Fast numerical evaluation of dark matter direct detection event rates

Abstract

The mathematical expression for the dark matter nuclear recoil event rate in a detector consists of a six dimensional integral over the velocity distribution of dark matter in the detector frame, and over the recoil momentum of the nucleus. While a significant part of this integral can be solved in closed form under traditional assumptions of the standard halo model and/or isotropic detector response, analysis of alternate assumptions is conventionally impeded by the inefficiency of multidimensional numerical integration methods. In this work we introduce a novel, fast and efficient algorithm for direct detection event rate computations. This algorithm takes advantage of a closed form expression for the Radon transform of three dimensional Zernike functions, which are used as basis functions for the velocity distribution. We demonstrate an implementation of this algorithm ZebraDM (https://github.com/sebsassi/zebradm), which is typically faster than an optimized numerical integration approach by a factor between $10^2$ and $10^4$.