Dark Matter Mediator Models

• Dark matter mediators are theoretical particles that dynamically connect the Standard Model with dark matter via non-gravitational interactions.
• Different mediator types—scalar, vector, and tensor—offer unique interaction channels that lead to diverse signatures in collider, direct, and indirect detection experiments.
• Experimental searches across colliders, direct detection, and astrophysical observations work in synergy to constrain mediator parameters and refine dark matter models.

A dark matter mediator is a hypothetical particle or resonance that provides a dynamical bridge between the Standard Model (SM) and the dark matter (DM) sector, enabling non-gravitational interactions between visible and dark components. Unlike the simple contact operator approach, where the coupling is parameterized as a local effective vertex, mediators introduce propagating degrees of freedom whose on-shell production, mass, quantum numbers, and couplings crucially shape the phenomenology of DM searches across colliders, direct/indirect detection, and cosmology.

1. Fundamental Roles and Model Classification

Mediators are inserted to provide explicit, renormalizable (or simplified) interactions enabling experimental access to dark matter. Their nature is characterized by:

• Spin: Scalar (spin-0), vector (spin-1), and tensor (spin-2) mediators are all actively studied. Each imposes a unique structure on the resulting DM-SM interaction.
• Gauge Charges: Mediators can be SM singlets, charged under SM gauge groups, or even share charges with quarks/leptons (e.g., diquark portals).
• Interaction Channels: Depending on the model, mediators may couple in t-channel (e.g., $$\mathcal{L}_\chi = \lambda\, \bar{\chi}_L q_R\, \phi^* + \mathrm{h.c.}$$ (An et al., 2013)) or s-channel (e.g., gravity-mediated resonances (Lee et al., 2014)) with both visible and dark matter fields in initial and/or final states.

The diversity of mediators yields models ranging from the classic "dark photon," $Z'$ boson, and axion-like particles (ALPs), to gravitons in extra dimensions, scalar doublet extensions, and more exotic structures (e.g., derivative portals (Zeng, 2022), scalar dilepton mediators (Kao et al., 2020), or diquark portal pairs (Carpenter et al., 2023)).

2. Collider Signatures and Parameter Sensitivity

The presence of an accessible mediator alters LHC search strategies and their interpretation. For example, a $t$-channel mediator (scalar $\phi$) introduces new subprocesses such as $qg\to q\chi\chi$ with prompt mediator decay $\phi\to q+\chi$ (An et al., 2013). This process produces characteristic monojet$+\not{E}_T$ and di-jet$+\not{E}_T$ final states. When the mediator mass $M_\phi$ is low, on-shell production enhances the signal and affects both rate and kinematic distributions, fundamentally differing from contact-operator predictions.

Complementary Channels:

• Monojet$+\not{E}_T$: Sensitive to DM pair production via initial-state radiation and to mediator production and decay for suitable masses.
• Mediator Pair Production: In $t$-channel models, QCD pair production can generate di-jet$+\not{E}_T$ signatures; for $s$-channel mediators (e.g., spin-2), resonance searches in dijet, diphoton, and dilepton channels provide stringent constraints (Kraml et al., 2017).

Parameter Dependence:

Collider sensitivity correlates with DM mass $M_\chi$, mediator mass $M_\phi$ (or $m_Y$, $m_G$ for spin-2), and coupling $\lambda$. The reach in $\lambda$ weakens with increasing $M_\chi$, especially for Dirac DM, due to phase space constraints. Majorana DM introduces characteristic mass scaling and transition between direct detection and collider limits (An et al., 2013).

3. Complementarity of Experimental Probes

The addition of a propagating mediator brings marked synergy between different experimental searches:

• Collider Searches: Can produce the mediator directly, probe its decays, and constrain coupling-mass combinations not accessible to direct detection.
• Direct Detection: If the mediator is off-shell, low-energy recoil experiments probe effective operators induced by integrating out the mediator. For example, the $t$-channel mediator, once integrated out, yields an operator

$$\mathcal{O}_1 = \frac{\lambda^2}{M_\phi^2}\, (\bar{\chi}_L q_R)(\bar{q}_R \chi_L)$$

which can be Fierz-transformed for direct detection calculations (An et al., 2013).

The nature of the DM (Dirac vs. Majorana) dictates the leading interactions – spin-independent (SI) scattering dominates for Dirac fermions, while Majorana DM typically yields spin-dependent (SD) signatures. Spin-2 mediators generate novel operator structures matched to nucleon gravitational form factors, fundamentally distinct from scalar or vector mediation (Carrillo-Monteverde et al., 2018).

• Relic Abundance: Mediator properties control DM annihilation rates during freeze-out. In several models, the allowed parameter space is sharply reduced by overlap with collider/direct detection null results, especially for Dirac DM (effectively ruled out under thermal relic assumptions in certain $t$-channel scenarios), whereas Majorana DM can remain viable for $M_\chi \gtrsim 100$\,GeV (An et al., 2013).
• Indirect Detection: Mediator-induced DM annihilation can yield high-energy gamma or cosmic ray signals. In gravity-mediated models, e.g., KK graviton exchange, vector DM can produce s-wave annihilation to photons with observable gamma-ray lines, constrained by Fermi-LAT and H.E.S.S. (Lee et al., 2014).

4. Impact on Theoretical Interpretation and Discovery Potential

Mediator-rich models enable the following:

• Discriminating Dark Matter Nature: Different SM and DM representations for the mediator can help distinguish Dirac/Majorana DM, identify the spin and coupling Lorentz structure, or pinpoint the dark charge assignments.
• Discovery of Mediator Implies New Physics: If an observed mediator (e.g., via monojet signals at the LHC) cannot explain the full relic DM abundance within the framework (insufficient cross-section for thermal freeze-out), additional particles or mechanisms must be invoked, motivating broader "dark sector" searches (An et al., 2013).
• Rich Parameter Space for Phenomenology: Light mediators (sub-GeV – GeV mass) with feeble couplings yield non-standard signatures, e.g., novel direct detection kinematics (inelastic $2\rightarrow3$ channels with light scalars (Curtin et al., 2013), "double-dark" portals (Curtin et al., 2014)), inelastic recoil spectra, or self-interactions consistent with astrophysical anomalies.

5. Key Formulas and Operator Matching

Theoretical predictions and experimental limits are often expressed through matched operator coefficients and cross-sections. Examples from $t$-channel mediation (An et al., 2013):

• Effective operator (after integrating out heavy mediator):

$$\mathcal{O}_1 = \frac{\lambda^2}{2 M_\phi^2}(\bar{\chi}_L \gamma^\mu \chi_L)(\bar{q}_R \gamma_\mu q_R)$$

• Spin-independent cross-section for Dirac DM:

$$\sigma_{\rm SI}^{(\rm D1)} \propto \frac{\lambda^4 \mu_{\chi N}^2}{(M_\phi^2-M_\chi^2)^2}$$

with $\mu_{\chi N}$ the DM-nucleon reduced mass.

• Spin-dependent enhancement for Majorana DM:

$$\sigma_{\rm SD}^{(\rm M1)} = 4 \sigma_{\rm SD}^{(\rm D1)}$$

Collider-level predictions are computed using event generators (MadGraph, PYTHIA, CalcHEP), with contributions from both QCD and DM-exchange diagrams. For spin-2 mediators the amplitude structure reflects energy-momentum tensor couplings, leading to unique gravitational operator matching (Carrillo-Monteverde et al., 2018).

6. Parameter Space and Future Directions

Models with explicit mediators are strongly constrained in typical regions of parameter space:

DM Type	Dominant Limit	Viable Mass Range	Relic Abundance?
Dirac (t-channel)	Collider + DD	Typically ruled out	No overlap
Majorana	Collider/DD	$M_\chi \gtrsim 100$ GeV	Yes, with limited phase space
Light scalars	Astrophysics/LHC	Model-dependent	Yes, if DD, astro, and cosmo allow

Assuming non-thermal production or additional annihilation channels may open broader regions of parameter space and requires further theoretical and experimental investigation, especially in the presence of observed mediator signatures not matching the thermal DM relic density.

A key direction is the systematic exploration of mediator parameter space using multi-channel data, improved operator matching, and the synergy of future direct, indirect, and collider experiments. The mediator paradigm elevates the complexity of DM–SM interactions but grants tangible model targets for both discovery and characterization.

7. Conclusion

Dark matter mediators, as propagating fields connecting the SM and DM, are essential components for contemporary dark matter model building and experimental searches. Their mass, quantum numbers, and couplings set the scale for most collider, direct, and indirect detection constraints. By going beyond the contact operator paradigm, mediator models (including $t$- and $s$-channel, spin-0, spin-1, spin-2 mediators) enable a more realistic and nuanced interpretation of collider signatures, direct detection, astrophysical data, and cosmological relic abundance, while sharpening the requirements for model viability and discovery prospects (An et al., 2013, Curtin et al., 2013, Lee et al., 2014, Curtin et al., 2014, Kraml et al., 2017, Carrillo-Monteverde et al., 2018).