Fundamental statistical limitations of future dark matter direct detection experiments

TL;DR

This paper analyzes the fundamental statistical limitations of future dark matter direct detection experiments, focusing on confidence interval coverage, bias, and how combining data sets can improve parameter reconstruction.

Contribution

It provides a detailed assessment of statistical biases and coverage issues in dark matter detection, highlighting the benefits of multi-target data combination.

Findings

Confidence intervals are conservative and cover true parameters.

Statistical fluctuations can cause significant bias even with high event rates.

Combining data from different targets improves coverage and reduces bias.

Abstract

We discuss irreducible statistical limitations of future ton-scale dark matter direct detection experiments. We focus in particular on the coverage of confidence intervals, which quantifies the reliability of the statistical method used to reconstruct the dark matter parameters, and the bias of the reconstructed parameters. We study 36 benchmark dark matter models within the reach of upcoming ton-scale experiments. We find that approximate confidence intervals from a profile-likelihood analysis exactly cover or over-cover the true values of the WIMP parameters, and are hence conservative. We evaluate the probability that unavoidable statistical fluctuations in the data might lead to a biased reconstruction of the dark matter parameters, or large uncertainties on the reconstructed parameter values. We show that this probability can be surprisingly large, even for benchmark models leading to a large event rate of order a hundred counts. We find that combining data sets from two different targets leads to improved coverage properties, as well as a substantial reduction of statistical bias and uncertainty on the dark matter parameters.