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

TL;DR

This paper analyzes how astrophysical uncertainties in dark matter velocity distributions impact direct detection experiments across various interaction operators, using information theory to quantify deviations without assuming specific models.

Contribution

It introduces a model-independent method using Kullback-Leibler divergence to assess astrophysical uncertainties for all operators in the effective theory of dark matter detection.

Findings

Uncertainties vary from less than one order of magnitude to three orders near threshold.

Different operators depend on distinct velocity moments like mean, variance, skewness.

The approach is broadly applicable to other physics problems involving uncertain distributions.

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.