[Paper Review] Identification of Dark Matter with directional detection

J. Billard, F. Mayet+1 more|arXiv (Cornell University)|Sep 28, 2010

Dark Matter and Cosmic Phenomena2 references3 citations

TL;DR

This paper presents a Bayesian likelihood framework for directional dark matter detection using 3D track data from future detectors like MIMAC. It introduces a map-based method to identify Galactic WIMP signals by analyzing angular distributions and a robust extended likelihood approach for setting exclusion limits, demonstrating high sensitivity for a 10 kg CF₄ detector over 3 years with 10° angular resolution.

ABSTRACT

Directional detection is a promising search strategy to discover galactic Dark Matter. Taking advantage on the rotation of the Solar system around the Galactic center through the Dark Matter halo, it allows to show a direction dependence of WIMP events. Data of directional detectors are composed of energy and a 3D track for each recoiling nuclei. Here, we present a Bayesian analysis method dedicated to data from upcoming directional detectors. However, we focus only on the angular part of the event distribution, arguing that the energy part of the background distribution is unknown. Two different cases are considered: a positive or a null detection of Dark Matter. In the first scenario, we will present a map-based likelihood method allowing to recover the main incoming direction of the signal and its significance, thus proving its Galactic origin. In the second scenario, a new statistical method is proposed. It is based on an extended likelihood in order to set robust and competitive exclusion limits. This method has been compared to two other methods and has been shown to be optimal in any detector configurations. Eventually, prospects for the MIMAC project are presented in the case of a 10 kg CF4 detector with an exposition time of 3 years.

Motivation & Objective

• To develop a statistically rigorous method for identifying galactic dark matter signals using directional recoil data from future detectors.
• To address the challenge of distinguishing WIMP-induced events from isotropic backgrounds without prior knowledge of individual event origins.
• To provide robust exclusion limits in the absence of a positive signal, ensuring competitiveness across diverse detector configurations.
• To evaluate the impact of realistic detector parameters—especially angular resolution—on detection sensitivity and exclusion power.
• To project the discovery potential and exclusion limits for the MIMAC 10 kg CF₄ detector over a 3-year exposure with 5–50 keV recoil energy range.

Proposed method

• Uses a binned, map-based likelihood function with Poisson statistics to compare observed recoil maps to theoretical models of WIMP and isotropic background distributions.
• Employs a four-parameter likelihood scan over WIMP mass, WIMP fraction (λ), and Galactic coordinates (ℓ, b) to identify the main incoming direction and signal significance.
• Applies an extended likelihood method to set exclusion limits in the null detection scenario, accounting for background uncertainty without assuming a known background energy spectrum.
• Incorporates detector angular resolution effects by convolving true WIMP directions with a Gaussian smearing function (σ_Θ), simulating realistic track reconstruction errors.
• Compares the proposed likelihood method with two existing methods (Maximum Gap and another standard approach) to validate robustness and optimality across detector configurations.
• Uses Monte Carlo simulations to assess performance across a range of exposures and background rates, ensuring generalizability to real detector conditions.

Experimental results

Research questions

• RQ1 Can a Bayesian map-based likelihood method reliably identify the Galactic origin of a WIMP signal by detecting anisotropy in the angular distribution of recoil events?
• RQ2 How does the proposed extended likelihood method perform in setting exclusion limits when no signal is detected, and how does it compare to alternative statistical approaches?
• RQ3 What is the impact of finite angular resolution on the sensitivity of directional detectors to WIMP signals and exclusion limits?
• RQ4 To what extent can a 10 kg CF₄ directional detector with 3-year exposure achieve a 3σ or 5σ discovery significance for WIMP-nucleon cross-sections in the 10⁻⁴ pb range?
• RQ5 How do realistic background rates and detector characteristics affect the robustness and competitiveness of exclusion limits in directional detection?

Key findings

• The map-based likelihood method successfully identifies a WIMP signal pointing toward Cygnus (ℓ ≈ 90°, b ≈ 0°) with a significance exceeding 3σ, recovering N_wimp = 106 ± 17 events at 68% CL in a simulated dataset.
• The extended likelihood method outperforms two alternative approaches in setting exclusion limits, demonstrating optimal performance across all tested detector configurations.
• Exclusion limits are only weakly sensitive to angular resolution: a 30% degradation occurs when σ_Θ increases from 0° to 45°, indicating robustness to realistic reconstruction errors.
• For a 10 kg CF₄ detector with 3 years of exposure and a background rate of 10 events/kg/year, the detector can achieve a 3σ discovery sensitivity for WIMP-nucleon cross-sections around 10⁻⁴ pb at 100 GeV/c².
• In the absence of signal, the detector can set competitive exclusion limits, with the 90% CL upper limit reaching ~10⁻⁵ pb for WIMP masses around 100 GeV/c².
• The study confirms that directional detection offers a unique path to unambiguous signal identification or robust exclusion, covering a large region of phenomenologically interesting parameter space.