Bino-Wino NLSP Models in SUSY

• Bino-wino NLSP models are supersymmetric scenarios featuring a bino-like LSP and nearly degenerate wino-like NLSPs, enabling efficient dark matter coannihilation.
• They utilize frameworks like mini-split SUSY and UV-complete models with anomaly mediation to ensure the compressed spectrum necessary for a relic density near Ωh²≈0.12.
• Distinct collider signatures, including displaced vertices, soft-lepton/monojet events, and low-energy photon channels, drive specialized search strategies at the LHC.

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 (Yanagida et al., 2019).

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 (Chakraborti et al., 2021, Nagata et al., 2015, Agin et al., 26 Jun 2025).

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 (Yanagida et al., 2019). 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 $\mu$ (Nagata et al., 2015).

• 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 (Agin et al., 26 Jun 2025, Han et al., 2014).
• 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 (Collaboration, 11 Nov 2025). 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 $\Delta m$ (Han et al., 2014).

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	(Collaboration, 11 Nov 2025)
20–25	1–50	$\lesssim$ 550	(Collaboration, 11 Nov 2025)
20–30	$1$–$100$	up to 900 (future)	(Nagata et al., 2015)
5–15	prompt	up to 150 (soft $\gamma$ + $\ell$)	(Han et al., 2014)

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 (Chakraborti et al., 2021, Han et al., 2014). 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 (Han et al., 2014).
• $E_7/SU(5)\times U(1)^3$ 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 (Yanagida et al., 2019).
• 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 (Barnard et al., 2012), 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 (Collaboration, 11 Nov 2025).
• 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 (Agin et al., 26 Jun 2025).
• 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 $\sigma_{\rm SI}$ (Chakraborti et al., 2021).
• 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 (Yanagida et al., 2019).

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)	(Nagata et al., 2015, Chakraborti et al., 2021, Yanagida et al., 2019)
$M_2-M_1$ ($\Delta m$)	10–30 GeV (coannihilation), $\lesssim$1% in $E_7$	(Nagata et al., 2015, Yanagida et al., 2019)
$\mu$ (higgsino mass)	$\gg$ TeV	(Nagata et al., 2015, Chakraborti et al., 2021)
LHC DV sensitivity	$m_{\tilde\chi_2^0}\lesssim550$ GeV @13 TeV	(Collaboration, 11 Nov 2025)
Relic density	$\Omega h^2 \simeq 0.12$	(Nagata et al., 2015, Chakraborti et al., 2021, Agin et al., 26 Jun 2025)
Direct detection $\sigma_{\rm SI}$	$10^{-46}$–$10^{-49}$ cm²	(Chakraborti et al., 2021, Han et al., 2014)
Key search channels	DV+$E_T^{\rm miss}$, soft-lepton+$E_T^{\rm miss}$, monojet, soft photon+$\ell$	(Nagata et al., 2015, Collaboration, 11 Nov 2025, Agin et al., 26 Jun 2025, Han et al., 2014)
UV completion	Mini-split, non-universal gauginos, $E_7$ GUT	(Yanagida et al., 2019)

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.