Singlino LSP in NMSSM: Properties & Phenomenology

• The singlino-dominated LSP naturally arises in NMSSM extensions through an effective μ-term, addressing the μ-problem and expanding the neutralino sector.
• Its highly suppressed Standard Model couplings lead to unique collider signatures, including reduced missing energy and soft decay products in cascade processes.
• Dark matter relic density and direct detection prospects are shaped by resonant annihilation, co-annihilation mechanisms, and blind-spot conditions in these models.

A singlino-dominated lightest supersymmetric particle (LSP) arises in supersymmetric models that extend the Minimal Supersymmetric Standard Model (MSSM) by a gauge singlet superfield, most notably in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), its variations such as the new minimal (nMSSM), and in models addressing dark matter and baryogenesis. The singlino, being the fermionic component of the singlet superfield, can emerge as the LSP over broad regions of parameter space, acquiring highly suppressed Standard Model (SM) couplings. This feature governs the collider phenomenology, dark matter properties, direct detection signatures, and model-building constraints in these theories.

1. Defining Features and Mass Generation for the Singlino LSP

In the NMSSM, the superpotential extends the MSSM by including $$\lambda \hat{S} \hat{H}_u\cdot \hat{H}_d + (\kappa/3) \hat{S}^3$$, where $\hat{S}$ is the singlet. Once the singlet scalar acquires a vacuum expectation value (vev) $\langle S \rangle = s$, it generates an effective $\mu$-term for the higgsinos, $\mu_\textrm{eff} = \lambda s$, solving the original "μ-problem". The inclusion of the singlet leads to an enlarged neutralino sector, where the singlino-dominated state can become the LSP.

In the limit of large singlet vev $s$, the (5,5) element of the neutralino mass matrix sets the singlino mass:

$$M_{\chi_1^0} \simeq 2 \kappa s = 2\left(\frac{\kappa}{\lambda}\right) \mu_\textrm{eff}$$

with mixing to the doublet higgsinos suppressed for small $\lambda$ (Das et al., 2012). The singlino admixture is quantified as $|N_{15}|^2$ in the neutralino composition, with highly singlino-dominated LSPs displaying $|N_{15}|^2 \gtrsim 0.99$ (Beskidt et al., 2017, Adhikary et al., 2022).

In variations such as the nMSSM (lacking $Z_3$ symmetry), the singlino mass vanishes at tree level and is induced only through mixing with doublet higgsinos:

$$m_{\tilde{s}} \simeq \frac{\mu^2 v^2}{\mu^2 + \lambda^2 v^2} \sin 2\beta$$

yielding $m_{\tilde{s}} \lesssim 75$ GeV under perturbativity and chargino mass limits (Barducci et al., 2015). Likewise, in Dirac leptogenesis-inspired models, extra singlet superfields interact with right-handed neutrinos, producing a singlino LSP via different mechanisms (Choi et al., 2012).

2. Implications for SUSY Collider Phenomenology

The singlino's suppressed couplings to MSSM fields induce distinctive cascade decay topologies. In the NMSSM, heavier neutralinos or sleptons/squarks often decay first to a MSSM-like NLSP (frequently bino-like), which subsequently decays to the singlino LSP and a lighter SM or NMSSM-specific state $X$:

$\chi_2^0 \rightarrow \chi_1^0 + X$

Typical $X$ includes soft photons, light singlet-like Higgses ($A_S$, $H_S$), or three-body final states (quarks, leptons) (Das et al., 2012, Ellwanger et al., 2014).

The energy in LSPs is much less than in the MSSM, as in the narrow phase-space limit:

$$\frac{E_\textrm{LSP}}{E_\textrm{NLSP}} \simeq \frac{M_\textrm{LSP}}{M_\textrm{NLSP}}$$

This reshapes canonical signatures:

• Suppressed Missing Transverse Energy ($E_T^\textrm{miss}$): The visible decay $X$ absorbs most NLSP energy. In jets plus $E_T^\textrm{miss}$ searches, efficiency falls by $\sim 1/3$ to $1/7$ relative to MSSM, dramatically weakening lower mass bounds for $M_{1/2}$ and other mass parameters (Das et al., 2012, Ellwanger et al., 2014).
• Enhanced Multijet/Multilepton Channels: Additional visible decay products can increase multijet or multilepton signature rates, though not always compensating for suppressed $E_T^\textrm{miss}$ (Das et al., 2012).

Dedicated search strategies circumventing $E_T^\textrm{miss}$—such as requiring reconstructed resonances from $b\bar{b}$ or $\tau^+\tau^-$ (from light $H_1$ decays) using advanced jet substructure—are now essential. This is especially necessary for scenarios with both light squarks/gluinos and a kinematically favored $H_1$ arising at the end of cascades (Ellwanger et al., 2014, Adhikary et al., 7 Aug 2024).

3. Direct Detection and Dark Matter Relic Density

A nearly pure singlino LSP has highly suppressed direct detection rates:

$$\sigma_\textrm{SI} \propto (N_{13}^2 + N_{14}^2), \qquad \sigma_\textrm{SD} \propto |N_{13}^2 - N_{14}^2|$$

where $N_{13,14}$ are up/down-higgsino admixtures. In blind-spot regions, destructive interference leads to cross sections below the neutrino floor, evading even future experiments (Beskidt et al., 2017, Roy et al., 17 Jan 2024). A distinctive blind-spot condition in the singlino-higgsino scenario is:

$\frac{m_S}{\mu_\textrm{eff}} \simeq \sin2\beta$

with additional cancellations possible in the presence of a light bino (Roy et al., 17 Jan 2024).

Thermal relic abundance is shaped by annihilation and co-annihilation:

• Resonant Annihilation: For $m_{\chi_1^0} \lesssim m_Z/2$, $s$-channel exchange of light singlet-like $A_1$ or $H_1$ can bring $\Omega_{\chi_1^0} h^2$ to the observed value. This is most effective for $m_{A_1}, m_{H_1} \simeq 2m_{\chi_1^0}$ (Adhikary et al., 7 Aug 2024, Barducci et al., 2015).
• Co-annihilation: For heavier LSPs or compressed spectra, co-annihilation with nearly degenerate higgsinos/charginos is key for efficient depletion (Kim et al., 2014, Ellwanger et al., 30 Apr 2024, Adhikary et al., 7 Aug 2024).
• Asymmetric Dark Matter: In Dirac leptogenesis scenarios with late-decaying right-handed sneutrinos, the singlino LSP can inherit a dark asymmetry directly correlated with the baryon asymmetry (Choi et al., 2012).

4. Model Parameter Dependence and Spectrum Structure

The properties of the singlino-dominated LSP and its phenomenology depend sensitively on model parameters. Key dependences include:

• Singlino Mass: Set by $m_{\chi_1^0} \sim 2\kappa s$, or in decoupling scenarios by $$m_{\tilde{s}} \simeq (\mu^2 v^2)/(\mu^2 + \lambda^2 v^2)\sin2\beta$$ (Barducci et al., 2015). For small $\lambda,\kappa$, the singlino is naturally light and mixing is minimal (Almarashi et al., 2022).
• Mixing and Co-annihilation: A nontrivial higgsino/bino admixture is required for efficient dark matter annihilation or for observable decays; this is tuned via $\lambda$, $\kappa$, $\mu_\textrm{eff}$, $M_1$, and $M_2$ (Abdallah et al., 2019, Potter, 2015).
• Collider-Accessible NLSPs: The composition and mass gaps between singlino and NLSP (bino-like or higgsino-like) control production and decay kinematics at the LHC, with the cascade typically passing through these NLSPs (Das et al., 2012, Wang et al., 2019, Adhikary et al., 2022).
• Mass Relations: For example, in $Z_3$-invariant NMSSM, singlino mass, singlet-like scalar, and pseudoscalar relate via $m_{\chi_1^0}^2 \simeq m_{h_1}^2 + (1/3)m_{a_1}^2$ (Wang et al., 2019).

5. Experimental Constraints and Search Strategies

Collider searches for a singlino-dominated LSP require tailored strategies:

• Jets + MET Suppression: Classic MET-based analyses lose sensitivity, with signal efficiency in 2/3-jet+MET channels reduced by factors of 1/3 to 1/7, allowing reduced lower bounds on sparticle masses (notably $M_{1/2}$) by up to $\sim$25% (Das et al., 2012).
• Alternative Final States: Production of NMSSM-specific Higgs bosons in decay chains (e.g., $b\bar{b}+\tau^+\tau^-+$jets, triple-boson final states) can be exploited using fat-jet substructure and other approaches (Ellwanger et al., 2014, Adhikary et al., 7 Aug 2024).
• Displaced Vertices: If the NLSP is long-lived due to suppressed couplings (near-pure singlino LSP, small mass splitting), one expects macroscopic secondary vertices at the LHC—a nearly background-free signature (Adhikary et al., 2022).
• Photon Signatures: Compressed spectra with singlino-higgsino or singlino-bino co-annihilation may produce soft photons via $\chi_2^0\to \chi_1^0 + \gamma$; searches exploit events with an initial state radiation jet plus soft photon and MET (Roy et al., 17 Jan 2024).
• Heavy Flavor and Multileptons: Enhanced efficiency in multijet, multilepton, and $2\tau$ channels imply combining various search categories to maximize discovery potential (Das et al., 2012, Kim et al., 2014, Adhikary et al., 7 Aug 2024).

Direct detection experiments are sensitive to the non-singlino admixture. For pure singlino LSPs, both SI and SD cross sections can be suppressed below the neutrino floor, whereas in regions with moderate mixing, advanced instruments such as XENON1T, LZ, and next-generation detectors can probe much of the NMSSM parameter space (Beskidt et al., 2017, Barducci et al., 2015, Almarashi et al., 2022).

6. Theoretical and Cosmological Context

A singlino-dominated LSP enables several theoretical advantages:

• Resolution of the μ-problem: Via the dynamical $\mu_\textrm{eff} = \lambda s$, the NMSSM links the electroweak scale to supersymmetry breaking (Potter, 2015).
• Naturalness and Fine Tuning: The presence of light higgsinos and singlinos moderates fine-tuning compared to models with heavy spectra (Abdallah et al., 2019, Potter, 2015).
• Dark Matter and Baryogenesis: Models incorporating asymmetric DM tied to leptogenesis exploit singlino LSPs for communicating a primordial asymmetry (Choi et al., 2012).
• Exotic Higgs Phenomenology: Light NMSSM-specific scalars/pseudoscalars (e.g., a 95 GeV singlet-like Higgs) offer explanations for collider excesses and enable alternative decay chains not present in the MSSM (Ellwanger et al., 30 Apr 2024).
• Parameter Constraints: Stringent correlations among $\lambda$, $\kappa$, $\mu_\textrm{eff}$, and mass relations place nontrivial conditions on the viable NMSSM parameter space, impacting both phenomenology and consistency with flavor observables and electroweak precision data (Almarashi et al., 2022, Adhikary et al., 2022).

7. Distinction from MSSM and Broader Phenomenological Patterns

The singlino-dominated LSP is phenomenologically distinct from the MSSM bino- or higgsino-dominated LSP:

• Collider signatures: NMSSM events can escape detection in standard MSSM search channels due to softer visible/neutral decay products, reduced $E_T^\textrm{miss}$, and the presence of novel cascades and resonances (Das et al., 2012, Ellwanger et al., 2014, Adhikary et al., 7 Aug 2024).
• Dark matter properties: Even with near-singlet decoupling (small $\lambda,\kappa$), the NMSSM does not revert to MSSM-like behavior; the LSP remains singlino-dominated, with distinct nuclear scattering rates and relic abundance mechanisms (Almarashi et al., 2022).
• Direct detection complementarity: While dark matter direct detection remains challenging for pure singlino LSPs due to suppressed couplings, collider searches (e.g., for triple-boson final states, displaced vertices, or low-mass scalars) offer critical discovery avenues (Adhikary et al., 7 Aug 2024, Adhikary et al., 2022).

In summary, the singlino-dominated LSP, realized generically in the NMSSM and related supersymmetric frameworks, leads to a qualitatively altered landscape of dark matter phenomenology, collider signatures, and model constraints compared to the MSSM. The interdependence of mass spectra, couplings, decay topologies, and annihilation processes defines both the theoretical appeal and the experimental challenges of these models, necessitating ongoing innovations in both parameter space exploration and signal extraction at the LHC and future facilities.