Dark Baryon: Beyond the Standard Model

• Dark baryon is a hypothetical particle carrying baryon number beyond the Standard Model, designed to unify dark matter relic abundance and baryogenesis.
• The stability of dark baryons arises naturally through gauged U(1)_B symmetry, which forbids decay via quantized baryon charges without requiring ad hoc discrete symmetries.
• Experimental probes include mediator particles like a leptophobic Z_B and Higgs portal interactions, offering testable signatures in direct detection and collider experiments.

A dark baryon is a hypothetical particle carrying baryon number in a sector beyond the Standard Model, typically proposed as a stable or metastable dark matter candidate. Theoretical frameworks involving local gauging of baryon number, new confining gauge interactions, or accidental symmetries frequently ensure stability or cosmological longevity. Dark baryons enable unified treatments of dark matter relic abundance and baryogenesis, connecting the observed baryon asymmetry and dark matter densities through common dynamical or symmetry mechanisms.

1. Dark Baryon Stability via Gauged Baryon Number

In models where baryon number $B$ is promoted to a local $U(1)_B$ gauge symmetry, the stability of any state carrying nonzero baryon number is automatic if it is the lightest such state. For instance, a scalar (or fermion) $X$ with $B=-2/3$ cannot decay to Standard Model (SM) particles without violating baryon number; all decays with $\Delta B\neq 0$ are forbidden by the gauge symmetry. The stability of the “dark baryon” does not require ad hoc discrete symmetries (such as $Z_2$), but arises from the gauge invariance itself. This feature generalizes: if $X$ is the lightest particle with non-vanishing $B$, then any decay $X \rightarrow \text{(SM states)}$ is forbidden unless $\Delta B=0$, which cannot be satisfied for SM decays due to the quantized baryon charges of SM quarks (e.g., $B=1/3$) (Dulaney et al., 2010).

Additionally, because $B$ and $L$ are both gauged and only spontaneously broken at the weak scale, no dangerous renormalizable operators arise that could induce proton or dark baryon decay. The protection extends beyond renormalizable couplings, as higher-dimensional effective operators are automatically suppressed or forbidden by $U(1)_B$ invariance.

2. Dark Baryon Annihilation: Mediators and Phenomenology

The dominant annihilation mechanisms for a dark baryon $X$ are determined by the available mediators coupling it to SM fields:

A. Leptophobic Gauge Boson ($Z_B$) Mediation

With $U(1)_B$ gauged, a new vector boson $Z_B$ couples to all particles with nonzero baryon number but not to leptons. Dark matter annihilation proceeds via

$XX^\dagger \to Z_B^* \to q\bar{q}$

with cross section (in the non-relativistic limit): $$\sigma_{Z_B} v = \frac{2g_B^4}{81\pi} \frac{M_X^2}{M_{Z_B}^4} \frac{v^2}{\left[(1-4M_X^2/M_{Z_B}^2)^2 + (\Gamma_{Z_B}^2/M_{Z_B}^2)\right]} \ \text{[phase-space factors]}$$ Here, $g_B$ is the $U(1)_B$ gauge coupling, $M_{Z_B}$ the gauge boson mass, $M_X$ the dark baryon mass, and $v$ the relative velocity.

Dark matter–nucleon elastic scattering, relevant for direct detection, is set by

$$\sigma_{\mathrm{SI}}^b = \frac{4g_B^4}{9\pi} \frac{\mu^2}{M_{Z_B}^4}$$

with reduced mass $\mu$. For $M_{Z_B}\lesssim 1~\mathrm{TeV}$, a robust lower bound on the cross section emerges, $$\sigma_{\mathrm{SI}}^b \gtrsim 5\times 10^{-46}\,\mathrm{cm}^2$$ (Dulaney et al., 2010).

B. Higgs Portal Annihilation

Alternatively, $X$ may annihilate through an off-shell SM Higgs boson ($H$),

$XX^\dagger \to H^* \to \text{SM}$

with cross section

$$\sigma_H v \sim \frac{\lambda_1^2}{4\pi M_H^2} \frac{\text{(mass, phase-space factors)}}{[1-(4M_X^2/M_H^2)]^2 + (\Gamma_H^2/M_H^2)}$$

where $\lambda_1$ is the $X$–Higgs coupling. Constraints from relic abundance and direct detection (due to nuclear recoil signals via Higgs exchange) tightly restrict $\lambda_1$ and $M_X$ (e.g., for $M_H=120$ GeV, $M_X\sim 51$–$63$ GeV).

The combination of annihilation and scattering channels fixes the viable parameter space in terms of $M_X$, $M_{Z_B}$ (or $M_H$), and appropriate couplings, enforced by relic abundance and direct detection constraints.

3. Interplay Between Baryon Asymmetry and Dark Matter Density

These models unify baryogenesis and dark matter genesis in a common symmetry framework. The dark baryon and baryon asymmetries are not independent: both arise from the same underlying gauge structure and early Universe dynamics.

The chemical potential analysis yields the baryon and dark baryon number densities: $$\frac{n_X - n_{\overline{X}}}{s} = \frac{15}{2\pi^2 g_* T}(7\mu_X - 6\mu_{u_L})$$ and

$$\frac{n_+ - n_-}{s} = \frac{15g}{4\pi^2 g_*} \frac{\mu}{T}$$

These relations (and variants with scalar asymmetries, e.g., $\Delta S_B, \Delta S'_L$) encode the transfer and balancing of asymmetries between sectors (Dulaney et al., 2010).

Satisfying the measured ratio $\Omega_{DM}/\Omega_B \simeq 5$ requires fine-tuning of the primordial asymmetries: $$M_X \leq M_p \frac{\Omega_{DM}}{\Omega_B} \frac{1971\Delta S_B + 66\Delta S'_L}{|3516\Delta S_B - 99\Delta S'_L|}$$ Tension arises since generating the required baryon asymmetry while also accommodating the correct dark matter abundance may necessitate modest fine-tuning of these primordial scalar asymmetries.

4. Anomaly Cancellation and Theoretical Consistency

Gauging $U(1)_B$ and $U(1)_L$ imposes strict anomaly cancellation conditions. In specific ultraviolet (UV) completions, this can require augmenting the particle content (e.g., introducing a fourth generation or new vectorlike fermions) to cancel $[U(1)_B]^3$ or mixed gauge anomalies.

Anomalies can affect early Universe dynamics and chemical equilibrium relations, ultimately constraining allowed charge assignments and possible new physics content in such models.

5. Model Predictions and Experimental Signatures

Because stability is guaranteed at the renormalizable level, a light ($\sim$Electroweak-scale) leptophobic $Z_B$ is a typical feature. Direct detection experiments can probe the lower bound on the cross section for $Z_B$-mediated scattering. For the Higgs portal, only a narrow range of dark baryon masses is allowed, given nuclear recoil constraints.

Collider experiments may test light $Z_B$ scenarios, and indirect detection bounds apply to the annihilation and possible decay products of dark baryons. In models with scalar or vector-portal couplings, signatures may include invisible Higgs decays or new missing energy channels at high-$p_T$ colliders.

Furthermore, the nontrivial dependence of viable mass ranges and couplings on primordial scalar asymmetries, combined with potential experimental probes via direct, indirect, and collider searches, renders these models highly predictive and falsifiable.

6. Broader Implications and Challenges

Unifying dark matter stability and the baryon asymmetry via local baryon number symmetry ties the properties of the relic dark baryon sector to the visible sector. The trade-off is a more constrained parameter space and a direct link between dark sector physics and the measured baryon abundance.

The necessity of mild fine-tuning in the scalar charge asymmetries and the connection between mediator mass scales and direct detection sensitivity lead to a concrete, testable class of models but also to inherent model-building challenges, especially as experimental limits improve.

Ultimately, this framework exemplifies how dark baryons—protected by local symmetries—constitute a natural, technically robust solution for both dark matter and matter-antimatter asymmetry, but only within well-specified regions of theory and parameter space that are increasingly accessible to experiment (Dulaney et al., 2010).