Probing Freeze-In Dark Matter via a Spin-2 Portal at the LHC with Vector Boson Fusion and Machine Learning

Abstract: The persistent absence of signals in traditional dark matter searches has intensified interest in scenarios beyond the canonical weakly interacting massive particle paradigm. In this work, we investigate the collider phenomenology of feebly interacting dark matter produced via the freeze-in mechanism through a spin-2 portal. We consider a framework in which a massive graviton-like mediator couples minimally and universally to the energy--momentum tensor of both the Standard Model (SM) and the dark sector. Such interactions arise naturally in extra-dimensional constructions and effective theories of gravity, providing a theoretically well-motivated and predictive setup. We systematically connect early-Universe cosmology with collider observables by identifying regions of parameter space consistent with freeze-in conditions and the observed dark matter relic abundance, and examining their testability at the Large Hadron Collider (LHC). Focusing on bosonic fusion production channels, which are particularly sensitive to spin-2 interactions, we analyze invisible mediator decay signatures and assess current and projected experimental sensitivities. To enhance sensitivity in this challenging regime of feeble couplings, we develop a search strategy based on machine-learning algorithms. Our results demonstrate that collider searches can probe substantial regions of the cosmologically viable freeze-in parameter space, highlighting the high-luminosity LHC as a powerful laboratory for feebly interacting dark sectors. This study establishes a concrete and complementary pathway to test freeze-in dark matter scenarios through spin-2 portals, thereby bridging gravitationally motivated new physics, cosmology, and high-energy collider experiments.

• The paper introduces a spin-2 mediated dark matter model where only photons couple to the mediator, enabling freeze-in production via photon-fusion.
• The study employs vector boson fusion and boosted decision trees to distinguish signal from background, achieving 95% CL limits for mG up to 1 TeV at HL-LHC.
• The analysis connects collider results with cosmological constraints, highlighting the complementarity between collider searches and non-collider dark matter probes.

Probing Freeze-In Dark Matter via a Spin-2 Portal at the LHC with Vector Boson Fusion and Machine Learning

Theoretical Framework: Spin-2 Mediators and Freeze-In Production

The paper systematically investigates a dark matter (DM) model in which the Standard Model (SM) communicates with a hidden scalar DM sector exclusively through a massive spin-2 mediator, $G_{\mu\nu}$. This mediator couples minimally via the energy-momentum tensor, providing a theoretically consistent and UV-motivated framework. The coupling structure is parametrized via two scales: $\Lambda_\gamma$ (coupling to photons) and $\Lambda_\chi$ (coupling to DM), with the possibility of asymmetric interactions between sectors.

A salient feature of this model is the "photon-only portal": $G_{\mu\nu}$ couples only to photons in the SM, suppressing standard resonance channels relying on quark or gluon initial states and evading stringent direct detection and astrophysical constraints. The dominant cosmological DM production mechanism is freeze-in via photon-fusion,

$\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$

where the feeble interaction (large $\Lambda_\gamma, \Lambda_\chi$) ensures DM never thermalizes. The relic abundance calculation determines the viable parameter space consistent with cosmological and reheating temperature ($T_R$) constraints, incorporating off-resonant (UV freeze-in) and resonant (on-shell $G$ production) regimes.

Figure 1: Ratio of decay width to spin-2 mediator mass for different $m_\chi$, indicating the relative lifetimes of the mediator as a function of model parameters.

Figure 2: Theoretically allowed parameter space for $\Lambda_\gamma, \Lambda_\chi$ set by freeze-in conditions and relic abundance for several $\Lambda_\gamma$0 values.

Collider Phenomenology: LHC Sensitivity and Experimental Considerations

Given the suppressed couplings and photon-only portal, conventional LHC searches (e.g., diphoton, dijet, dilepton) lack sensitivity to this framework, especially for $\Lambda_\gamma$1 GeV. The work focuses on electroweak production mechanisms—particularly vector boson fusion (VBF), where photon-fusion dominates—yielding a unique LHC signature characterized by missing transverse energy ($\Lambda_\gamma$2) recoiling against two forward jets.

To test this, a Monte Carlo simulation chain is established, incorporating leading-order event generation with MadGraph5_aMC@NLO, detector effects via Delphes, and realistic pileup at HL-LHC conditions. The primary backgrounds are SM processes featuring genuine $\Lambda_\gamma$3 and forward jet activity, notably $\Lambda_\gamma$4jets and diboson production.

Figure 3: Representative Feynman diagrams for SM background $\Lambda_\gamma$5 production.

Figure 4: Signal Feynman diagram for $\Lambda_\gamma$6 via photon-photon fusion producing the spin-2 mediator.

Advanced Analysis: Machine Learning for Signal-Background Separation

Because of the challenging kinematics and low cross sections, the analysis employs a multivariate approach using boosted decision trees (BDTs) built with XGBoost. The BDTs are trained on eight engineered features: $\Lambda_\gamma$7, leading/subleading jet $\Lambda_\gamma$8, $\Lambda_\gamma$9, jet $\Lambda_\chi$0, and $\Lambda_\chi$1, $\Lambda_\chi$2 between jets. This approach leverages subtle, correlated differences between signal and background beyond reach for standard cut-based analyses.

Figure 5: Dijet invariant mass distributions demonstrate the broad VBF signature for signal versus sharply peaked backgrounds.

Figure 6: Missing transverse energy ($\Lambda_\chi$3) distribution for signal and backgrounds highlights the harder spectrum for signal.

Figure 7: Pseudorapidity separation between jets ($\Lambda_\chi$4), showing the pronounced forward jet signature of VBF processes.

Figure 8: Leading jet $\Lambda_\chi$5 distributions, emphasizing the harder spectrum in signal events typical of VBF production.

Feature importance studies confirm $\Lambda_\chi$6, $\Lambda_\chi$7, and $\Lambda_\chi$8 as dominant for discrimination.

Figure 9: Relative importance of input variables in BDT training for $\Lambda_\chi$9 TeV benchmark.

BDT output distributions for benchmark masses indicate strong separation between signal and SM backgrounds and are utilized in a profile likelihood framework—including shape and normalization uncertainties—to derive projected exclusion limits.

Figure 10: BDT classifier output for $G_{\mu\nu}$0 TeV, showing clear separation between signal and background events.

Projected Sensitivity and Implications for Cosmology

The high-luminosity LHC (HL-LHC) projections, assuming 3000 fb$G_{\mu\nu}$1, provide $G_{\mu\nu}$2 CL upper limits on

$G_{\mu\nu}$3

reaching the $G_{\mu\nu}$4 pb level for $G_{\mu\nu}$5 up to 1 TeV. The projected reach covers $G_{\mu\nu}$6 in the $G_{\mu\nu}$7--$G_{\mu\nu}$8 GeV range, intersecting with cosmologically viable regions for low $G_{\mu\nu}$9 ($\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$0 MeV), particularly in the off-resonant freeze-in regime.

Figure 11: Projected $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$1 CL upper limits on inclusive signal cross section as a function of $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$2 at HL-LHC compared to theoretical predictions.

A key result is the HL-LHC's ability to exclude parameter space that yields the observed relic abundance for low $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$3, directly testing a substantial fraction of the FIDM parameter space. For higher $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$4 or in resonant production regimes, required couplings are too feeble for HL-LHC sensitivity.

Comprehensive phase space overlays illustrate the interplay between collider reach and cosmological constraints for $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$5~GeV.

Figure 12: Projected collider constraints on $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$6 for several mediator masses, superimposed on theoretical/ cosmological boundaries for three $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$7 values.

Discussion and Outlook

This study demonstrates an end-to-end framework connecting early universe cosmology with LHC collider phenomenology for feebly interacting spin-2 mediated DM. The synergy between the distinctive VBF signature and machine learning-based analysis bypasses limitations of traditional resonance searches in this suppressed-coupling regime, substantially improving LHC reach.

These results emphasize several important implications:

• Complementarity with non-collider probes: The suppressed couplings render conventional direct detection and astrophysical searches ineffective, making collider VBF searches with ML crucial for testing such FIDM scenarios.
• Parameter space coverage: The HL-LHC can directly probe cosmologically favored regions for low $\gamma\gamma \rightarrow G^* \rightarrow \chi\chi,$8, underscoring the importance of precise theoretical modeling of the early universe reheating history.
• Future directions: Higher energy or luminosity colliders could further extend sensitivity, while refined ML techniques or alternative kinematic variables may optimize reach. Extensions to broader mediator coupling structures, multi-component DM scenarios, or combination with cosmological probes remain open.

Conclusion

This work provides a detailed and quantitative assessment of HL-LHC sensitivity to freeze-in DM produced via a spin-2 portal, leveraging advanced VBF production and BDT-based discrimination. The HL-LHC emerges as a uniquely sensitive probe for cosmologically viable, feebly-coupled spin-2 DM models in regimes inaccessible to alternative detection strategies, setting a new benchmark for experimental tests of gravitationally-motivated dark sector scenarios.