Sector Node in Supersymmetric Models

• Sector Node is a fundamental concept in supersymmetric theories that connects visible and hidden sectors through singlet portal mechanisms and kinetic mixing.
• It uses unsuppressed renormalizable interactions to transmit the electroweak scale and induce distinct mass mixings and decay signatures in experimental probes.
• The framework predicts phenomenological outcomes such as supersymmetric cascade decays, displaced vertices, and potential signals of hidden dark matter.

A sector node in theoretical physics refers to a fundamental structural feature that connects distinct sectors—most notably, the visible and hidden sectors—via renormalizable interactions in field-theoretic extensions of the Standard Model. In singlet-extended supersymmetric models, such as the next-to-minimal supersymmetric standard model (NMSSM), ultraviolet completions induce marginal kinetic mixing operators between gauge singlet chiral superfields belonging to different sectors. This mixing, which remains unsuppressed in the infrared, functions as a portal through which mass scales and particle mixings are transferred between sectors. The sector node under this framework embodies both the linkage mechanism and the corresponding phenomenological consequences, including scale setting in the hidden sector, the propagation of supersymmetric cascade decays, and the emergence of experimental signatures.

1. Singlet Portal Mechanism and Sector Node Definition

Singlet portals connect sectors through kinetic mixing between singlet chiral superfields, S (visible sector) and S′ (hidden sector), with the marginal operator

$$\mathcal{L} \supset \epsilon \int d^4 \theta\, S^\dagger S' + \mathrm{h.c.}$$

where $\epsilon$ is typically generated at one loop, $\sim 1/(16\pi^2)$, via heavy fields that couple to both singlets. In NMSSM-type extensions, S couples to MSSM Higgs doublets via the superpotential term

$W \supset \lambda S H_u H_d$

After electroweak symmetry breaking and Higgs VEV acquisition, a nonzero F-term for S induces a linear “Polonyi” term for S′ in the effective superpotential: $$W_\mathrm{eff} \supset -\Lambda_\mathrm{eff}^2 S', \quad \Lambda_\mathrm{eff}^2 \approx \epsilon \frac{\lambda}{2} v^2 \sin 2\beta$$ The sector node, realized through $\epsilon$, transmits the visible sector’s electroweak scale to set the mass scale for hidden sector states (typically $m' \sim 0.1 - 100$ GeV). This mechanism is not suppressed by the ultraviolet cutoff, making the portal robust and non-decoupling.

2. Physical Implications of Kinetic Mixing

Kinetic mixing plays several roles:

• Scale Induction: The portal injects the EW scale into the hidden sector so that $W_\mathrm{eff}$ contains a Polonyi-type term.
• Mass Mixing: After canonical normalization, hidden singlino ($s'$-ino) and visible sector singlino/Higgsinos mix via an angle $\theta_\mathrm{mix} \sim \epsilon m'/m$ (with $m'$ the hidden mass and $m$ a visible weak-scale mass). Similarly, scalar components of $S'$ mix into the Higgs mass eigenstates, scaling with $\theta_\mathrm{mix}$.
• Decay Pathways: Supersymmetric cascades in R-parity-conserving theories must decay into hidden sector states. These cascades, forced by the Higgs sector coupling, typically produce Higgs bosons with branching ratios in the $0.01 - 1$ range.

3. Experimental Probes and Constraints

• Astrophysical Bounds: For $m' \lesssim$ few GeV, constraints analogous to those for axion-like particles apply: e.g., energy loss limits from globular clusters, white dwarfs, and SN 1987A require very small $\epsilon$ (e.g., $\epsilon \lesssim 10^{-3}$ for $m' \sim 10$ MeV).
• Rare Meson Decays: For $m'$ typically in the range 100 MeV–few GeV, experiments constrain the mixing angle from searches for $K^\pm \to \pi^\pm s'$, $B \to K s'$ with $s' \to \mu^+\mu^-$.
• Collider Signatures: For higher $m'$, cross sections for $s'$ production are quadratic in $\theta_\mathrm{mix}$; signatures include Higgs bosons in SUSY cascades and displaced decays of low-mass hidden sector states.

4. Supersymmetric Cascade Dynamics

Within R-parity-conserving SUSY, the lightest observable-sector supersymmetric particle (LOSP) can decay to the hidden sector, which contains an R-parity-odd state lighter than the LOSP:

• Portal-In: Cascade decay of a visible superparticle into the hidden sector proceeds via singlino or scalar mixing, e.g., $\psi_\mathrm{higgsino} \to h s'$, with branching ratios determined by $\epsilon m'/m$ and Higgsino/singlino content.
• Portal-Out: Hidden $s'$ or $s'$-ino decay back to SM particles via Higgs mixing, with preference for the heaviest kinematically accessible SM states (e.g., $b\bar{b}$, $\tau^+\tau^-$, $WW$, $ZZ$). Small mixing leads to displaced vertices.

These dynamics guarantee that supersymmetry events predominantly include a boosted Higgs boson and possibly long-lived hidden sector particles with heavy-flavor decay products.

5. Hidden Sector Dark Matter and Direct Detection

The sector node can be extended to accommodate hidden dark matter candidates by introducing a $Z_2$-stabilized chiral multiplet $H'$ with $W_\mathrm{hidden} \supset (\lambda'/2) S' H'^2$. The lightest component of $H'$ is stable:

• Direct Detection: Spin-independent DM–nucleon scattering proceeds via $t$-channel $s'$ exchange, with cross section $\sigma \propto (\lambda'/m'^4) (\epsilon m'/m)^2$.
• Experimental Reach: Typical cross sections are $\sigma \lesssim 10^{-48}$ cm$^2$ but may be enhanced by large $\tan\beta$, $\lambda'$, or increased Higgs-down mixing. Upcoming experiments might reach sensitivity, but detection is challenging due to suppression.

6. Neutrino-Portal Variant

When the hidden singlet mixes kinetically with the right-handed neutrino $N$ (not $S$), the operator $$\mathcal{L} \supset \epsilon \int d^4\theta N^\dagger N' + \mathrm{h.c.}$$ connects the visible and hidden sectors:

• The right-handed neutrino mass mixing is $\theta_n \sim \epsilon (m'/M)$, with $M$ the Majorana mass.
• Decays of hidden $n'$ (hidden singlino) via $n' \to \ell^\pm W^\mp$ have widths $\Gamma \sim [\epsilon^2 y_\nu^2 m'^3/(8\pi M^2)]$, allowing for macroscopic displaced vertices at colliders, even for large $M \sim 10^8$ GeV.
• Distinct from the Higgs-portal scenario, this variant lacks automatic hidden scale generation (no Polonyi term), and the final states provide a probe of high-scale phenomena such as leptogenesis.

7. Phenomenological Summary and Sector Node Characterization

The singlet portal functions as a “sector node”: a renormalizable interface connecting observable and hidden physics. Marginal kinetic mixing not only injects the electroweak scale into the hidden sector, but also dictates small mass and fermion mixings that drive supersymmetric cascade decays into hidden sector states. Cascades produce typical collider signatures including Higgs boson emission and long-lived, displaced decays to heavy-flavored SM particles. Direct detection is suppressed but not excluded, with prospects depending on model parameters. The neutrino-portal variant offers complementary signatures (leptonic displaced vertices) and probes for extremely high mass scales. Consequently, the sector node, in the sense of the singlet portal, establishes the hidden sector as an experimentally testable extension directly linked to standard physics through observable mixing and decay processes.