Can blind spots save neutralino dark matter in natural supersymmetry models?

Technical Summary: Can Blind Spots Save Neutralino Dark Matter in Natural Supersymmetry Models?

Problem Statement
Natural Supersymmetry (SUSY) models, defined by the requirement of low electroweak fine-tuning ($\Delta_{EW} \lesssim 30$), predict a light higgsino-like lightest supersymmetric particle (LSP) with a mass in the range of $100-350$ GeV. In R-parity conserving (RPC) scenarios where the QCD axion solves the strong CP problem, the higgsino LSP is expected to constitute only a fraction ($\xi$) of the total dark matter (DM) density, with the remainder being axions. While this reduced abundance ($\xi \sim 0.1$ for thermal production) previously allowed higgsino-like WIMPs to evade indirect detection limits, the recent LZ experiment has placed stringent constraints on spin-independent (SI) direct detection (DD) rates. These limits effectively exclude light higgsino-like WIMPs even when they comprise only their thermally-produced abundance.

The central question addressed is whether "blind spots"—regions in parameter space where cancellations in DD couplings suppress scattering rates—can rescue stable, light higgsino dark matter within the natural SUSY framework. Specifically, the authors investigate if blind spots arising in gravity-mediated models with positive gaugino masses ($M_{1,2} > 0$) and a negative higgsino mass parameter ($\mu < 0$) can satisfy LZ constraints while maintaining naturalness.

Methodology
The authors employ a multi-faceted computational approach to scan the parameter space of natural SUSY:

1. Spectrum Generation: They utilize Isajet 7.92 with Isasugra to calculate the SUSY spectrum, incorporating one-loop corrections for sparticle masses. Crucially, they adopt loop-corrected values for the wino mass ($M_2$) and higgsino mass ($\mu$) in the chargino mass matrix to ensure $\sim 1\%$ precision.
2. Relic Density and Scattering: The IsaReD code (using CalcHEP) calculates neutralino annihilation and co-annihilation processes to determine the thermally-produced relic density ($\Omega_{\tilde{\chi}}^{TP} h^2$). Direct detection rates are computed using IsaReS.
3. Model Scans:
   • NUHM2 and NUHM3 Models: The authors first analyze the $\mu$ vs. $m_{1/2}$ plane for Non-Universal Higgs Mass models (NUHM2 and NUHM3). NUHM3 includes split generations ($m_0(1,2) \gg m_0(3)$) to address SUSY flavor/CP problems while keeping third-generation scalars light.
   • General Parameter Scan: A broader scan is performed over a wide range of parameters ($m_0, m_{1/2}, A_0, \tan\beta, \mu, m_A$) including both $\mu > 0$ and $\mu < 0$ cases.
4. Constraints: The scans are constrained by:
   • Naturalness: $\Delta_{EW} < 30$.
   • Higgs Mass: $123 < m_h < 127$ GeV.
   • LHC Limits: Gluino and top-squark pair production limits, as well as soft-dilepton searches for higgsino-like electroweakinos.
   • Direct Detection: The LZ2025 limits on $\xi \sigma_{SI}$.

Key Contributions and Results
The paper systematically evaluates the viability of blind spots in saving natural higgsino dark matter:

• Blind Spot Conditions: The study focuses on the blind spot condition derived by Cheung et al., which factorizes into terms involving the neutralino mass, $\mu$, and gaugino masses. For models with $M_{1,2} > 0$, blind spots generally require $\mu < 0$.
• NUHM2 and NUHM3 Analysis:
  • In the NUHM2 model, a narrow band of "allowed" points exists at small negative $\mu$ where the LSP is nearly pure higgsino, resulting in low DD rates. However, these points lie on the boundary of the natural region ($\Delta_{EW} \approx 30$) and are likely excluded by LHC soft-dilepton searches.
  • A second blind spot exists at large $|\mu|$ (unnatural region) where the LSP is bino-like. This region is explicitly outside the naturalness requirement.
  • In the NUHM3 model (split generations), charge-and-color-breaking (CCB) minima exclude large portions of low $m_{1/2}$ parameter space. While blind spots allow survival against LZ limits at small and large $|\mu|$, no regions with $\Delta_{EW} < 30$ survive the combined constraints.
• General Scan Results:
  • $\mu > 0$: All points with $\mu > 0$ are excluded by LZ limits because the sign condition for blind spots ($\text{sign}(M_i/\mu) = -1$) cannot be met.
  • $\mu < 0$: A band of blind spot points survives LZ limits but is predominantly in the unnatural region ($\Delta_{EW} > 30$).
  • Natural Candidates ($\mu < 0, \Delta_{EW} < 30$): A few blue points in the general scan survive the LZ thermal WIMP bounds while maintaining naturalness. However, these are subsequently excluded by:
    1. LHC Soft-Dilepton Searches: Points with $m_{\tilde{\chi}} \lesssim 200$ GeV are ruled out by ATLAS/CMS limits on higgsino pair production decaying to soft dileptons.
    2. Higgs Mass Constraint: Points with $m_{\tilde{\chi}} \gtrsim 200$ GeV that survive the LHC limits fail to reproduce the measured Higgs mass ($m_h < 123$ GeV). This occurs because the natural blind spot for higgsinos requires $\tan\beta \sim 1$, which suppresses the radiative corrections necessary to uplift $m_h$ to 125 GeV.

Significance and Conclusions
The authors conclude that within the framework of RPC natural SUSY with thermally produced neutralinos, direct detection blind spots cannot rescue stable light higgsino dark matter from the strong LZ bounds. The few surviving natural candidates are eliminated by a combination of LHC soft-dilepton searches and the measured Higgs mass.

The paper suggests that the failure of blind spots to save natural higgsino WIMPs points toward alternative paradigms:

1. Unstable WIMPs: Models where light higgsinos decay before Big Bang Nucleosynthesis (BBN) via R-parity violating (RPV) operators (e.g., generated via the Kim-Nilles mechanism) are favored. In such scenarios, dark matter could consist entirely of axions or a mixed axion/axino component, bypassing direct detection constraints entirely.
2. Entropy Dilution: A scenario involving large entropy dilution from late-decaying saxions or moduli could reduce the neutralino abundance below thermal expectations, though this requires specific conditions on the lifetimes of these fields to avoid BBN constraints.

Ultimately, the work reinforces the tension between naturalness, the Higgs mass, and direct detection limits, suggesting that stable, light higgsino dark matter in its simplest natural form is disfavored.