Statistics of Daily Modulation in Dark Matter Direct Detection Experiments

TL;DR

This paper analyzes the statistical detectability of daily modulation signals in dark matter direct detection experiments, emphasizing the importance of detector orientation and exposure time for maximizing discovery potential.

Contribution

It provides a statistical framework for detecting daily modulation signals, including optimization strategies for detector orientation and exposure to enhance significance.

Findings

Discovery significance scales as $f_{RMS} \, \sqrt{T}$ in background-dominated regimes.

Optimizing detector orientations can reduce required exposure by about a factor of 5.

Significance continues to improve with exposure, unaffected by systematic background uncertainties.

Abstract

The time-dependent modulation of the event rate in dark matter direct detection experiments, arising from the motion of the Earth with respect to the Galactic rest frame, is a distinctive signature whose observation is crucial for claiming a discovery of dark matter. While annual modulation has been well studied for decades, daily modulation due to the Earth's rotation has attracted increased attention recently due to the identification of anisotropic solid-state detector materials that yield a direction-dependent scattering rate without sacrificing the overall rate. We perform a statistical analysis of daily modulation in dark matter scattering experiments, with the goal of maximizing the statistical significance of a modulating signal in the presence of an unknown background rate, which may be either flat (non-modulating), or modulating over a 24-hour period with a known or unknown phase. In the background-dominated regime, we find that the discovery significance scales as $f_\text{RMS} \sqrt{T}$, where $T$ is the total exposure time and $f_\text{RMS}$ is the root-mean-square modulation amplitude; in particular, the significance continues to improve with exposure rather than saturating due to systematic uncertainties in the background rate. Using anisotropic trans-stilbene detectors for sub-GeV dark matter as a benchmark example, we provide prescriptions for optimizing the significance for a given total detector mass and location. In an example analysis using three detectors, optimizing the detector orientations can reduce the required exposure by a factor of $\sim 5$ for a desired discovery or exclusion significance, even after profiling over an unknown modulating background phase.