[Paper Review] Dish Antenna Searches for WISPy Dark Matter: Directional Resolution Small Mass Limitations

Joerg Jaeckel, S. Knirck|arXiv (Cornell University)|Feb 14, 2017

Dark Matter and Cosmic Phenomena10 references3 citations

TL;DR

This paper investigates the limitations of dish antenna experiments in detecting WISPy dark matter—specifically hidden photons and axion-like particles—when the dark matter de Broglie wavelength exceeds the antenna size. Using wave-based electromagnetic modeling, it shows that directional resolution collapses in the stationary regime (long wavelengths), where interference effects dominate and ray-tracing approximations fail, fundamentally limiting directional sensitivity for low-mass dark matter candidates.

ABSTRACT

Hidden photon and axion-like dark matter may be detected using spherical reflective surfaces such as dish antenna setups converting some of the dark matter particles into photons and concentrating them on a detector. These setups may be used to perform directional searches measuring the dark matter momentum distribution. We briefly review the photon distribution one expects to detect with such an antenna and directional resolution in ray approximation. Furthermore we consider the regime $m_{DM} \lesssim (R_{sp}\,v_{DM})^{-1}$ where this approximation does not hold anymore due to the photon wavelength exceeding the expected distribution widths. We discuss how this affects the expected distributions and experimental implications.

Motivation & Objective

• To assess the validity of ray-tracing approximations in dish antenna searches for WISPy dark matter when the dark matter de Broglie wavelength becomes comparable to or larger than the antenna size.
• To identify the transition regime between wave-based interference effects and classical ray optics, particularly in the context of directional dark matter detection.
• To quantify how the directional resolution of dish antennas degrades for low-mass dark matter (mDM ≲ (Rsp vDM)−1) due to wavelength effects.
• To provide a criterion for when wave effects dominate over ray optics, enabling better design and interpretation of directional dark matter experiments.
• To clarify the experimental implications of these limitations for both discovery and directional sensitivity in hidden photon and axion-like particle searches.

Proposed method

• Model the electromagnetic field emission from a spherical dish antenna using a wave-based dipole approximation, where surface currents are induced by incident dark matter particles.
• Integrate the far-field radiation pattern of elementary dipoles over the spherical surface, incorporating the spatial phase variation from the dark matter wave vector kDM.
• Use the time-averaged Poynting vector to compute the intensity distribution at the detector, accounting for interference between waves from different surface elements.
• Derive a scalar intensity model I(x) = |∫Ψ(r′) exp(−i kDM·r) d²r|², with Ψ(r′) proportional to kγ exp(ikγ r′)/r′, to simplify the calculation for incoherent polarization averaging.
• Numerically evaluate the intensity distribution for varying dark matter wavelengths, comparing results to both the ray approximation and the stationary (long-wavelength) limit.
• Define a characteristic length scale R̂ = √(1−cos(θsp,max)) max(tan(θsp,max);1) R to distinguish between the stationary and ray-optics regimes based on wavelength.

Experimental results

Research questions

• RQ1 At what dark matter mass does the ray-tracing approximation for dish antenna detection of WISPy dark matter break down?
• RQ2 How do wave interference effects alter the expected intensity distribution in dish antennas when the de Broglie wavelength of dark matter exceeds the antenna size?
• RQ3 What is the quantitative relationship between the full width at half maximum (FWHM) of the detected signal and the photon wavelength in the stationary regime?
• RQ4 How does the directional resolution of dish antennas degrade for low-velocity, low-mass dark matter candidates due to wave effects?
• RQ5 What criterion can be used to determine whether a given experimental setup operates in the wave-dominated (stationary) or ray-optics regime?

Key findings

• For dark matter with de Broglie wavelength λDM ≳ R, the ray-tracing approximation fails and the intensity distribution becomes dominated by wave interference effects.
• In the stationary regime (λγ ≲ 10 × λγ / v), the FWHM of the intensity distribution scales as λγ / √(1−cos(θsp,max)), indicating a strong wavelength dependence.
• The transition between the stationary and ray-optics regimes occurs when the characteristic length scale R̂ ≈ 0.5 × λγ / v to 10 × λγ / v, depending on the aperture angle.
• The ray-tracing approximation remains valid only when R̂ ≳ 10 × λγ / v, which corresponds to mDM ≳ (Rsp vDM)−1 for typical experimental parameters.
• Directional resolution is fundamentally limited in the stationary regime, where interference patterns smear the signal and prevent accurate reconstruction of the dark matter momentum distribution.
• For directional sensitivity experiments, the minimum detectable dark matter velocity must be chosen such that the wavelength remains short enough to avoid the stationary regime, otherwise directional information is lost.