Information-theoretic astrophysical uncertainties in the effective theory of dark matter direct detection

TL;DR

This paper addresses how astrophysical uncertainties in the local DM velocity distribution affect direct-detection signals within the non-relativistic EFT framework across all operators. It introduces a convex-optimization approach using the Kullback-Leibler divergence $D_{\mathrm{KL}}$ to bound deviations from the Maxwell-Boltzmann distribution without assuming a parametric form, solving for conservative and aggressive upper limits on Wilson coefficients for XENONnT and PICO60. Results reveal a hierarchy: operators with higher velocity or momentum dependence exhibit larger sensitivity to velocity distribution uncertainties, with near-threshold effects ranging from about one order of magnitude for $\mathcal{O}_1$ to several orders of magnitude (up to $10^3$–$10^4$) for $\mathcal{O}_5$, $\mathcal{O}_8$, and $\mathcal{O}_{14}$ when $D_{\mathrm{KL}}\in {0.1,1}$. The analysis links the rate to velocity-weighted integrals $\int_{v_{\min}}^{\infty} dv\, v^n f(v)$, connecting to conditional mean, variance, and skewness of the speed distribution, and provides a framework ready for extension to multi-target, inelastic, Migdal, or electron-scattering EFT problems.

Abstract

The impact of astrophysical uncertainties in direct detection searches can vary significantly across particle dark matter models and detector targets, due to the different velocity and momentum dependencies of the scattering cross section. We address these uncertainties for all operators of the non-relativistic effective field theory of dark matter-nucleon interactions, making use of the Kullback-Leibler (KL) information divergence to measure the deviation of the true dark matter velocity distribution from the Maxwell-Boltzmann form. This approach quantifies how astrophysical uncertainties affect each operator in the effective theory, without assuming any specific functional form for the velocity distribution. While for some operators the uncertainties are smaller than one order of magnitude for entropically-motivated deviations from the Maxwell-Boltzmann form, for other operators these uncertainties can be as large as three orders of magnitude near threshold. Furthermore, we identify the dependence of the scattering rate for various operators of the effective theory with different velocity-weighted moments of the velocity distribution, functionally analogous to the mean, variance, or skewness. This provides new analytic insight into which features of the velocity distribution are most relevant to detect a given particle dark matter model. Our technique is general and could be applied to a broader class of physics problems where a physical observable depends on the statistical moments of an uncertain theoretical distribution.

Figures (5)

• Figure 1: 90% C.L upper limits on the dark matter-nucleon coupling from XENONnT, for different values of the KL-divergence between the Maxwell-Boltzmann distribution and the true velocity distribution. For comparison, we show the upper limits obtained from other velocity distributions motivated in the literature: Aquarius Vogelsberger:2008qb, SHM$^{++}$Evans:2018bqy, Gaia/SDSS Necib:2018iwb, Eagle Schaye:2014tpa, and S1-stream+SHM OHare:2018trr.
• Figure 2: 90% C.L upper limits on the dark matter-nucleon coupling from PICO60, for different values of the KL-divergence between the Maxwell-Boltzmann distribution and the true velocity distribution. For comparison, we show the upper limits from other velocity distributions motivated in the literature.
• Figure 3: Ratio of limits on the cross section in the SHM vs the KL-informed minima.
• Figure :
• Figure :