---
title: Bino-Wino NLSP Models in SUSY
url: https://www.emergentmind.com/topics/bino-wino-nlsp-models
type: topic
---

# Bino-Wino NLSP Models in SUSY

Bino-wino NLSP models describe scenarios in supersymmetric extensions of the Standard Model where the lightest supersymmetric particle (LSP) is a bino-like neutralino, and the next-to-lightest supersymmetric particles (NLSPs) are wino-like neutralinos and charginos with a small mass splitting. Such models are motivated by dark matter relic abundance via bino-wino coannihilation and frequently arise in frameworks such as mini-split supersymmetry, specific GUT models, and UV-complete scenarios with heavy higgsinos. The compressed mass spectrum and the associated suppressed visible decays present characteristic experimental signals, notably long-lived neutral winos leading to displaced vertex signatures at the LHC.

## 1. Theoretical Framework and Spectrum Structure

Bino-wino NLSP models are formulated within the MSSM or its extensions, where the gauge-eigenstate gaugino soft masses satisfy $M_1 < M_2 \ll \mu$, with $M_1$ the bino soft mass, $M_2$ the wino soft mass, and $\mu$ the higgsino mass parameter. In the mini-split or spread SUSY limit, scalars (sfermions, heavy Higgs) and the higgsinos are decoupled ($\widetilde m,\, \mu \sim 10$–$10^3$ TeV), yielding:

- LSP: $\tilde\chi_1^0 \approx \tilde B$ (bino-like neutralino)
- NLSPs: $\tilde\chi_2^0 \approx \tilde W^0$ (neutral wino), $\tilde\chi_1^\pm \approx \tilde W^\pm$ (charged wino)
- Typical mass hierarchy: $M_2 > M_1$, $\mu \gg M_{1,2}$
- Loop-induced mass splitting between neutral and charged wino: $\Delta M_{\rm EW} \approx 160$ MeV

Bino-wino coannihilation becomes efficient when the mass difference $\Delta m \equiv M_2 - M_1 \lesssim 10 \text{--} 30$ GeV, with $\Delta m \sim 20$–$30$ GeV typical for $M_1 \simeq 300$–$500$ GeV to reproduce the observed dark matter relic abundance.

In UV-complete scenarios such as $E_7/SU(5)\times U(1)^3$ non-linear sigma models, gaugino masses arise predominantly from anomaly mediation and couplings to a shift-charged singlet field $S$. Demanding electroweak vacuum metastability enforces
\[
|M_2 - M_1| / M_1 \lesssim 1\%
\]
thus realizing the required mass degeneracy for bino-wino coannihilation [1907.07168].

## 2. Relic Abundance and Coannihilation Dynamics

The cosmological relic density in bino-wino NLSP models is controlled by coannihilation processes due to the compressed spectrum:

- The coupled Boltzmann equation for the total number density $n=n_{\tilde\chi_1^0} + n_{\tilde\chi_1^\pm} + n_{\tilde\chi_2^0}$,
\[
\frac{dn}{dt} + 3Hn = -\langle \sigma_{\rm eff} v \rangle (n^2 - n_{\rm eq}^2)
\]
where the effective cross section,
\[
\langle \sigma_{\rm eff} v \rangle = \sum_{i,j} \frac{n_i^{\rm eq} n_j^{\rm eq}}{(n^{\rm eq})^2} \, \langle \sigma_{ij} v \rangle
\]
accounts for all coannihilating species.

Dominant annihilation and coannihilation channels include:
- $\tilde\chi_1^+\tilde\chi_1^- \to W^+W^-$
- $\tilde\chi_1^0\tilde\chi_1^+ \to W^+\gamma$, $W^+Z$
- $\tilde\chi_2^0\tilde\chi_2^0,\, \tilde\chi_1^0\tilde\chi_2^0 \to f\bar f,\, W^+W^-,\, Z Z$

The relic density is approximated by
\[
\Omega_{\rm DM}h^2 \approx \frac{1.07 \times 10^9 \,\,{\rm GeV}^{-1}}{\sqrt{g_*} M_{\rm Pl}} \frac{x_f}{J(x_f)}
\]
where $x_f\sim 20$–$30$ and $J(x_f)=\int_{x_f}^\infty dx\, \langle\sigma_{\rm eff} v\rangle x^{-2}$.

For $M_1 \simeq 200$–$650$ GeV, $M_2 \sim (1$–$1.1) M_1$, and $\Delta m \sim 10$–$60$ GeV, this coannihilation yields $\Omega h^2 \approx 0.12$, consistent with Planck data [2112.01389, 1506.08206, 2506.21676].

Notable in $E_7$–based models, the coannihilation is not an artifact of fine-tuning but emerges naturally from boundary conditions dictated by symmetry and vacuum stability [1907.07168]. In such constructions, $m_{\tilde\chi_1^0} \sim 1.3$–$2.7$ TeV and $\Delta m_{\chi} \sim$ a few GeV can be realized.

## 3. Collider Phenomenology and Search Strategies

The compressed nature of the bino-wino spectrum leads to specialized collider signatures distinct from classic SUSY searches:

- **Displaced Vertices (DV):** In mini-split SUSY with $\mu \gg M_{1,2}$, $\tilde\chi_2^0 \to \tilde\chi_1^0 f\bar f$ decay is suppressed, yielding macroscopic lifetimes for the neutral wino. The decay length is
\[
c\tau \sim 10 \,{\rm cm} \times \left(\frac{\mu}{100 \,{\rm TeV}}\right)^2 \left(\frac{10\,{\rm GeV}}{\Delta m}\right)^5 \left(\frac{1}{\sin^2 2\beta}\right)
\]
spanning ${\cal O}$(1 mm)–${\cal O}$(1 m) depending on $\Delta m$ and $\mu$ [1506.08206].

- **Soft-lepton/monojet/ISR searches:** For $\Delta m \sim 10$–$30$ GeV, decay products are too soft for conventional searches. Searches target initial-state radiation (ISR) jets recoiling against missing transverse energy, possibly with accompanying soft leptons or photons [2506.21676, 1409.4533].

- **CMS and ATLAS DV searches:** Recent analyses exploit low-momentum displaced tracks and large missing $p_T$ to set leading constraints on models with $0.2 \lesssim c\tau \lesssim 200$ mm, excluding $m_{\tilde\chi_2^0} \lesssim 550$ GeV for $\Delta m = 20$–$25$ GeV [2511.08212]. DV acceptance is maximized for $c\tau\sim$ a few cm–tens of cm, falling outside this range due to prompt decays or decays outside the detector.

- **Special photon + soft lepton + $E_T^{\rm miss}$ final states:** In scenarios where $\tilde\chi_2^0 \to \gamma \tilde\chi_1^0$ is sizable (loop-induced), $pp \to j \tilde\chi_2^0 \tilde\chi_1^\pm \to j+\gamma+\ell+\slashed E_T$ can offer sensitivity up to $m_{\tilde\chi_2^0} \sim 150$ GeV at 14 TeV LHC with 500 fb$^{-1}$ for small $\Delta m$ [1409.4533].

A summary of LHC mass reach and benchmarks:

| $\Delta m$ (GeV) | $c\tau$ (mm–cm) | LHC mass reach (GeV) | References          |
|------------------|----------------|----------------------|---------------------|
| 12–15            | 0.5–200        | $\lesssim$ 300       | [2511.08212]        |
| 20–25            | 1–50           | $\lesssim$ 550       | [2511.08212]        |
| 20–30            | $1$–$100$      | up to 900 (future)   | [1506.08206]        |
| 5–15             | prompt         | up to 150 (soft $\gamma$ + $\ell$) | [1409.4533] |

These searches close key "blind spots" for conventional searches in compressed spectra, especially when standard lepton and jet triggers have low efficiency.

## 4. Direct Detection and Complementary Probes

Bino-wino NLSP models predict spin-independent nucleon-LSP cross sections for direct detection experiments dominated by Higgs-exchange, with the coupling
\[
g_{\chi\chi h} = (g'N_{11} - gN_{12})(N_{13}\cos\beta + N_{14}\sin\beta)
\]
For pure gaugino LSP/NLSP spectra (with $N_{13,14} \ll 1$), $g_{\chi\chi h} \sim 10^{-2}$–$10^{-3}$, yielding
\[
\sigma_{\rm SI} \sim 10^{-46} \text{–} 10^{-49} \, {\rm cm}^2
\]
with values near or below the projected sensitivities of upcoming XENON-nT and LZ for $m_{\tilde\chi_1^0} \lesssim 400$ GeV; direct-detection rates for lower relic density points (underabundant) may fall below the neutrino floor [2112.01389, 1409.4533]. Models with $\Omega_{\chi}h^2$ underabundant for a given parameter point must rescale $\sigma_{\rm SI}$ by $\Omega/\Omega_{\rm DM}^{\rm obs}$.

## 5. Model Realizations: UV Completions and Unification

Bino-wino NLSP and coannihilation arise naturally in several UV frameworks:

- **Non-universal gaugino mass models:** Choice of $M_1 \ll M_2 \ll \mu$ at the weak scale realizes the compressed spectrum needed for efficient coannihilation [1409.4533].
- **$E_7/SU(5)\times U(1)^3$ non-linear sigma models:** Boundary conditions mediated by $S$-field and anomaly mediation, with vacuum stability, predict $\Delta m/M_1 \lesssim 1\%$. This "miraculous" tuning is not ad hoc but enforced by the structure of the theory. In these models, gauge and $b$–$\tau$ Yukawa couplings unify at $1\%$ level at the GUT scale [1907.07168].
- **Gauge mediation:** Natural gauge mediation models can yield a bino NLSP; however, these typically produce a $\gamma\gamma+\slashed E_T$ final state with prompt NLSP decays if the LSP is a gravitino [1208.6062], distinguishing them from the classic bino-wino NLSP compressed scenario.

## 6. Outlook, Constraints, and Future Directions

Key aspects and state-of-the-art exclusions:
- LHC Run 2 and Run 3 analyses now probe $m_{\tilde\chi_2^0}$ up to 550 GeV for $c\tau \sim 1$–$100$ mm and $\Delta m = 20$–$25$ GeV. This covers parameter space not accessible to traditional searches [2511.08212].
- Bayes factor combination of LHC analyses in the compressed $M_1\simeq300$ GeV, $M_2\simeq320$ GeV ($\Delta m\simeq20$ GeV) region shows coherence with mild excesses observed in the soft-lepton and monojet final states, and full relic density is achieved [2506.21676].
- Next-generation $e^+e^-$ colliders with $\sqrt{s}\leq 1\,$TeV and polarized beams can fully cover the compressed coannihilation parameter space, including scenarios inaccessible to direct detection due to low $\sigma_{\rm SI}$ [2112.01389].
- High-scale models with automatic coannihilation via vacuum stability (e.g., $E_7$) lead to tight correlations between mass parameters and the requirement of heavy scalars, with gluino and sfermion masses typically several TeV [1907.07168].

A plausible implication is that the discovery or exclusion of displaced-vertex signals at the LHC or future colliders will directly test the mini-split SUSY paradigm, discriminate between UV completions, and elucidate the mechanisms of dark matter coannihilation.

## 7. Summary Table: Key Features of Bino-Wino NLSP Models

| Feature                     | Value/Range                                    | References         |
|-----------------------------|------------------------------------------------|--------------------|
| $M_1$ (bino mass)           | 200–650 GeV (TeV scale in some GUTs)           | [1506.08206, 2112.01389, 1907.07168]   |
| $M_2-M_1$ ($\Delta m$)      | 10–30 GeV (coannihilation), $\lesssim$1% in $E_7$ | [1506.08206, 1907.07168]     |
| $\mu$ (higgsino mass)       | $\gg$ TeV                                      | [1506.08206, 2112.01389]     |
| LHC DV sensitivity          | $m_{\tilde\chi_2^0}\lesssim550$ GeV @13 TeV    | [2511.08212]      |
| Relic density                | $\Omega h^2 \simeq 0.12$                       | [1506.08206, 2112.01389, 2506.21676]   |
| Direct detection $\sigma_{\rm SI}$ | $10^{-46}$–$10^{-49}$ cm²                | [2112.01389, 1409.4533]      |
| Key search channels         | DV+$E_T^{\rm miss}$, soft-lepton+$E_T^{\rm miss}$, monojet, soft photon+$\ell$ | [1506.08206, 2511.08212, 2506.21676, 1409.4533]  |
| UV completion               | Mini-split, non-universal gauginos, $E_7$ GUT  | [1907.07168]      |

The experimental and theoretical status of bino-wino NLSP models indicates continued strong motivation for specialized collider searches, refined direct detection analyses, and UV model-building correlating mass degeneracy, relic abundance, and unification properties.

Source: https://www.emergentmind.com/topics/bino-wino-nlsp-models