Model-independent WIMP Scattering Responses and Event Rates: A Mathematica Package for Experimental Analysis

TL;DR

This paper introduces a versatile Mathematica package that enables comprehensive analysis of WIMP-nucleus interactions by integrating effective theory coefficients with nuclear response functions, facilitating experimental and theoretical research in dark matter detection.

Contribution

It provides a general, adaptable tool that combines effective theory parameters with nuclear physics data, streamlining WIMP analysis for diverse models and targets.

Findings

Outputs response functions and form factors for WIMP interactions.

Calculates differential event rates based on galactic WIMP velocities.

Remains relevant as new theories and nuclear data become available.

Abstract

The community's reliance on simplified descriptions of WIMP-nucleus interactions reflects the absence of analysis tools that integrate general theories of dark matter with standard treatments of nuclear response functions. To bridge this gap, we have constructed a public-domain Mathematica package for WIMP analyses based on our effective theory formulation. Script inputs are 1) the coefficients of the effective theory, through which one can characterize the low-energy consequences of arbitrary ultraviolet theories of WIMP interactions; and 2) one-body density matrices for commonly used targets, the most compact description of the relevant nuclear physics. The generality of the effective theory expansion guarantees that the script will remain relevant as new ultraviolet theories are explored; the use of density matrices to factor the nuclear physics from the particle physics will allow nuclear structure theorists to update the script as new calculations become available, independent of specific particle-physics contexts. The Mathematica package outputs the resulting response functions (and associated form factors) and also the differential event rate, once a galactic WIMP velocity profile is specified, and thus in its present form provides a complete framework for experimental analysis. The Mathematica script requires no a priori knowledge of the details of the non-relativistic effective field theory or nuclear physics, though the core concepts are reviewed here and in arXiv:1203.3542.