Dark Standard Model (DSM)

• Dark Standard Model (DSM) is a theoretical framework that extends the Standard Model to include unified visible and dark sectors with new symmetries and stable dark matter candidates.
• DSM models employ additional gauge structures, such as SO(10)ₓ and U(1)ₓ, and use portal interactions and solitonic mechanisms to generate observable phenomena.
• These models provide testable predictions including neutrino oscillation anomalies, X-ray lines, collider signatures, and potential gravitational wave signals.

A Dark Standard Model (DSM) designates a class of theoretical frameworks extending or reinterpreting the Standard Model (SM) of particle physics to incorporate stable or metastable states—often with additional symmetries or sectors—which constitute the dark matter component of the universe. These DSMs embed both visible and dark states within a common gauge or structural unification, generating distinctive phenomenology, cosmological implications, and constraints.

1. Unified Gauge and Field Structure

DSM models are characterized by augmenting the SM gauge group with new symmetries, with the unification of visible and dark sectors in a compact group or an extended field space:

• SO(10)$_x$ DSM: All SM left-chiral fermions and dark sector partners are unified within a 16-dimensional irreducible spinor of an SO(10)$_x$ gauge symmetry. Unlike conventional SO(10) grand unified theories, SO(10)$_x$ here does not only cover SM interactions but encompasses both the visible and a new dark family, yielding a complete joint treatment of four chiral families—three SM-like and one "dark"—in a single representation (Khruschov, 2016).
• Portal DSMs: Minimal extensions introduce a hidden abelian $U(1)_D$ (or similar), under which SM fields are neutral and dark matter fields (e.g., fermions $\chi_L, \chi_R$) are charged. Such models also incorporate new scalar fields (dark Higgs) to break the new symmetry and provide mass to the associated gauge bosons ("dark photons") (Ma, 2022, Dittmaier et al., 25 Jul 2024).
• Composite and Topological DSMs: Models such as the “Dormant Skyrmion Standard Model” (DSSM) exploit nonperturbative dynamics within the SM scalar sector, where the Higgs doublet supports topologically stable soliton solutions (skyrmions) stabilized by a dynamically generated Hidden Local Symmetry (HLS) gauge boson (Matsuzaki et al., 2016).
• Minimal Gauge DSMs: The most reduced formulations posit a scalar field with only a dark $U(1)$ gauge symmetry, completely decoupled from SM particles. The dark sector admits stable solitonic configurations with self-consistent gravitational and gauge structure (Barranco et al., 30 Nov 2025).

2. Particle Content, Mass Spectra, and Mixing

Typical DSMs feature:

• Extended Fermion Multiplets: The SO(10)$_x$ scenario yields a $4 \times 4$ chiral-field matrix per generation, where the fourth "dark" column contains a sterile neutrino ($\nu_s$), a light dark fermion ($o$), and heavier states ($N, S$), with all states unified under the same 16 (Khruschov, 2016).
• Mixing Mass Matrices: The neutrino–dark sector contains a $7\times7$ mass matrix after symmetry breaking. Its structure is generically block-diagonal, with submatrices for active Majorana neutrinos, Dirac mixings, and dark-sector states. Predicted masses are:
  • Sterile neutrino ($\nu_4$): $\sim 1\,\mathrm{eV}$
  • Light dark fermion ($o$): $\sim 10\,\mathrm{keV}$
  • Heavy dark fermions ($N, S$): $\sim 1\,\mathrm{GeV}$ or larger.
  • Mixing parameters satisfy stringent constraints from short-baseline oscillation and astrophysical X-ray searches ($|a_4|^2 \lesssim 0.01$, $|a_5|^2 \lesssim 10^{-6}$) (Khruschov, 2016).
• Gauge and Scalar Spectra: DSMs with extra $U(1)_D$ produce massive vector bosons ($Z_D$), and a dark Higgs, mixing weakly with the SM Higgs via portal couplings ($\lambda_{HD}$).
• Solitonic Boson Stars and Topological Objects: Models with scalar–gauge gravity coupling yield soliton spectra where mass and radius relations depend on the scalar mass $\mu$ and dark coupling $q$. For $\tilde q < \tilde q_{\mathrm{crit}}$, dynamically stable compact objects arise, with astrophysical constraints imposing $\mu \gtrsim 10\,\mathrm{eV}$ (Barranco et al., 30 Nov 2025). In DSSM, soliton mass $M_{X_s} \sim 13-18\,\mathrm{GeV}$ is predicted, with portal-mediated couplings to SM Higgs (Matsuzaki et al., 2016).

3. Symmetry Breaking Chains and Portal Interactions

DSM models implement hierarchical symmetry breaking to isolate SM physics and generate viable dark matter:

• SO(10)$_x$ Chain:
  • $$SO(10)_x \xrightarrow{\langle 210_H \rangle} SU(4)_C \times SU(2)_L \times SU(2)_R$$
  • Breaks further through $\langle 45_H \rangle$ and additional Higgs fields, ending at SM plus possible dark remnant $U(1)$ factors, which are broken at or above the TeV scale to eliminate light dark gauge bosons (Khruschov, 2016).
• Higgs and Kinetic Portals: Scalar quartic couplings ($\lambda_{HD}(H^\dagger H)(H_D^\dagger H_D)$) and gauge kinetic mixing ($\epsilon B_{\mu\nu} X^{\mu\nu}$) transmit interactions between sectors. After symmetry breaking, scalar mass matrices mix dark and visible scalars; the physical Higgs and dark Higgs are admixtures (Ma, 2022, Dittmaier et al., 25 Jul 2024).
• Nonperturbative and Emergent Symmetries: In solitonic DSMs, stability is achieved via emergent gauge sectors (HLS) not introduced at the Lagrangian level but generated dynamically through the scalar sector (Matsuzaki et al., 2016).

4. Dark Matter Candidates and Cosmological Implications

DSM frameworks yield several viable dark matter candidates, often with precise mass, lifetime, and mixing predictions:

• Sterile neutrinos and dark fermions: The SO(10)$_x$ DSM assigns dark matter roles to eV–GeV mass eigenstates derived from the extended mixing matrix. The light ($o$) and intermediate ($N, S$) mass states map onto potential warm and cold dark matter, while a sterile neutrino ($\nu_s$) at the eV scale is motivated by short-baseline anomalies (Khruschov, 2016).
• Solitonic compact objects: Stable boson stars with dark gauge charge, mass, and radius controlled by $(\mu, q)$, are consistent with gravitational microlensing constraints. Dynamical stability requires $\tilde q < \tilde q_{\rm crit}$, and the population is bounded below asteroid mass by survey data (Barranco et al., 30 Nov 2025).
• Dormant Skyrmion Standard Model: Solitonic skyrmions have fixed mass and size determined by the SM Higgs vacuum expectation value and nonperturbative dynamics. The relic abundance and direct detection rates are calculable: $M_{X_s} \sim 13-18\,\mathrm{GeV}$, with direct detection cross-sections bounded by LUX and CMS limits (Matsuzaki et al., 2016).
• Condensate/quasiparticle models: "Superconducting" DSMs predict dark matter as Higgs/Goldstone modes of Cooper-paired right-handed neutrinos or vector-like quarks. This yields fuzzy DM ($m_\mathrm{DM} \sim 10^{-19}\,\mathrm{eV}$) to WIMP-scale candidates, relating baryon and dark matter densities via shared thermodynamic origins (Alexander et al., 14 May 2024).

5. Experimental and Astrophysical Signatures

DSM models predict characteristic signatures in oscillation experiments, colliders, cosmological surveys, and astrophysical observations:

• Short-baseline Neutrino Oscillations: Enhanced active–sterile neutrino mixing explains LSND and MiniBooNE anomalies; predicted mass and mixing parameters are tightly constrained by null results (Khruschov, 2016).
• X-ray Lines: keV-scale dark fermions decay with radiative signatures detectable via X-ray telescopes (e.g., 3.5 keV line from $o \to \nu\gamma$) (Khruschov, 2016).
• Collider Signatures: GeV-scale dark fermions with weak portal couplings induce displaced vertex signatures, while scalar and gauge portal mixing impacts Higgs boson invisible decays and can produce multi-lepton final states from cascade decay chains in the dark sector (Matsuzaki et al., 2016, Ma, 2022).
• Microlensing and Gravitational Waves: Compact DSM solitons are tightly constrained by microlensing surveys (requiring $\mu \gtrsim 10\,\mathrm{eV}$) and could be sources of distinctive gravitational wave signals in mergers (Barranco et al., 30 Nov 2025).

6. Theoretical and Phenomenological Constraints

DSM realizations are subject to multiple theoretical consistency and experimental constraints:

• Mixing Angles and Admixture Bounds: Unitary mixing matrices for the combined visible–dark sector are bounded by neutrino oscillation, cosmology, and direct detection: e.g., $|a_4|^2 \lesssim 0.01$, $|a_5|^2 \lesssim 10^{-6}$ for SO(10)$_x$ models (Khruschov, 2016).
• Relic Abundance: Freeze-in and freeze-out mechanisms are computed precisely in models with simple portal couplings, with observed $\Omega_\mathrm{DM}$ fixing combinations of couplings and dark sector masses (Ma, 2022).
• Direct Detection Limits: Nucleon scattering cross-sections from portal couplings are tightly constrained (multi-TeV partner masses, Higgs invisible branching ratios) (Matsuzaki et al., 2016, Ma, 2022).
• Astrophysical Population Constraints: Soliton masses above asteroid scale are excluded for all viable couplings, bounding model parameter spaces (Barranco et al., 30 Nov 2025).
• Vacuum Stability and Higgs Physics: Additional scalar content and portal couplings in certain DSMs help stabilize the Higgs potential and can resolve SM vacuum instability issues at high scales.

7. Broader Implications and Model-Building Approaches

DSM constructions exemplify multiple theoretical strategies for unifying visible and dark matter:

• SO(10)$_x$ unification supplements the SM with a dark family, automatically embedding myriad dark fermion and sterile neutrino states, enabling rich oscillation and decay phenomenology (Khruschov, 2016).
• Hidden gauge symmetries ($U(1)_D$ and analogues) with portals enable minimally extended, anomaly-free cosmologies compatible with precision terrestrial and astrophysical data (Ma, 2022, Dittmaier et al., 25 Jul 2024).
• Nonperturbative solitonic constructions (DSSM) demonstrate that the SM Higgs sector itself, in polar and HLS variables, suffices for topologically stabilized dark matter, eschewing additional new fields (Matsuzaki et al., 2016).
• Models invoking quantum condensates directly relate dark matter and baryon densities, offering potential explanations for the cosmic $\Omega_\mathrm{DM}/\Omega_b$ coincidence (Alexander et al., 14 May 2024).

Collectively, DSM models provide a systematic framework for embedding the dark sector within or adjacent to the established SM gauge and matter content, delivering both theoretical unification and experimentally testable consequences.