Dark Matter Direct Detection - II

Nassim Bozorgnia

GRAPPA InstituteUniversity of Amsterdam

School on Dark Matter, São Paulo, BrazilJuly 7, 2016

• Direct detection principles

• Expected event rate: particle physics & astrophysics dependences

• Dark matter signatures

• Annual modulation and directionality

• Direct detection experiments

• Null results

• Hints for a signal

• Interpretation of experimental results

OutlineLecture 1

Lecture 2

Lecture 3

Dark Matter Signatures

• The Sun is rotating around the center of the Milky Way, going through the DM halo.

• A “WIMP Wind” is coming towards us with an average velocity in the opposite direction of the Sun’s velocity.

Annual modulation

Galactic Center

Sun

Earth

220 km/s

WIMP Wind

• Due to the motion of the Earth around the Sun, the DM velocity distribution changes in a year.

Annual modulation

• Depending on the time of the year, we should receive more or less DM flux at Earth.

Annual modulation

DecJune

time dependence in rate has a period of 1 year.

• Nice DM signature: backgrounds usually not expected to show such a time dependence.

Annual modulation

halo

inte

gral

⌘(vm) ⌘Z

v>vm

d3vf(v)

v

Reminder from Lecture 1:

halo integral

• The speed of the Earth’s revolution around the Sun is significantly smaller than the speed of the Sun’s rotation around the center of the Galaxy.

• The amplitude of the modulation is small (few %). Need at least ~1000 events to detect it.

• The rate can be written as a Taylor expansion:

Annual modulation

dR

dE(E, t) ' S0(E) + Sm(E) cos!(t� t0)

time-averaged rate

modulation amplitude

phase of modulation

2π/year

• Amplitude of the annual modulation assuming the SHM:

Annual modulation

The amplitude of the modulation changes sign at low recoil energies.

Sm(E) =1

2

dRJune1

dE� dRDec1

dE

�

• Modulation fraction:

• The modulation fraction is ~1-10% for a large range of minimum velocities.

• For the SHM, the modulation has a sinusoidal shape and is symmetric around t0.

• In the presence of several halo components, the phase and the shape of the modulation may be modified.

Annual modulation

• The Earth’s motion through the galaxy produces a direction dependence in the recoil spectrum.

• Since the maximum WIMP flux is coming towards us from one direction, the resulting WIMP-induced nuclear recoils will preferentially cluster around the same direction (opposite to the direction of Solar motion).

• One can then see a dipole feature in the recoil rate: recoil rates in the forward and backward directions are different by a factor of ~10.

Directionality

[Spergel 1988]

Directionality

WIMP flux

recoil distribution

Galactic coordinates

0 0.2 0.4 0.6 0.8 1.0

Arbitrary units

0 0.2 0.4 0.6 0.8 1.0

Arbitrary units

• No known backgrounds can mimic this directional signature! Smoking gun evidence for DM.

• Directional detectors can measure both the energy and direction of the WIMP-induced recoils. measure the dipole feature.

Directionality

• Another directional feature: because of the Earth’s rotation, the peak recoil direction in the lab frame varies over the course of a day. daily modulation

• The double differential event rate per unit detector mass as a function of both the recoil energy and direction is given by:

Directionality

: infinitesimal solid angle around the recoil direction.

• Azimuthal symmetry of the scattering around the WIMP arrival direction: m~v0

m~v

~q

✓0

✓

• Recall:

Directionality

which gives:

• Impose this relation through a Dirac delta function:

• Remember the energy differential cross section for standard contact interactions:

Directionality

• We have:

is the three-dimensional Radon transform of the velocity distribution: [Gondolo, hep-ph/0209110]

• Using the Radon transform, one can evaluate the event rate analytically for most halo models.

• For the SHM with a truncated Maxwellian velocity distribution, the Radon transform in the lab frame is:

Directionality

if , and zero otherwise.

: velocity of the lab with respect to the Galaxy.

Directionality

• Two regimes of interest:

• If , argument of first exponential minimized when is in the opposite direction of . dipole feature

• If , i.e. for low recoil energies and large WIMP masses, maximum of the Radon transform happens at an angle between and . ring-like feature in the recoil map. [Bozorgnia, Gelmini, Gondolo, 1111.6361]

• Differential directional recoil rate in fluorine, assuming 5 keV recoil energy and 100 GeV WIMP.

Directionality

0.081 0.243 0.405 0.567 0.729 0.891

Direct detection Experiments

• Many direct detection experiments all over the world: DAMA (NaI), LUX (Xe), XENON (Xe), CDMS (Ge, Si), SuperCDMS (Ge) CoGeNT (Ge), CRESST (CaWO4), Edelweiss (Ge), KIMS (CsI), ZEPLIN (Xe), XMASS (Xe), PICO (CF3I), SIMPLE (C2CIF5), DRIFT (CS2, CF4), PandaX (Xe), DarkSide (Ar), …

• Different target materials and different techniques used in the experiments.

Experiments around the world

• The majority of direct detection experiments are direction-insensitive, and they measure the recoil energy of the nucleus.

• Signals in direct detection experiments:

• phonons (heat)

• scintillation (light)

• ionization (charge)

• Different types of detectors:

• crystalline detectors operating at very low temperatures (mK), crystals at room temperature, noble liquid detectors, …

Direct detection techniques

Direct detection techniques

Phonons

Ionization Scintillation

CDMSEdelweiss

CRESST

LUXXENONZEPLIN

CoGeNTDAMAKIMS

XMASS

Bubble ChambersPICO

SIMPLE

• WIMPs are expected to produce

• WIMPs interact only once in the detector. They interact with the target nuclei.

• In most material, scattering from the atomic nucleus leads to different physical effects compared to scattering from electrons.

• Neutrons are an important background for WIMP searches, and can mimic WIMPs by interacting with the target nucleus.

Background discrimination

• Cosmic rays and secondaries: hadrons (p, n), muons, and secondary particles can mimic nuclear recoils.

• Go underground to reduce the rate of these background events. Detectors up to several 1000 meters below Earth’s surface.

Background discrimination

• Hadronic components (n, p) are reduced by few meter water equivalent.

Background discrimination

Flux of cosmic rays in a Pb shield as a function of shielding depth

• Muons and muon induced neutrons are most problematic.

• Need to go deep underground.

Background discrimination

• Radioactivity:

• From the environment, target material, and detector shielding. Produces mainly α, β and γ particles.

• Use lots of radiopure (clean) shielding material to reduce radioactive backgrounds. Also, need to know the decay process of radioactive isotopes.

• Interactions induced by external radioactivity concentrate near the surface of the detector.

Background discrimination

• Radioactive decay of surrounding material:

Background discrimination

A =dN

dt= ��N

• Radioactivity in human body: 4000 Bq from 40K, 4000 Bq from 14C

• External, natural radioactivity: 238U, 238Th, 40K decays in rocks and concrete walls of the lab.

N: number of radioactive nucleiλ: decay constant[A]= Bq= decays/s

• Still some background remains:

• Detectors need to distinguish between the remaining background (nuclear and electron recoils), and the expected signal from WIMPs (nuclear recoils).

• Combine two techniques of detection: ionization + phonons, ionization + scintillation, scintillation + phonons

• Any event remaining above background might be a signal.

Background discrimination

• Discrimination between electron and nuclear recoils:

Background discrimination

• Example: measuring both charge and phonons in a Ge detector

• ER: background NR: WIMPs (or neutron background)

Background discrimination

Background discrimination• Distinguishing neutrons from WIMPs:

• Different mean free path: few cm (neutrons), versus 1010 m (WIMPs).• Differential recoil spectrum depends on the target material.• Time dependence of the WIMP signal.

Signal from WIMPs• Finding a needle in a haystack!

Signal from WIMPs• WIMP parameters probed by direct detection searches:

WIMP mass and cross section.

• Recall the SI differential rate in events/kg/day/keV:

dR

dE=

⇢ A2 �SI2mµ2p

F 2(E) ⌘(vm)

• We have already made an assumption on the particle physics model in the above equation.

• Make an assumption on the halo model: SHM.

• WIMP parameters probed by direct detection searches: WIMP mass and cross section.

• If the events observed in a direct detection experiment are consistent with the background expectation, one can derive an exclusion limit in the plane of interaction cross section and WIMP mass.

• In case of a positive signal, we can specify the allowed region in the cross section-mass plane.

Signal from WIMPs

• Recall the SI differential rate in events/kg/day/keV:

Predicted number of events

dR

dE=

⇢ A2 �SI2mµ2p

F 2(E) ⌘(vm)

• The predicted number of events in the detected energy interval is given by:[E1, E2]

detector mass exposure time detector response function: includes detection efficiencies and energy resolution

• In a null-result experiment:

• Obtain an upper bound on the predicted number of events at a confidence level CL. implies an upper bound on the scattering cross section for each WIMP mass.

• Exclusion limits in the cross section-mass plane placed using:

• “Maximum gap” or “optimum interval” methods, if backgrounds are not modeled.

• Likelihood analysis, if backgrounds are modeled.

Exclusion limit

Exclusion limit

Exclusion limit

Direct detection requirements

• Large exposure: Mass x Time

• Low background

• Excellent discrimination between signal and background

• Low energy threshold

• Many direct detection experiments so far have found no evidence for dark matter, and have set exclusion limits in the cross section - mass plane.

• The strongest exclusion limits are set by:

• LUX: at large DM masses,

• CDMSlite: at

• CRESST: at small DM masses,

Null-result experiments

• LUX (Large Underground Xenon) is a dual phase (liquid + gas) detector, and operates in Sanford Underground laboratory in South Dakota, USA.

LUX

• Measures ionization and scintillation.

LUX

scintillation signal

ioni

zatio

n si

gnal

nuclear events

electronic events

LUX, 1512.03506

LUX

• Exposure of 1.4 x 104 kg days.

• Low recoil energy threshold of 1.1 keV.

• Found no evidence of WIMP candidate events, and the signal is consistent with the background model.

LUX

LUX, 1512.03506

CDMSlite• CDMSlite (CDMS low ionization threshold): cryogenic

Ge crystals operating at mK temperatures in Soudan Mine in Minnesota.

• Measures phonons and ionization (through phonons).

• No discrimination between electronic and nuclear recoils.

CDMSlite• Exposure: 70 kg day, Energy threshold: 56 eV

SuperCDMS, 1509.02448

CRESST-II• CRESST (Cryogenic Rate Event Search with

Superconducting Thermometers): scintillating CaWO4 crystals operating in Gran Sasso, Italy.

• Measures scintillation and phonons.

CRESST-II• Low threshold (0.6 keV) analysis of upgraded detector;

29.35 kg days;

CRESST, 1509.01515

• We discussed two important DM signatures:

• annual modulation signal

• directional signatures

• Direct detection experimental techniques: distinguish background from signal.

• Many null-result experiments. Strongest limits set by: LUX ( ), CDMSlite ( ), and CRESST ( ).

Summary

• Bertone, Particle Dark Matter: Observations, Models and Searches, Cambridge University Press, 2010

• Freese, Lisanti and Savage, Rev. Mod. Phys. 85 (2013) 1561

• Kurylov and Kamionkowski, Phys. Rev. D 69 (2004) 063503

Classic papers:

• Lewin and Smith, Astrop. Phys. 6 (1996) 87

• Jungman, Kamionkowski and Griest, Phys. Rep. 267 (1996) 195

• Gondolo, arXiv: hep-ph/9605290

• Spergel, Phys. Rev. D 37 (1988) 1353

• Drukier, Freese and Spergel, Phys. Rev. D 33 (1986) 12

• Goodman and Witten, Phys. Rev. D 31 (1985) 12

Further reading