_1^*$): 5$\sigma$ reach $m_{\tilde t_1}\lesssim1.7$ TeV, exclusion to $m_{\tilde t_1}\lesssim2.0$ TeV.
• Wino production (same-sign dibosons): $M_2\lesssim1.1$ TeV (5$\sigma$), $M_2\lesssim1.4$ TeV (95% CL).
• Gluino pair production: reach to $m_{\tilde g}\sim2.8$ TeV.
• Heavy Higgses ($A,H\to\tau^+\tau^-$ and $A,H\to\tilde\chi_i\tilde\chi_j$), $H^\pm\to tb, \tau\nu$: discovery to $m_A\sim1.5$ TeV at moderate/large $\tan\beta$ (Zhang, 3 Jan 2026, Baer et al., 15 Feb 2025, Tata, 2020).

Table: Representative HL-LHC Observatory Reach

Channel (Process)	5σ Discovery Reach	95% CL Exclusion
Higgsino pair (soft dileptons)	$m_{\tilde\chi_2^0}\lesssim300$ GeV	—
Stop pair ($t\bar t$+MET)	$m_{\tilde t_1}\lesssim1.7$ TeV	$m_{\tilde t_1}\lesssim2.0$ TeV
Wino pair (SS dibosons)	$M_2\lesssim1.1$ TeV	$M_2\lesssim1.4$ TeV
Gluino pair ($pp\to\tilde g\tilde g$)	$m_{\tilde g}\sim2.8$ TeV	—
Heavy Higgses ($A,H$)	$m_A\sim1.5$ TeV	—

HL-LHC probes the core of the radiatively-driven natural parameter space; however, higher-energy colliders (HE-LHC, FCC-hh) or dedicated Higgsino factories (ILC/CLIC, $\sqrt{s}\gtrsim0.6$~TeV) are required to fully cover the landscape-favored parameter space (Baer et al., 2017, Tata, 2020).

7. Synthesis and Outlook

Weak-scale SUSY, especially in NUHM and radiatively-driven models, remains robust against existing experimental constraints due to environmental selection effects inherent in the string landscape. The interplay of statistical preference for large soft terms and anthropic restriction on the weak scale naturally predicts:

• A SM-like Higgs ($m_h \simeq 125$ GeV)
• Light Higgsinos ($\mu\lesssim350$ GeV)
• TeV-scale stops and gluinos
• Multi-TeV first/second-generation sfermions (addressing flavor/CP)
• Phenomenology accessible primarily through compressed-spectrum searches, multi-jet/multi-lepton final states with MET, and heavy Higgs and electroweakino channels

HL-LHC will probe a significant portion of the viable parameter space. The conceptual developments—electroweak naturalness, stringy naturalness, and the atomic principle—have reframed the expectations for SUSY discovery, shifting focus toward challenging, but testable, compressed and heavy spectra (Zhang, 3 Jan 2026, Baer et al., 2024, Baer et al., 15 Feb 2025, Baer et al., 2023).

Future experimental efforts, both at advanced hadron colliders and lepton machines, will be decisive in validating or excluding minimal radiative SUSY as the resolution to the hierarchy problem. The landscape framework synthesizes statistical and environmental principles with low-energy phenomenology, forming a predictive basis for experimental targets and theoretical model-building in weak-scale supersymmetry.