Reconstructing Dark Matter Mass and Discriminating Standard and Non-Standard WIMP-Nucleus Interactions with Paleo-Detectors

This paper investigates the ability of paleo-detectors to reconstruct dark matter (DM) mass and to discriminate between standard and non-standard WIMP–nucleus interactions, using the framework of Non-Relativistic Effective Field Theory (NREFT). The study builds on previous sensitivity projections and extends them to detailed parameter reconstruction and hypothesis discrimination.

Mass Reconstruction:

The paper demonstrates that paleo-detectors can reconstruct WIMP masses in a variety of scenarios. For elastic scattering, in the high-resolution (HR) scenario, gypsum paleo-detectors can reconstruct DM masses in the range 1–10 GeV/c2 with relative uncertainties as small as Δmχ/Mχ ∼ 10−1, a regime challenging for conventional experiments. In the high-exposure (HE) scenario, for operators such as O1s and O11s, paleo-detectors are projected to reconstruct DM masses in the range 40–1000 GeV/c2 with relative uncertainties of order unity. The paper states: "gypsum paleo-detectors are projected to reconstruct the DM mass with a relative uncertainty as small as ∆mχ /Mχ ∼ 10−2 (light blue regions) for Mχ ≃ 1–10 GeV/c2, a mass range that is difficult to probe with conventional direct-detection experiments. In the HE scenario, mass reconstruction remains possible over the range Mχ ≃ 40–1000 GeV/c2 with a relative uncertainty ∆mχ /Mχ ≳ 1 for the operators O1s and O11s." For inelastic scattering with a mass splitting δm = 50 keV/c2, gypsum paleo-detectors are projected to reconstruct DM masses between 30 and 400 GeV/c2 with relative uncertainties down to Δmχ/Mχ ∼ 10−2. The paper notes that at very large DM masses, the reconstructed mass intervals broaden substantially because the recoil spectrum becomes only weakly dependent on the DM mass through the reduced WIMP–nucleus mass.

Operator Discrimination:

The paper assesses the ability of paleo-detectors to reject the standard spin-independent (SI) O1s hypothesis when the true signal is generated by non-standard operators. Using a profile-likelihood-ratio approach, the authors find that discrimination power is strongly correlated with qualitative differences in track-length spectra. Specifically, operators such as O15s and O3s, which generate spectra that differ significantly from the standard SI interaction, can lead to rejection of the standard SI hypothesis at confidence levels exceeding 5σ for achievable exposures and DM masses mχ ≳ 100 GeV/c2. In contrast, operators such as O8s, with spectra nearly indistinguishable from the standard SI case, cannot be discriminated even with large exposures. The paper states: "The standard SI hypothesis can be rejected with the highest significance for scattering via O15s and O3s, whereas it cannot be rejected in the LR scenario for light DM (mχ = 5 GeV/c2) for any interaction operator. For signals generated by O8s, the SI hypothesis cannot be rejected at either DM mass." The discrimination power decreases significantly for mχ ≲ 30 GeV/c2 in the low-resolution (LR) scenario, and for inelastic scattering, the confidence levels decrease with increasing mass splitting δm.

Methodology:

The analysis uses a profile-likelihood-ratio approach with Asimov data sets, assuming Poisson statistics for the binned track-length spectra. The track-length spectrum serves as a proxy for recoil energy, and the analysis includes backgrounds from neutrinos, radiogenic neutrons, and 238U → 234Th + α recoils. Two benchmark read-out scenarios are considered: high-resolution (HR, σx = 1 nm, M = 10 mg) and high-exposure (HE, σx = 15 nm, M = 100 g). The paper focuses on gypsum as a representative target mineral for spin-independent interactions and halite for spin-dependent interactions, with results for halite presented in the Appendix.

Conclusions:

The paper concludes that paleo-detectors provide a powerful and complementary probe of DM interactions, enabling both precise DM mass reconstruction and statistically significant discrimination between competing interaction hypotheses. The authors note that "paleo-detectors could reconstruct WIMP masses up to 1 TeV/c2 for hypothetical signals within their accessible parameter space, extending the mass range over which reconstruction is possible by up to a factor of ∼ 2 compared with analogous studies of conventional direct-detection experiments. They also highlight that at WIMP masses ≳ 10 GeV/c2, we project that canonical NREFT interactions can be excluded by paleo-detectors in the cases of nearly all non-canonical interactions without measurement of nuclear recoil direction, which conventional experiments typically require in addition to measurement of nuclear recoil energy."

Improvements to AI Systems:

1. Physics-Aware Bayesian Inference for Mass Reconstruction

• Implement a hierarchical Bayesian model that incorporates the NREFT operator-specific recoil spectra and track-length distributions as priors.

• Use Markov Chain Monte Carlo (MCMC) or nested sampling to jointly estimate DM mass, interaction operator, and mass splitting (δm) from binned track-length data, including systematic uncertainties from mineral composition and read-out resolution.

• Capability: The improved AI can automatically produce posterior distributions for DM mass with quantified uncertainties (e.g., Δmχ/Mχ 10−2) and flag when mass reconstruction becomes degenerate (e.g., >1 TeV/c2), enabling robust parameter extraction from future paleo-detector data.

2. Hypothesis Testing with Profile-Likelihood-Ratio Neural Networks

• Train a neural network to approximate the profile-likelihood-ratio test statistic directly from simulated track-length spectra, replacing the need for manual binning and analytic likelihoods.

• Incorporate a learnable feature extractor that identifies spectral shape differences (e.g., O15s vs. O1s) and outputs confidence levels for rejecting the standard SI hypothesis.

• Capability: The AI can rapidly discriminate between standard and non-standard WIMP–nucleus interactions (e.g., O3s, O15s) at >5σ significance, even for low-exposure scenarios, and automatically identify operators (like O8s) that are fundamentally indistinguishable, preventing false claims.

3. Multi-Mineral and Multi-Scenario Transfer Learning

• Pre-train a transformer-based model on simulated data from gypsum (HR/HE) and halite (spin-dependent) detectors, then fine-tune on new mineral compositions or read-out resolutions.

• Use domain adaptation to handle variations in track-length resolution (σx = 1 nm vs. 15 nm) and exposure (10 mg vs. 100 g).

• Capability: The AI can generalize to untested detector configurations, predicting mass reconstruction accuracy and operator discrimination power without retraining from scratch, accelerating experimental design.

4. Background-Aware Anomaly Detection

• Develop a deep generative model (e.g., normalizing flow) trained on background-only track-length spectra (neutrinos, radiogenic neutrons, 238U recoils) to learn the null distribution.

• Use the model’s likelihood ratio to flag any signal-like excess, with explicit uncertainty propagation from background rate variations.

• Capability: The AI can detect faint DM signals even when background contamination is poorly constrained, and quantify the minimum exposure needed to achieve 3σ or 5σ discovery for a given operator and mass.

5. Automated Experimental Design Optimization

• Implement a reinforcement learning agent that proposes optimal detector parameters (mineral type, mass, resolution, exposure time) to maximize a utility function combining mass reconstruction precision and operator discrimination power.

• Simulate the full paleo-detector pipeline (track formation, read-out, analysis) as a differentiable surrogate model.

• Capability: The AI can recommend the most cost-effective detector configuration for probing a specific DM mass range (e.g., 1–10 GeV/c2) or for distinguishing O1s from O15s, reducing trial-and-error in experimental planning.

6. Uncertainty-Aware Spectral Classification

• Build an ensemble of convolutional neural networks (CNNs) that classify track-length spectra into NREFT operator classes, with Monte Carlo dropout to estimate epistemic uncertainty.

• Train on simulated spectra with varying DM masses, δm, and backgrounds, and output a probability vector over operators.

• Capability: The AI can provide a probabilistic operator assignment (e.g., 85% O3s, 10% O1s, 5% O8s) for a given dataset, with confidence intervals that reflect both statistical and systematic uncertainties, aiding in theoretical model selection.

7. Cross-Experiment Synergy Prediction

• Create a meta-learner that combines paleo-detector projections (from this paper) with results from conventional direct-detection experiments (e.g., XENON, LZ) to predict joint constraints on DM mass and interaction operators.

• Use Gaussian process regression to interpolate over mass–operator–δm space.

• Capability: The AI can identify complementary regions where paleo-detectors uniquely constrain non-standard interactions (e.g., O11s at high mass) and suggest combined analysis strategies to break degeneracies that single experiments cannot resolve.

What the Improved AI System Can Do:

• Automatically analyze raw track-length data from paleo-detectors to reconstruct DM mass with high precision (down to 10−2 relative uncertainty) and identify the underlying interaction operator with >5σ confidence, even in low-resolution or low-exposure scenarios.

• Optimize future detector designs by simulating thousands of configurations and recommending the best mineral, mass, and resolution for specific physics goals.

• Provide real-time hypothesis testing and background rejection, enabling rapid decision-making during data collection.

• Integrate results across multiple experiments to produce a unified, model-agnostic map of DM parameter space, highlighting where paleo-detectors offer unique advantages over conventional methods.

Paleo-detectors record and retain crystal damage in ancient minerals from nuclear recoils induced by dark matter scattering over geological timescales. Previous studies have shown that paleo-detectors can provide sensitivity to a variety of dark matter (DM) scenarios which is complementary to conventional direct-detection experiments. In this paper, we complete the first detailed study of how well paleo-detectors can reconstruct DM parameters or distinguish between different types of DM interactions with nuclei in the presence of a DM signal, considering both elastic and inelastic DM-nucleus scattering. For representative nuclear recoil track read-out scenarios, we demonstrate that weakly interacting massive particle (WIMP) DM masses can be reconstructed for a variety of Non-Relativistic Effective Field Theory (NREFT) interactions between WIMPs and nuclei. In particular, paleo-detectors are projected to be capable of reconstructing WIMP masses 10 GeV, a regime that is challenging for conventional direct-detection experiments; further, we find that paleo-detectors could reconstruct WIMP masses up to 1 TeV for hypothetical signals within their accessible parameter space, extending the mass range over which reconstruction is possible by up to a factor of about 2 compared with analogous studies of conventional direct-detection experiments. In addition, we demonstrate that paleo-detectors could discriminate between canonical spin-independent or spin-dependent NREFT interactions and non-canonical interactions which can depend on the relative velocity or momentum transferred between the WIMP and nucleus. Specifically, at WIMP masses 10 GeV, we project that canonical NREFT interactions can be excluded by paleo-detectors in the cases of nearly all non-canonical interactions without measurement of nuclear recoil direction, which conventional experiments typically require.