Dark Matter Direct Detection: Liquid-Xenon Detector and Recoil Spectrum

What is measured. If dark matter is made of weakly interacting massive particles (WIMPs), a few of them should bump into a nucleus inside a very quiet detector and make it recoil. In a dual-phase liquid-xenon chamber the recoil gives a prompt flash of light (S1) and knocks out electrons that are drifted up by an electric field and, at the liquid surface, produce a second flash (S2). The delay between the two gives the depth.

Kinematics. For elastic scattering the recoil energy is ER = muN2 v2 (1 - cos theta) / mN with the WIMP-nucleus reduced mass muN; the largest possible recoil is 2 muN2 v2 / mN. A 100 GeV WIMP at 500 km/s gives a few tens of keV on xenon.

Rate. dR/dER = (rho / mchi) sigma0 mN F2(ER) eta(vmin) / (2 muN2) per target nucleus, with local density rho = 0.3 GeV/cm³, vmin = sqrt(mN ER / (2 muN2)), and the spin-independent nuclear cross-section sigma0 = sigman A2 (muN / mun)2 (the A² is why heavy nuclei like xenon win). The halo is a Maxwellian with v0 = 220 km/s cut at the escape speed 544 km/s and boosted by the Earth's speed 232 + 15 cos(2 pi (t - 152.5) / 365.25) km/s; the velocity integral eta is the closed form of Savage et al. (2006). The nuclear form factor is the Helm form factor (Lewin and Smith 1996).

Counting. Events are Poisson distributed, so if a run sees none the 90 % upper limit on the cross-section is where 2.303 events would have been expected (exp(-2.303) = 0.1). The reach curve is that cross-section against WIMP mass, with an ideal detector.

Simplifications, honestly. Spin-independent, isospin-conserving contact interaction only; a standard halo with no streams or substructure; nuclear recoils of 100 percent efficiency above a sharp threshold (real detectors have a smooth, smaller acceptance); the background is a flat rate after the cuts you set, not a model of radioactivity; neutrinos (the coherent scattering floor) are not included; the dates only change the Earth speed, so the annual modulation is a few percent. The S1 and S2 pulse sizes in the waveform graph and the light patterns on the sensors are illustrative: they scale smoothly with recoil energy and are not a calibrated detector response. The flashes are drawn thousands of times slower than reality, the drift is drawn at 1.6 m/s instead of 1.5 mm/us, and the run is compressed so that years of exposure fit into the seconds you choose. This is not a search result: the sliders show what a hypothetical particle would do, and no WIMP has been detected.