Electroweak-Like Dark Sectors

• Electroweak-like dark sectors are hidden extensions of the Standard Model that mimic electroweak dynamics through mirror symmetries and non-Abelian gauge groups.
• These frameworks naturally produce dark matter candidates and address the baryon–dark matter coincidence via mechanisms like dark baryogenesis and asymmetric symmetry breaking.
• Portal operators and finite-temperature phase transitions in these models yield observable signals such as gravitational waves detected by future space-based observatories.

Electroweak-like dark sectors are hidden extensions of the Standard Model (SM) featuring non-Abelian gauge symmetries, fermion representations, and symmetry breaking structures closely paralleling those found in the SM electroweak sector. These frameworks can naturally accommodate a range of dark matter (DM) candidates, distinctive cosmological signatures (such as strong first-order phase transitions), and unique connections to the SM via portals involving kinetic mixing, Higgs-coupling operators, or higher-dimensional fermionic couplings. Theoretical motivations include explanations of the baryon–dark matter relic density coincidence, robust mechanisms for dark baryogenesis, and experimental accessibility through cosmological, collider, and gravitational-wave observables.

1. Gauge Frameworks and Mirror Structures

Electroweak-like dark sectors universally extend the SM gauge group by introducing an additional non-Abelian structure, most commonly SU(2)′ × U(1)′, sometimes with SU(3)′ for mirror QCD-like dynamics (Ritter et al., 2021, Dick, 2017, Foguel et al., 30 Oct 2025). Mirror or "twin" models implement a discrete symmetry (mirror Z₂), duplicating the visible sector’s field content and interactions with parity, chirality, and symmetry assignments reversed:

• Mirror fermions: For each SM generation, a complete set of SU(3)′ × SU(2)′ × U(1)′ representations, with sector-exchanging Z₂.
• Extended Higgs:
  • Doublet models: Two Higgs doublets in each sector (2HDM); VEV alignment and breaking can differ (asymmetric symmetry breaking, ASB).
  • Singlet extensions and composite sectors: Scalar singlets (Carena et al., 2022), pseudo-Nambu–Goldstone bosons from global symmetry breaking (Carmona et al., 2015).
• Gauge structure:
  • Gauge couplings and field strengths duplicate those of SU(2) × U(1), sometimes with dynamically aligned symmetry breaking to a diagonal subgroup via bi-charged ("link") scalar fields (Dick, 2017).

The manifest duplication supports natural solutions to the DM mass scale coincidence (Ω_DM/Ω_VM ~ 5) in asymmetric dark matter (ADM) setups and facilitates strongly first-order phase transitions analogous to electroweak baryogenesis.

2. Symmetry Breaking, Scalar Potentials, and Phase Transitions

A defining feature is the duplication of electroweak symmetry breaking (EWSB) dynamics in the dark sector. The scalar potential is constructed to preserve mirror or global symmetries while allowing sector-specific vacuum expectation values (VEVs):

• Mirror 2HDM scalar potential (Ritter et al., 2021):

$$V = m_{11}^2(\Phi_1^\dagger\Phi_1 + \Phi_1^{\prime\dagger}\Phi_1') + m_{22}^2(\Phi_2^\dagger\Phi_2 + \Phi_2^{\prime\dagger}\Phi_2') + \cdots$$

with numerous quartic, portal, and Z₂-breaking terms.

• Asymmetric symmetry breaking: Achieved by arranging $v_1 \gg v_2$ in the visible, $w_2 \gg w_1$ in the dark, leading to distinct scales $v \simeq 246$ GeV and $w = v \cdot \rho$, with $\rho \gg 1$.
• Composite/PNGB scenarios: Nonlinear σ-models produce stable, neutral pseudo-Goldstone DM candidates (Carmona et al., 2015).
• SU(2)′ and U(1)′ breaking: Scalar VEVs, including triplet or doublet representations, drive the mass spectrum and possible residual unbroken subgroups (e.g., U(1)_D dark photon) (Ghosh et al., 2020).
• Finite-temperature dynamics: Daisy-resummed, one-loop effective potentials are used to analyze the strength and characteristics of electroweak-like phase transitions (EWPT), frequently employing order parameter $\xi \equiv \phi_c / T_c \gtrsim 1$ for strong first-order transitions and bubble nucleation action $S_3(T)/T$ for calculating nucleation temperatures (Addazi, 2016, Ritter et al., 2021).

Key consequence: Strong first-order dark EWPTs in these sectors give rise to gravitational-wave backgrounds in the mHz–Hz band, potentially observable by LISA, DECIGO, or BBO (Addazi, 2016, Ghosh et al., 2020).

3. Dark Baryogenesis and Asymmetric Matter Generation

Electroweak-like dark sectors frequently invoke mechanisms analogous to SM baryogenesis but residing in the hidden sector:

• CP violation and dark sphalerons: CKM-like mixing and large Jarlskog invariants in the dark sector catalyze baryon asymmetry generation in the presence of strong CP-violating sources and out-of-equilibrium dynamics during a first-order EWPT (Ritter et al., 2021).
• Relevant dynamics:

$$\delta_{CP}' = \frac{d_{CP}'}{T_c^{12}} \sim 10^{-7} - 10^{-10}$$

• Sphaleron transitions: Dark sphaleron rates are parametrically similar to the SM but depend on the dark VEV $w$ and SU(2)′ coupling $g_2'$,

$$\Gamma_{sp}' ∼ κ α_2'^4 T^4 \exp\left(-\frac{E_{sp}'(T)}{T}\right)$$

where $E_{sp}'(T) ≈ \frac{4\pi w}{g_2'}$.

This narrative allows for a dark matter abundance linked to the visible sector’s baryon density, enabling natural explanations for Ω_DM/Ω_B order unity through mechanisms such as baryon–dark baryon number transfer (Ritter et al., 2021).

4. Portal Interactions and Sector Coupling

Communication between the visible and electroweak-like dark sectors typically proceeds via portal operators, which play a central role in cosmological evolution and experimental phenomenology:

• Neutron portal (Ritter et al., 2021):

$$\mathcal{L}_{\text{port}} = \frac{1}{M^5} \epsilon^{abc}(u_{R,a} d_{R,b} d_{R,c})(u'_{L} d'_{L} s'_{L}) + \text{h.c.}$$

mediates B–B′-conserving asymmetry transfer between sectors.

• Kinetic mixing and Higgs portals: Dimension-six (or lower) operators involving gauge kinetic mixing (e.g., $$\phi^\dagger \sigma^a \phi\, X^a_{\mu\nu} B^{\mu\nu}$$) (Foguel et al., 30 Oct 2025) or Higgs bilinears ($(\Phi^\dagger\Phi)(\Phi'^\dagger\Phi')$) (Ritter et al., 2021, Ghosh et al., 2020). These portals control chemical and kinetic equilibrium epochs, phase transition interplay, and dark radiation decoupling.
• Freeze-out and equilibrium conditions: The decoupling temperature $T_{\text{dec}}$ for portal operators satisfies $\Gamma \sim H$ and is critical in determining the degree of dark sector radiation at BBN and CMB epochs.

Correct tuning of portal coupling scales (e.g., $M \lesssim 50$ GeV for the dimension-9 neutron portal) is demanded by both relic abundance and dark radiation ($\Delta N_{\text{eff}}$) constraints.

5. Dark Matter Phenomenology: Mass Spectrum, Relic Density, and Self-Interactions

Electroweak-like dark sectors furnish a variety of viable DM candidates:

• Stable baryons: Mirror nucleons ($n'$) with $m_{n'} \sim \mathcal{O}(\text{GeV})$ and a dark confinement scale $\Lambda_{DM} \gtrsim \Lambda_{QCD}$ account for Ω_DM $\simeq 5$ Ω_VM (Ritter et al., 2021).
• Gauge bosons and PTNG bosons: Models offer stable vector DM ($X^\pm$ or $A^a$) protected by dark custodial symmetry (Foguel et al., 30 Oct 2025, Carone et al., 2013), or pseudo-Goldstone bosons stabilized by discrete parity (Carmona et al., 2015).
• Thermal histories: Both relic abundance via standard freeze-out (2→2), freeze-in (UV-dominated), and SIMP (3→2) mechanisms are realized (Foguel et al., 30 Oct 2025, Ghosh et al., 2020). Key equations include

$$\Omega_{DM} h^2 \sim \frac{0.1}{\langle \sigma v \rangle}$$

with cross sections calculable from non-Abelian gauge and portal-coupling diagrams.

• DM self-interactions: Massless gauge bosons (e.g., residual U(1)_D "dark photons") can mediate long-range self-interactions, alleviating structure formation difficulties (Ghosh et al., 2020).
• Direct detection: Interaction with nucleons is highly model-dependent—can be loop- or portal-suppressed (Hisano et al., 2011, Carmona et al., 2015, Carone et al., 2013). Many realizations have cross sections below current detection tower sensitivity due to cancellation, discrete symmetry suppression, or small mixing angles.

6. Cosmological and Gravitational-Wave Signatures

The finiteness and strength of the dark-sector electroweak-like phase transition have direct implications for observable astrophysical signals:

• Gravitational waves (GWs): Strongly first-order phase transitions produce a stochastic GW background with energy density

$$h^2 \Omega_{\text{GW}}(f) \sim \left(\frac{H_*}{\beta}\right)^2 \left(\frac{\kappa_\phi \,\alpha}{1+\alpha}\right)^2 S(f)$$

peaking in the mHz–Hz regime, with $\alpha$ (transition strength), $\beta/H$ (inverse duration), and $T_*$ (transition temperature) controlled by scalar potential parameters (Addazi, 2016, Ghosh et al., 2020).

• Dark radiation: Energy injection into the visible sector at late times (after $T_{\mathrm{dec}} \sim1$ GeV) needs to respect $\Delta N_{\text{eff}}$ constraints; the ratio $T'/T$ post-decoupling is dynamically set by the portal decoupling and the dark confinement scale (Ritter et al., 2021).
• Baryogenesis and relic coupling: The period at which asymmetry transfer freezes out must align with allowed $B'/B$ ratios, relic DM abundance, and visible baryogenesis requirements.

7. Experimental Constraints, Prospects, and Model Discrimination

Combinations of particle, cosmological, and astrophysical searches constrain the viable parameter space for electroweak-like dark sectors:

• Direct detection: Nucleon recoil cross sections for mirror-sector or composite DM models with GeV–TeV masses face strong bounds, depending crucially on portal strength and suppression mechanisms (Dick, 2017, Carmona et al., 2015).
• Collider signals: Suppressed dark Higgs mixing, heavy vector resonances, and long-lived dark-sector states represent promising targets for future colliders at scales $f_D$ and $g_D$ (Carmona et al., 2015, Ghosh et al., 2020).
• Gravitational-wave observatories: To probe first-order PTs in dark SU(2)′ × U(1)′ sectors, space-based detectors (LISA, DECIGO, BBO) have projected sensitivity to transition strengths $\alpha \gtrsim 0.05$ and durations $\beta/H \lesssim 1000$ at $T' \sim 100 - 200$ GeV (Addazi, 2016, Ghosh et al., 2020).

Absence of new signals (null detection) places strong constraints on allowed ranges for portal coupling strengths, effective operator scales, and the temperature ratios between sectors.

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Electroweak-like dark sectors thus provide a rigorous, symmetry-driven extension framework that tightly links theoretical internal consistency (gauge structure, symmetry breaking, phase transitions) to observable consequences across multiple experimental and cosmological frontiers. These models remain robust, flexible laboratories for dark matter, baryogenesis, and cosmology, with strong prospects for near-term empirical scrutiny (Ritter et al., 2021, Foguel et al., 30 Oct 2025, Ghosh et al., 2020, Addazi, 2016, Carmona et al., 2015, Dick, 2017).