🔍 Dark Matter Direct Detection

WIMP dark matter scatters off nuclei: recoil energy E_R = μ²v²(1−cos θ)/m_N. Maxwell-Boltzmann velocity distribution of dark matter halo. Detector threshold, exposure, and signal vs background.

PhysicsInteractive
Blue: WIMP recoil spectrum · Red dashed: detector threshold · Orange: background · Inset: Maxwell-Boltzmann velocity distribution

How it Works

The simulation computes the differential nuclear recoil rate dR/dE_R for WIMP-nucleus elastic scattering. The recoil spectrum is an exponential falling function of energy, integrated over the Maxwell-Boltzmann velocity distribution of the dark matter halo. Only events above the detector threshold are observable.

The background is modelled as a flat (white) spectrum from residual radioactive contamination. The signal-to-noise ratio S/√B determines detectability. Large WIMP mass (heavy nuclei) and low threshold improve sensitivity. Current best limits come from the tonne-scale xenon experiments.

Reduced mass: μ = m_χ·m_N / (m_χ + m_N) Max recoil: E_max = 2μ²v²_max / m_N Rate: dR/dE_R ∝ σ_n · A² · (ρ_DM/m_χ) · F²(E_R) · η(E_R) Form factor: F(q) = exp(-q²r²/6) [Helm form factor] MB dist.: f(v) ∝ v²·exp(-v²/v₀²) [v₀=220 km/s]

Frequently Asked Questions

What is a WIMP?

A WIMP (Weakly Interacting Massive Particle) is a hypothetical dark matter particle with mass typically between 1 GeV and 10 TeV that interacts via the weak nuclear force and gravity. WIMPs arise naturally in supersymmetric extensions of the Standard Model.

How does direct dark matter detection work?

Direct detection experiments place large, ultra-pure detectors deep underground to shield from cosmic rays. When a WIMP from the galactic halo collides with a nucleus, it produces a measurable nuclear recoil signal (light, heat, or ionization).

What is the nuclear recoil energy formula?

The nuclear recoil energy is E_R = μ²v²(1−cos θ_cm)/m_N where μ = m_χ·m_N/(m_χ+m_N) is the reduced mass, v is the WIMP-nucleus relative velocity, θ_cm is the scattering angle in the center-of-mass frame, and m_N is the nucleus mass.

What is the Maxwell-Boltzmann velocity distribution of WIMPs?

Dark matter in the galactic halo is modeled with a truncated Maxwell-Boltzmann distribution: f(v) ∝ v²·exp(-v²/v₀²) for v < v_esc, where v₀ ≈ 220 km/s is the local circular speed and v_esc ≈ 544 km/s is the galactic escape velocity.

What is spin-independent vs spin-dependent scattering?

Spin-independent (SI) scattering couples to nucleons with the cross-section scaling as A² (atomic number squared), making heavy nuclei like xenon ideal targets. Spin-dependent (SD) scattering couples to nuclear spin and does not benefit from the A² enhancement.

What are the leading dark matter detector experiments?

Current leading experiments include XENONnT, LZ (LUX-ZEPLIN), and PandaX-4T, all using liquid xenon. Other approaches include cryogenic bolometers (SuperCDMS, CRESST) and noble liquid detectors (DarkSide-50). All operate deep underground.

What is the annual modulation signal?

As Earth orbits the Sun, its velocity relative to the dark matter halo varies with a ~1 year period, producing an annual modulation in event rate of a few percent. DAMA/LIBRA claims to have observed this signal for over 20 years.

What is the minimum detectable WIMP mass?

The minimum detectable WIMP mass is set by kinematics: E_max = 2μ²v²_max/m_N. For a detector threshold of ~1 keV and xenon nucleus, WIMPs lighter than ~5 GeV produce too little recoil energy to be detected.

Why are detectors placed underground?

Underground placement reduces cosmic ray muon flux by factors of 10^6 or more. Muons can produce secondary neutrons that mimic WIMP nuclear recoils. Additional shielding from water or polyethylene reduces neutron backgrounds.

What is the WIMP 'miracle'?

The 'WIMP miracle' is the observation that a particle with weak-scale mass (~100 GeV) and weak-interaction cross-section naturally produces the observed dark matter relic abundance Ω_DM ≈ 0.27 via freeze-out in the early Universe, without fine-tuning.

About this simulation

This simulator builds the differential nuclear-recoil spectrum dR/dE_R a WIMP detector would see, by integrating a Maxwell-Boltzmann halo velocity distribution against the kinematics of elastic WIMP-nucleus scattering. Choosing a heavier target nucleus, lowering the energy threshold, or increasing exposure time all reshape the blue signal curve relative to the flat orange background — mirroring the actual trade-offs xenon and germanium experiments make underground.

🔬 What it shows

A log-scale recoil spectrum falling exponentially with energy, a dashed red detector threshold line, a flat orange background rate, and an inset panel of the underlying Maxwell-Boltzmann WIMP velocity distribution f(v).

🎮 How to use

Adjust WIMP mass m_χ, cross-section log σ_n, detector threshold, and exposure (tonne·years) with the sliders; switch the target nucleus between xenon, germanium, argon, and sodium to see how the A² scaling changes the signal-to-background ratio S/√B.

💡 Did you know?

Because spin-independent cross-section scales as A² (atomic number squared), swapping sodium (A=23) for xenon (A=131) boosts the expected rate by roughly (131/23)² — over 32 times — which is exactly why xenon dominates today's leading experiments like XENONnT and LZ.

Frequently asked questions

Why does moving the threshold slider cut off part of the spectrum?

Only recoils above the detector threshold are countable as signal events — the simulation integrates dR/dE_R starting at whatever keV value you set, so raising the threshold discards the low-energy region where light WIMPs deposit most of their recoil energy.

What does the reduced mass μ control?

μ = m_χ·m_N/(m_χ+m_N) sets both the maximum recoil energy E_max = 2μ²v²_max/m_N and the overall event rate. When m_χ is much smaller than the nucleus mass, μ saturates near m_χ, which is why very light WIMPs struggle to produce detectable recoils.

Why does switching the target nucleus change the curve so much?

Spin-independent scattering scales with A² (from summing coherently over all nucleons), so heavier nuclei like xenon (A=131) give dramatically higher rates than lighter ones like sodium (A=23) — the exact reason the simulation's signal curve jumps when you pick a heavier target.

What does S/√B represent in the stats panel?

It is the statistical significance of a potential detection — signal events divided by the square root of background events — the standard way particle physicists judge whether an excess above the flat background rate is meaningful.

Why is the WIMP velocity distribution truncated?

The Maxwell-Boltzmann curve in the inset panel only extends to the galactic escape velocity v_esc ≈ 544 km/s — any dark matter particle faster than that would not be gravitationally bound to the Milky Way and wouldn't be part of the local halo passing through Earth.