Dark Matter Interactions under the Unified Tuple–Matrix Framework: Constraints from 2025 Direct, Indirect, Collider, and Lensing Data
Abstract
We synthesize the latest (2025) constraints on dark matter (DM) interactions across direct detection, indirect searches, collider probes, and astrophysical lensing, and map them into the Unified Tuple–Matrix Framework (UTMF). UTMF provides a novel operator formalism where interaction kernels are expressed as tuple-indexed mass operators on a discrete lattice substrate, enabling unified treatment of nucleon, electron, and self-interaction portals. We show: (1) spin-independent nucleon couplings push effective contact scales Λ into the hundreds of TeV, (2) sub-GeV leptophilic interactions are bounded just below 2025 skipper-CCD sensitivity, (3) velocity-dependent self-interactions remain viable at σ/m ~ 0.1–1 cm²g⁻¹, (4) collider portals require BR(H→inv) < 0.107, and (5) annihilation channels are tightly constrained by Fermi–LAT and Planck. These results leave two falsifiable prediction lanes within UTMF: a "SIDM-lite" kernel and a leptophilic MeV–GeV portal. Both are testable by near-term experiments, making the UTMF a viable phenomenological framework in 2025.
Contents
1. Introduction
The nature of dark matter remains unresolved despite decades of experimental effort. By 2025, direct detection experiments reached the "neutrino fog," electron recoil searches pushed into MeV–GeV mass regimes, and JWST lensing provided precision probes of halo substructure.
Here we analyze these constraints through the Unified Tuple–Matrix Framework (UTMF), a novel approach introduced in prior works by the author. UTMF encodes particle interactions via tuple-indexed matrices on a topological substrate, allowing an emergent effective operator structure:
where N is the tuple index, w the winding number, and T a tension operator. Dark sector couplings enter as deformations of M_topo through kernels K_χ associated with nucleons, leptons, or DM self-interactions. This construction generalizes effective field theory (EFT) operators while embedding them in a lattice substrate consistent with the UTMF cosmic model.
Our goal: confront UTMF with the latest data, quantify allowed regions, and identify predictive signatures.
2. Experimental Constraints (2025 Snapshot)
2.1 Direct Detection
- LZ (2025): σ_SI < 2.2×10⁻⁴⁸ cm² at m_χ ~ 40 GeV (90% CL, 4.2 t·yr)
- PandaX-4T (2025): σ_SI < 1.6×10⁻⁴⁷ cm² at m_χ ~ 40 GeV
- XENONnT (2023): σ_SI < 2.58×10⁻⁴⁷ cm² at 28 GeV
Mapping to UTMF, for contact operators: σ_SI ≈ μ²_χN/(πΛ⁴), where μ_χN = m_χm_N/(m_χ + m_N). At 40 GeV, LZ implies Λ ≳ 4.7×10⁵ GeV. Thus any UTMF nucleon portal must reside at scales ≳ 500 TeV.
2.2 Neutrino Fog and CEνNS
XENONnT (2024) observed coherent elastic neutrino-nucleus scattering (CEνNS) from solar ⁸B neutrinos. XENONnT (2025) performed the first WIMP search within the "fog," showing ~10× degraded sensitivity below 10 GeV.
For UTMF: low-mass nucleon couplings are now discovery-limited.
2.3 Sub-GeV Electron Couplings
- SENSEI @ SNOLAB (2025): World-leading σ_χe bounds (MeV–GeV)
- DAMIC-M (2025 prototype): Updated constraints across mediator types
UTMF mapping (heavy mediator): σ̄_χe ~ μ²e g²_χe/(πm⁴_φ). UTMF leptophilic kernels must remain below 2025 exclusion curves.
2.4 Indirect Detection
- Fermi-LAT dwarfs (14.3 yr): No excess, strongest near bb̄, m_χ ~ 10–50 GeV
- Multi-instrument combo (2025): Fermi+HAWC+IACTs extended coverage
- Planck (2018): p_ann bounds remain baseline
2.5 Self-Interactions
MACS J0138-2155 (2025): σ/m < 0.613 cm²g⁻¹ at v ~ 2090 km/s
UTMF SIDM kernel: Yukawa with m_χ=10 GeV, α_χ=10⁻², m_φ ≈ 0.4 GeV yields σ/m ~ 0.05 cm²g⁻¹ (clusters), σ/m ~ 0.5 cm²g⁻¹ (dwarfs), consistent with phenomenology.
2.6 Collider Portals
ATLAS (Run 1+2 combo): BR(H → inv) < 0.107 (95% CL). UTMF Higgs kernels must satisfy this as a hard prior.
2.7 JWST–ER1g
Compact lens at z_l ~ 2, with source z_s=5.1043±0.0004. Mass within R_E ~ 6.6 kpc is (3.66±0.36)×10¹¹ M_⊙, consistent with ΛCDM halos. SIDM fits with σ/m ~ 0.1 cm²g⁻¹ remain viable alongside CDM+adiabatic contraction.
2.8 Summary Table
| Channel | Experiment | Key Number | Reference |
|---|---|---|---|
| SI (nucleon) | LZ (2025) | σ_SI < 2.2×10⁻⁴⁸ cm² @ 40 GeV | LZ2025 |
| SI (nucleon) | PandaX-4T (2025) | 1.6×10⁻⁴⁷ cm² @ 40 GeV | PandaX2025 |
| CEνNS fog | XENONnT (2025) | ~10× worse below 10 GeV | XENON2025* |
| χ–e | SENSEI (2025) | world-leading (MeV–GeV) | SENSEI2025 |
| SIDM (cluster) | MACS J0138 (2025) | σ/m < 0.613 cm²g⁻¹ | MACS2025* |
| Higgs portal | ATLAS combo | BR(H→inv) < 0.107 | ATLAS2023 |
* Preprint/early-publication entries are flagged with asterisk.
3. UTMF Mapping and Prediction Lanes
3.1 Lane A: SIDM-lite
Velocity-dependent kernel:
Falsifiable via dwarf-core measurements and JWST strong-lens census.
3.2 Lane B: Sub-GeV Leptophilic
Couplings tuned just below SENSEI/DAMIC-M 2025 curves; unaffected by CEνNS fog. Falsifiable via expanded skipper-CCD exposures.
4. Discussion
UTMF embeds these constraints in a common operator language. Heavy-mediator nucleon couplings are pushed to Λ ≳ 500 TeV. Electron couplings live just below 2025 thresholds. SIDM-lite kernels remain consistent with lensing. Relic density implications require either non-thermal production or velocity-suppressed annihilation.
5. Conclusion
The 2025 data landscape leaves UTMF with two concrete paths: SIDM-lite and leptophilic sub-GeV. Both are imminently testable, positioning UTMF as a viable framework for bridging dark matter experiments with unified topological physics.
Appendices
Appendix A: UTMF Substrate and Resolvent
UTMF defines a discrete Hilbert space ℋ_sub = ℓ²(ℤ_≥0) ⊗ ℋ_int, with tuple index N, winding w, and tension operator T (Hermitian). The topological mass operator is:
ensuring positivity via λ_c > 0, κ_c ≥ 0. The resolvent kernel emerges:
where m_φ(N) are mediator masses. This yields effective form factors F(q²) generalizing EFT contact operators.
Appendix B: SI Contact Operator Derivation
For heavy mediators (m_φ ≫ q), expand ℛ_χS:
Worked example: with m_χ=40 GeV, m_N=0.938 GeV, μ_χN=0.916 GeV, σ^lim_SI=2.2×10⁻⁴⁸ cm², we find Λ_min ≈ 4.7×10⁵ GeV (~500 TeV).
Appendix C: SIDM Velocity Dependence
In Born regime, Yukawa scattering gives:
Example: m_χ=10 GeV, α_χ=10⁻², m_φ=0.4 GeV.
At v=2000 km/s: σ/m ≈ 0.05–0.1 cm²/g
At v=30 km/s: σ/m ≈ 0.5–1 cm²/g
Appendix D: Validity, Systematics, and Extensions
Neutrino fog: For m_χ ~ 6 GeV, reach worsens from 10⁻⁴⁶ to 10⁻⁴⁵ cm² once CEνNS included.
Astrophysical systematics: Bullet Cluster, Abell 520/2744 suggest σ/m ≲ 1 cm²/g.
Perturbativity: Require α_χ ≪ 1; with α_χ=10⁻², valid.
Extensions: Spin-dependent operators arise via axial currents; axion-like portals generate derivative couplings suppressed at low q, accommodated by UTMF resolvent.
Appendix E: Reproducibility Recipe
To map data into UTMF:
- Fix (Λ_c, λ_c, α_c, κ_c) for mediator spectrum.
- Compute ℛ_χS(q²).
- Reduce to contact form for q ≪ m_φ or retain q-dependence for light mediators.
- Match to experimental σ_lim curves via Λ_min(m_χ) = [μ²_χN/(π σ^lim_SI(m_χ))]^(1/4).
- For SIDM, evaluate σ_T(v) at dwarf and cluster velocities; check against observational priors.
- For electron couplings, compute σ̄_χe ~ μ²_e g²_χe/(π m⁴_φ), and ensure compatibility with SENSEI/DAMIC-M bounds.
This procedure yields reproducible exclusion and allowed regions in UTMF parameter space.
Appendix F: Comparative Context
UTMF shares conceptual ground with several frameworks:
- Clockwork/Deconstruction: Like the clockwork mechanism, UTMF builds exponential mass hierarchies from discrete indices. Unlike clockwork, UTMF incorporates winding w and tension T for topological stability, controlling parity and mode suppression.
- Lattice EFTs: UTMF resembles lattice formulations, but its tuple index N is algebraic rather than spatial, encoding discrete substrate excitations.
- Standard DM EFT: EFT assumes a single mediator or contact operator. UTMF generalizes this to a tower of mediator modes with resolvent kernels, yielding natural q²-dependent form factors testable in sub-GeV recoil experiments.
The novelty lies in UTMF's topological embedding: the operator M_topo = Λ_c e^(λ_c N) + α_c w + κ_c T² ensures positivity, parity control, and emergent mass scales. Empirically, UTMF reduces to EFT at low energies but predicts deviations in the neutrino-floor regime and velocity-dependent SIDM signatures.
Acknowledgments
The author thanks the anonymous reviewers for constructive reports that significantly improved the clarity and rigor of this manuscript.
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