A Model Independent Approach to Inelastic Dark Matter Scattering

TL;DR

This paper develops a model-independent framework for analyzing inelastic dark matter scattering in direct detection experiments, modifies existing methodologies for inelastic kinematics, and applies it to interpret experimental signals and constraints.

Contribution

It introduces a modified kinematic variable for inelastic scattering, extends the calculation of scattering matrix elements, and applies the framework to analyze DAMA/LIBRA signals and experimental constraints.

Findings

Xenon and germanium experiments have small rates in certain dark matter scenarios.

Iodine experiments impose stronger constraints, limiting parameter space.

Uncertainties in iodine quenching factors significantly affect the constraints.

Abstract

We present a model independent analysis of inelastic dark matter transitions at direct detection experiments by modifying the elastic methodology of Fitzpatrick, et al. By analyzing the kinematics of inelastic transitions, we find the relevant variables to describe these scattering processes, the primary change being a modification of the $\vec{v}^\perp$ variable. Taking this into account, we list the relevant scattering matrix elements and modify the Mathematica package of Anand, et al. to calculate the necessary form factors. As an application, we determine the matrix elements of inelastic scattering for spin transitions between a fermion to fermion, scalar to vector, and scalar to scalar. Finally, we consider fits to the DAMA/LIBRA annual modulation signal for the magnetic inelastic dark matter scenario as well as a model independent scan over relativistic operators, constraining them with limits from direct detection experiments. In the magnetic inelastic dark matter scenario or if the dark matter couples through relativistic operators involving only protons, we find that experiments with xenon and germanium targets can have consistently small rates. However, limits from iodine experiments are much more constraining, leaving small regions of allowed parameter space. We point out that existing uncertainties in the iodine quenching factor strongly affects the constraints, motivating further study to pin down the correct values.