An Analytic Approach to Light Dark Matter Propagation

TL;DR

This paper introduces a new, efficient analytic method for modeling the attenuation of light dark matter in Earth's crust, improving upon previous computationally intensive simulations, and revises sensitivity estimates for sub-dominant dark matter.

Contribution

The paper presents a novel isotropic scattering approximation method that accurately models light dark matter attenuation and is computationally faster than Monte Carlo simulations.

Findings

The new method agrees well with Monte Carlo results.

It significantly reduces computation time for large numbers of scatterings.

Previous sensitivity estimates for sub-dominant dark matter are overestimated.

Abstract

If dark matter interacts too strongly with nuclei, it could be slowed to undetectable speeds in Earth's crust or atmosphere before ever reaching a detector. For sub-GeV dark matter, analytic approximations appropriate for heavier dark matter fail, necessitating the use of computationally expensive simulations. We present a new method of modeling attenuation of light dark matter in the Earth, based on the approximation that the scattering is isotropic in the lab frame. We show that this approach agrees well with Monte Carlo results, and can be much faster when the number of scatterings becomes large, as the runtime for Monte Carlo methods increases exponentially with cross section. We use this method to model attenuation for sub-dominant dark matter--that is, particles that make up a small fraction of the dark matter density--and show that previous work on sub-dominant dark matter overestimates the sensitivity of direct detection experiments.