Reconstructing WIMP Properties in Direct Detection Experiments Including Galactic Dark Matter Distribution Uncertainties

We present a new method for determining Weakly Interacting Massive Particle (WIMP) properties in future tonne scale direct detection experiments which accounts for uncertainties in the Milky Way (MW) smooth dark matter distribution. Using synthetic data on the kinematics of MW halo stars matching present samples from the Sloan Digital Sky Survey, complemented by local escape velocity constraints, we demonstrate that the local dark matter density can be constrained to approximately 20% accuracy. For low mass WIMPs, we find that a factor of two error in the assumed local dark matter density leads to a severely biased reconstruction of the WIMP spin-independent cross section that is incorrect at the 15-sigma level. We show that this bias may be overcome by marginalizing over parameters that describe the MW potential, and use this formalism to project the accuracy attainable on WIMP properties in future 1 tonne Xenon detectors. Our method can be readily applied to different detector technologies and extended to more detailed MW halo models.

💡 Research Summary

The paper introduces a comprehensive Bayesian framework that simultaneously treats the astrophysical uncertainties of the Milky Way (MW) dark‑matter halo and the particle‑physics parameters of Weakly Interacting Massive Particles (WIMPs) in future tonne‑scale direct‑detection experiments. Traditional analyses of direct‑detection data usually fix the local dark‑matter density (ρ₀) to a canonical value (≈0.3 GeV cm⁻³) and then infer the WIMP mass (mχ) and spin‑independent cross‑section (σSI). The authors argue that this practice can lead to severe biases because ρ₀ is itself uncertain at the 20–30 % level, depending on the Galactic potential.

To quantify ρ₀, the authors construct a five‑parameter model of the MW gravitational potential: (i) disk scale length, (ii) disk mass, (iii) halo scale radius, (iv) halo central density, and (v) a non‑axisymmetric component (e.g., bar). They constrain these parameters using synthetic stellar‑kinematics data that mimic the current Sloan Digital Sky Survey (SDSS) halo‑star sample, together with a local escape‑velocity measurement (v_esc≈533 km s⁻¹±30 km s⁻¹). By performing a joint likelihood analysis, they find that ρ₀ can be recovered with roughly 20 % precision (0.30 GeV cm⁻³ ± 0.06 GeV cm⁻³).

The next step is to propagate this astrophysical uncertainty into WIMP parameter reconstruction. The authors generate mock recoil spectra for a 1‑ton xenon detector (e.g., XENONnT) assuming realistic energy thresholds (≈5 keV), resolution, and background rates. They consider a grid of WIMP masses from 5 GeV to 100 GeV and cross‑sections from 10⁻⁴⁶ to 10⁻⁴⁸ cm². Two analysis strategies are compared: (a) the conventional approach that fixes ρ₀, and (b) the new approach that marginalizes over the five MW potential parameters.

For low‑mass WIMPs (≈10 GeV), a mis‑estimate of ρ₀ by a factor of two leads to a σSI bias of roughly a factor of two, corresponding to a 15‑σ statistical discrepancy. When the MW parameters are marginalized, the correlation between ρ₀ and σSI is automatically accounted for, reducing the bias to well below the statistical uncertainty. In this regime the authors achieve ≈15 % precision on mχ and ≈30 % precision on σSI after one year of exposure. For heavier WIMPs (≥50 GeV) the bias is smaller but still non‑negligible (≈10 % systematic shift in σSI).

Importantly, the methodology is detector‑agnostic. By swapping the detector response functions, the same astrophysical marginalization can be applied to argon‑based, silicon‑based, or germanium‑based experiments. Moreover, the framework can be extended to more sophisticated halo models (triaxial halos, streams, sub‑halos) and to incorporate forthcoming Gaia data, which could shrink the ρ₀ uncertainty to below 10 %.

In conclusion, the paper demonstrates that incorporating Galactic‑halo uncertainties directly into the statistical analysis of direct‑detection data is essential for unbiased WIMP property reconstruction. The proposed Bayesian marginalization over MW potential parameters eliminates the large systematic errors that would otherwise arise from fixing ρ₀, especially for low‑mass WIMPs. This integrated astrophysics‑particle‑physics approach paves the way for robust interpretation of upcoming tonne‑scale experiments and highlights the synergistic value of combining astronomical surveys with dark‑matter searches.