Lecture 3: Direct Dark Matter Detection

Lecture 3:

Direct Dark Matter Detection

Graciela Gelmini - UCLA

23d.Spring School, Tainan, Taiwan, 3/31-4/3 2010

Graciela Gelmini-UCLA

Content:

• WIMPs: Cross sections and rates

• Milky Way Halo Model

• WIMP’s: Annual modulation

• WIMP’s: Search and signal discrimination techniques

• WIMPs: Main experiments and best present bounds

• DAMA signal, compatible with other negative results?

• Axions

23d.Spring School, Tainan, Taiwan, 3/31-4/3 2010 1


Milky Way’s Dark Halo Fig. from L.Baudis; Klypin, Zhao and Somerville 2002

1010(GeV/mχ) WIMP’s passing through us per cm2 per second!



WIMP DM searches:

• Direct Detection- looks for energy deposited within a detector by acollision of a WIMP is the halo of our galaxySignature: same σ and m seen by different experiments with different

nuclei + annual modulation and/or recoil direction

• Indirect Detection- looks for WIMP annihilation (or decay) products(Next lecture)



Direct DM Searches:

• Small ERecoil ≤ 50keV(m/100 GeV)

• Rate: depends on WIMP mass,

cross section, dark halo model, nuclear

form factors...

typical... < 1 event/ 100 kg/day

(need to go underground underground to

shield from cosmic rays)

• Single hits: single scatters, uniform

through volume of detector

• Annual flux modulation (few % effect)

• Directional detection (daily modulation-

requires measuring the recoil direction)



WIMPs vs photons

• WIMPs interact with nuclei and produce

phonons besides ionization/scintillation.

• Photons and electrons interact mostly

with atomic electrons.



WIMP-Nucleous Interaction:

WIMPs are not relativistic: v ≃ 300km/s ≃ 10−3 c. Thus, for the typical momentum

exchanged q = µv/√

2 (µ = mM(m+M) is the reduced mass)

1

q> RNucleus ≃ 1.25 fm A1/3

or, using 1= 197 MeV fm (1 femtometre, fm = 10−15 m)

q ≃ MeV

„

mχ

GeV

«

< MeV

„

160

A1/3

«

WIMP interact coherently with all the nucleons in a pointlike nucleus.

For larger q and heavier nuclei- A large- the loss of coherence is taken into account with

a nuclear form factor F (E) =R

e−iqrρNucleon(r)dr. Conventional Helmi form factor:

F (E) = 3e−q2s2/2[sin(qr) − qr cos(qr)]/(qr)3,

with s = 1 fm, r =√

R2 − 5s2, R = 1.2A1/3 fm, q =√

2ME.



WIMP-Nucleous Interaction:

For a non relativistic elastic collision, the maximum recoil energy impartedto a Nucleus by a WIMP moving at v is Emax = 2µ2v2/M and

dσ

dE=

(

σ

Emax

)

pointlike

|F (E)|2

Minimum WIMP speed required to produce a nuclear recoil energy E:

vmin =

√

ME

2µ2=

√

(m + M)2E

2Mm2

µ = mM(m+M): reduced mass, m: WIMP mass, M : is the nucleus mass.



Event rate: events/(kg of detector)/(keV of recoil energy)

dR

dE=

∫

NT

MT× dσ

dE× nvf(v, t)d3v

=ρσ(q)

2mµ2

∫

v>vmin

f(v, t)

vd3v

-NTMT

= Avogadro’s number per mol = Number of atoms per gram

- ρ = nm, f(v, t):local DM density, ~v distribution depend on halo model

- spin-independent σ(q)= σ0F2(q), σ0 = A2(µ2/µ2

p)σp for fp = fn

- spin-dependent σ(q) =32µ2G2

F (JN+1)

JN

[

〈Sp〉ap + 〈Sn〉an

]2



- spin-independent: σ(q)= σ0F2(q)

From scalar and vector couplings in the Lagrangian- fp,n effective couplings to p, n

σ0 =[

〈Zfp + (A − Z)fn

]2(µ2/µ2

p)σp = A2(µ2/µ2p)σp for fp = fn

- spin-dependent: σ(q) =32µ2G2

F (JN+1)

JN

[

〈Sp〉ap + 〈Sn〉an

]2

From axial couplings in the Lagrangian- ap,n couplings to p, n

〈Sp,n〉 expectation values of the spin content of p,n in the target nucleus

Example: 73Ge (JN = 9/2, 7.8% in isotopic composition) Single particle shell model:

〈Sn〉 = 0.5, 〈Sp〉 = 0 (Odd-group model: 0.23, 0; Shell Model 0.488, 0.011)

Need non zero nuclear spin JN . Examples:29Si (JN = 1/2, 4.7%), 129Xe (JN = 1/2, 26.4%), 131Xe (JN = 1/2, 21.2%)

- SD Form Factor is O(1) thus SI cross sections are A2 larger than SD



Bounds on SI better that on SD Example: XENON collaboration



Standard Halo Model (SHM) The of halo models

ρSHM = 0.3 GeV/cm3

Maxwellian ~v distribution

at rest with the Galaxy

v⊙ =220 km/s, vesc = 500 - 650 km/s

Local ρ and velocity could be very different if the Earth is within a DM clump or stream

or if there is a “Dark Disk”. Simulations advancing fast....



Standard Halo Model (SHM) The of halo models

Maxwellian distribution truncated at the local Galactic escape speed vesc

fh(v, t) =

8

>

<

>

:

1

Nh(2πσ2h)

3/2e−|v+v⊙+v⊕(t)|2/2σ2

h if |v + v⊙ + v⊕(t)| < vesc = 650 km/s,

0 otherwise.

v: WIMP velocity relative to the Earth

v⊕(t): velocity of the Earth relative to the Sun (29.8 km/s tangent to orbit)

v⊙: velocity of the Sun relative to the Galactic Rest Frame (in which halo WIMPs assumed

to be stationary)= 232 km/s in direction λ⊙ = 340◦, β⊙ = 60◦ ecliptic coordinates ;

σh: velocity dispersion of WIMPs ( 220/√

2 km/s (in isothermal model),

Nh = erf(z/√

2) − (2/π)1/2ze−z2/2, with z = vesc/σh: normalization factor.

With this model: maximum possible heliocentric WIMP velocity is vesc +v⊙ = 882 km/s.



The Actual Halo of the Milky Way

The Sagittarius (Sgr) Dwarf Galaxy is being eaten-up by the Milky Way.Using its tidal disruption leading and trailing streams (in stars) of the D.Law and S. Majewski and K. Johnson have modeled the shape of the DarkHalo (Jan 2010). It is a triaxial “beachball”.



Possible Dark Halo profiles Important for indirect DM searches.

Cuspy profiles: fits to N-bodyDM only simulations

Cored profiles: Fits to observedrotation curves



Rotation curves of the Milky Way (Fig from M. Weber)

v⊙ = 244 ± 10.2km/s ((Reid, Brunthaler, 0808.2870)

ρ⊙−DM = 0.3 ± 0.1 GeV/cm3((Honma et al

0709.0820)

Possible Inner Ring (at r ≃4 kpc) andOuter Ring (at r ≃13 kpc) of DM likelypart of a Dark Disk can explain betterthe curves, contributing to ρ⊙−DM < 1.0GeV/ cm3 ??? ((Weber, de Boer [0910.4272])



Dark Disk: Read, Lake, Agertz, Debattista MNRA 389, 8/2008;Read, Mayer, Brooks, Governato, Lake 0902.0009

Read et al include baryons in

simulations: “A stellar/gas disc,

already in place at high redshift,

causes merging satellites to be dragged

preferentially towards the disc plane

where they are torn apart by tides.”

Dark Disk: equilibrium structure

ρD ≤ 2 × ρSHM

vlag ≃ 50 km/s with respect to Sun

vdisp ≃ 50 km/s

Threshold of XENON 10

Bruch, Read, Baudis, Lake Ap.J.696:920-923,2009 and arXiv:0811.4172



State of the art non-linear N-body simulations No baryons!



Dark halo substructure:

Haloes grow hierarchically incorporating

lumps and tidal streams from earlier

phases of structure formation.

Can the solar system be within a DM lump

or a stream?

“Via- Lactea II” simulations: “lots of

subhalos and tidal streams down to 8kp”

“fewer subhaloes in inner regions (but more

concentrated)”

Kuhlen Diemand Madau arXiv:0805.4416



Dark halo substructure: VIRGO Collaboration-Aquarius Programme

Most subhaloes are at large distances

from the galactic center, far from the

Sun. Subhaloes are more effectively

destroyed near the center

The chance of a random point close

to the Sun lying in a substructure is

< 10−4

Local v distribution smooth (no

streams) but differs from Gaussian due

to the detailed assembly history of the

halo (rates may deviate by 10%)Vogelsberger et al. 0812.0362 [astro-ph]



WIMP wind arrival direction to Earth

Standard halo

Extreme model with only streams(Sikivie)

Gelmini, Gondolo 2000



Annual Modulation: sensitive to velocity distributionStandard: Std. halo and Maxwellian distribution, max. vel in June, min. vel in Dec.

Mod. Amplitude≃ (vEarth/vSun)2 ≃ (30km/sec/300km/sec)2 ≃ 0.01

Sikivie: Extreme analytic model with ONLY DM streams Gelmini, Gondolo 2000

Right: with just one stream Freese, Gondolo, Newberg 2003



Direct DM Searches: Many experiments!



Direct DM Searches:Fig. from KIMS



WIMP vs. photons Many experiments!

• Single Channel Techniques:-Ionization (Ge, Si, CdTe): IGEX, HDMS, GENIUS, TEXONO, CoGeNT

-Scintillation (NaI, Xe, Ar, Ne, CsI): DAMA (2 keVee), NAID, DEAP, CLEAN, XMASS,

KIMS

-Phonons (Ge, Si, Al2O3, TeO2): CRESST-I (0.6 keV), Cuoricino, CUORE (5 keV)

-Threshold detectors: PICASSO (bubbles of C4F10),

COUPP (superheated bubble chamber)

• Hybrid detector techniques for discrimination:-Ionization + Phonons (Ge, Si): CDMS, SuperCDMS, EDELWEISS, EURECA

-Ionization + Scintillation(Xe, Ar, Ne): XENON, LUX, ZEPLIN, WARP, ArDM, XAX

-Scintillation+Phonons (CaWO4, Al2O3): CREST-II

• Very promising: (Liquid) Noble-Gas Detectors act as their own veto,

up-scalable to multi tonnes



Noble Liquid detectors:

• Single-Phase: Scintillation

-XMASS - Xe (Japan, Kamioka)

-DEAP/CLEAN - Ar/Ne (US/Canada, SNOLab)

• Two-phase liquid and gas: Scintillation and ionizationBoth seen as light pulses (one delayed)

-XENON - Xe (US/Switzerland/Germany/France/

Portugal/Italy/Japan/China, LNGS)

-WARP - Ar (Italy/US, LNGS)

-ZEPLIN - Xe (UK/US, Boulby)

-LUX - Xe (US/UK, Sanford Lab- later DUSEL)

-ArDM - Ar (Switzerland/Spain/UK, Canfranc)



WIMPs vs photons

• WIMPs interact with nuclei and produce

phonons besides ionization/scintillation.

• Photons and electrons interact mostly

with atomic electrons.

In crystals: quenching factor Q= fraction of ERecoil that goes into Ionization scintillator.

QGe = 0.4, QSi = 0.25, QNa = 0.3, QI = 0.09

In liquid/gas Xe: Leff=scintillat. efficiency of WIMP relative to a 122 keV γ ≃ 0.2.

Electron-equivalent energy Eee = QE or LeffE (in keVee) = Energy deposited in e to

have the same ionization/scintillation signal



WIMPs vs photons

In CDMS (crystal)



WIMPs vs photons

In XENON (liquid Xe)



Present best bounds from CDMS and XENON 10

CDMS (Soudan Mine): 19 Ge detectors (4.75 kg) and 11 Si (1.1 kg) ZIPs in 5 towers

Rejection: ionization (Q= 0.3)-phonons and timing to discriminate surface vs bulk events

Recently 2 events

0.9 backg. expec-

ted, 612 kgday

(prior set: 0 ev.,

0.6 expected,

∼ 400 kg day)

Future: Super CDMS with 16 kg Ge



Present best bounds from CDMS and XENON 10

XENON 10 at Gran Sasso: 22 kg of L Xe (15 kg in active volume), 136 kg day

Rejection: Prompt scintillation light (S1) - propagated light from charge drifted into gas

phase (S2)

(2-12 keVee = 4.5-27 keVr- 1800 events- in red 50%acceptance)

New bounds from Xenon 100 expected soon (100 kg active) + “Ugrade”



Best SI: CDMS Dec/09, m > 30 GeV

Right: CDMS (diamonds), ZEPLIN-II (circles), KIMS

(triangles), NAIAD (squares), PICASSO (stars), COUPP

(pluses) and SuperK (crosses)

Best SD n-only:XENON-10 May/08

WIMP Mass [GeV/c2]

SD

pur

e pr

oton

cro

ss s

ectio

n [c

m2 ]

101

102

103

10−40

10−38

10−36

10−34

WIMP Mass [GeV/c2]

SD

pur

e ne

utro

n cr

oss

sect

ion

[cm

2 ]

101

102

103

10−40

10−38

10−36

10−34



Best SD p-only bound:

COUPP at FNAL1.5 kg of CF3I, room-temperature

bubble chamber (60 Kg detector

under construction)

WIMP: single bubble,

n: multiple bubbles

and KIMS in Korea 4× 6kg CsI(Tl)-237d



Low Threshold:TEXONO (4× 5 g of Ge) and CoGent (500g of PPC Ge)PRD79:061101,2009 arXiv:1002.4703 Excess events at low mass??

10-44

10-43

10-42

10-41

10-40

10-39

10-38

10-37

10-36

1 10 102

01234567

2 3 4 5 6 7



Directional detectors: low density gas TPCsDRIFT at Boulby (CS2) and DM-TPC at MIT-WIPP (CF4)Measure direction of recoil- track reconstructed through drift of e



DAMA/LIBRA

• The DAMA collaboration, has found an annual modulation in its datacompatible with the signal expected from dark matter particles boundto our galactic halo-which has been confirmed by DAMA/LIBRA inApr/2008

• All other experiments have not found any signal from WIMPs

• Are these results compatible?

For light usual WIMPs incompatible only to the 2-3 σ level...

possibly compatible also for inelastically scattering WIMPs (IDM)...



DAMA/LIBRA 25 NaI (Tl) crystal of 9.5 kg each, 4y in LIBRA (11years total), 0.83 ton × year, 8.2σ modulation signal.

2-4 keV

Time (day)

Res

idua

ls (

cpd/

kg/k

eV) DAMA/NaI (0.29 ton×yr)

(target mass = 87.3 kg)DAMA/LIBRA (0.53 ton×yr)

(target mass = 232.8 kg)

Rate

0

2

4

6

8

10

2 4 6 8 10 Energy (keV)

Rat

e (c

pd/k

g/ke

V)



Savage,Gelmini, Gondolo, Freese JCAP 0904:010,2009

36 bins (likelihood ratio 4 param. fits

100 101 102 10310-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

MWIMP HGeVL

ΣΧ

pHp

bL

spin-independent CDMS I SiCDMS II Ge

XENON 10

Super-K

CoGeNT

TEXONO

CRESST I

DAMA H3Σ�90%Lwith channeling

DAMA H7Σ�5ΣLwith channeling

DAMA H3Σ�90%L

DAMA H7Σ�5ΣL

With channeling, light usual WIMPs,

m ≃ 7 to 10 GeV

are still a possible explanation

(in conflict with CDMS and XENON at the

2-3σ level)

100 101 102 10310-4

10-3

10-2

10-1

100

101

102

103

104

MWIMP HGeVL

ΣΧ

pHp

bL

spin-dependentHan = 0, proton onlyL CDMS I Si

CDMS II Ge

XENON 10

Super-K

CoGeNT

TEXONO

CRESST I



DAMA H3Σ�90%L

DAMA H7Σ�5ΣL

100 101 102 10310-4

10-3

10-2

10-1

100

101

102

103

104

MWIMP HGeVL

ΣΧ

nHp

bLspin-dependent

Hap = 0, neutron onlyL CDMS I SiCDMS II Ge

XENON 10

CoGeNT

TEXONO

CRESST I



DAMA H3Σ�90%L

DAMA H7Σ�5ΣL



Channeling effect: important for light WIMPs When ions move along

crystal axes and planes penetrate longer and give their energy to electrons, so Q = 1

instead of QI = 0.09 and QNa = 0.3 (Drobyshevki, 07; DAMA- Eur. Phys. J. C 53, 205-2313, 2008)

ER (keV)

frac

tion

Iodine recoils

Sodium recoils

10-3

10-2

10-1

1

0 10 20 30 40 50 60

However, here not taken into account that the recoiling nucleus starts froma lattice site (this reduces the channeling fraction) Bosognia, Gelmini, Gondolo in preparation



Other possibilities to explain the DAMA signal:

• Very tuned DM stream (aligned with Sun motion-3% of local density) marginal solution

appears for 2 to 4 GeV WIMP (very unlikely)

• Light keV mass DM particles which interact only with e?

• MeV and above mass DM particles which interact with e-bound to nuclei (not at rest)?

• Inelastic DM scattering?



Inelastic DM (IDM) Tucker-Smith, Weiner 01 and 04; Chang, Kribs, Tucker-Smith, Weiner 08;

March-Russel, McCabe, McCullough 08; Cui, Morrisey, Poland, Randall 09

In addition to the DM state χ with mass mχ there is an excited state χ∗

mχ − mχ∗ = δ ≃ 100keV

Inelastic scattering χ + N → χ∗ + N dominates over elastic.



Inelastic DM (fig from T. Schwetz)

vinelmin =

√

MER2µ2 + δ√

2MER

velmin =

√

MER2µ2

Only high-velocity DM particles have enough energy to up-scatter, and vinelmin decreases

with increasing target mass M , thus targets with high mass are favored (better I than

Ge...). Notice no low ER events.



Inelastic DM Tucker-Smith, Weiner 04 mχ = 50GeV, δ = 100keV

10 kev 50 kev 90 kev 130 kev

Recoil Energy

Rates

10 kev 50 kev 90 kev 130 kev

Spectrum in Ge

June December June

0.7

0.8

0.9

1

1.1

1.2

1.3

June December June

0.7

0.8

0.9

1

1.1

1.2

1.3

Annual modulation: elastic (dashed) and

inelastic (solid)

Leads to very different spectrum (no low ER events) The modulation of the signal is

enhanced (the number of WIMPs changes more rapidly at high v)



Inelastic DM Chang, Kribs, Tucker-Smith, Weiner 08 mχ = 50GeV, δ = 100keV

DAMA, benchmarks, vesc = 500km/s Modulated fraction, mχ = 100GeV.

A spectrum with no low ER events and larger modulation (as δ increases) fit well the

DAMA/LIBRA data



IDM Chang, Kribs, Tucker-Smith, Weiner 08



IDM benchmarks, vesc = 500km/s Chang, Kribs, Tucker-Smith, Weiner 08

XENON-dataXENON- expected spectrum

-Different spectra: IDM events expected at higher energy. Xenon, Zeplin,CRESST, may have already seen DM events and taken then for background!



IDM: fixed relative even rates for Ge, Xe, I, and W should test thisexplanation for the DAMA signal Chang, Kribs, Tucker-Smith, Weiner 08



IDM: recent bound from the CDMS collaboration

New bounds from XENON 100 expected soon...



Outlook



Outlook: plenty of direct detection data to come!In the near future:

- Xenon 100 and Upgrade at Gran Sasso: almost finished 100 kg fiducial mass

- SuperCDMS at Soudan: 16 kg of Ge

- WARP at Gran Sasso: 3.2 kg L Ar prototype-140 kg under construction

- EDELWEISS at LSM (Modane-Frejus): 10 kg NbSi Ge

- LUX for DUSEL: 50 kg L Xe tested at CWRU -300 L Xe (100 kg fiducial)

- ArDM at CERN: 1 ton L Ar TPC/Calorimeter prototype

- COUPP at FNAL: 60kg module under construction

- KIMS at Yangynag Undeground Lab-Korea: in 2008 12× 6kg CsI(Tl) crystals (before 4)

- CRESST at Gran Sasso: 10 kg of 33 CaWO4

-XMASS at Kamioka: 3kg fiducial of Xe- 100 kg next step?

For DAMA/LIBRA: - DAMA/LIBRA is reducing its threshold to 1 keVee

A signal in another detector with other techniques is needed to confirm a DM discovery:

XENON, KIMS, CRESST II, can test IDM, and these + COUPP, TEXONO can test light

WIMPs - KIMS (100 kg CsI) should in a few years reproduce the statistics of DAMA?



Further away:

- Directional detectors: gas TPC (DRIFT at Boulby; DM-TPC for DUSEL)

- Tonne to multi-tonne detectors: SuperCDMS 1t?, WARP 1t?, XENON 1t?, EURECA?,

XMASS?, XAX?

plenty to look-out for!



AXION

• introduced to solve the “strong CP problem” in QCDPeccei & Quinn

• “invisible axion” (ma∼6µeV(1012GeV/fa) and gall ∼ 1/fa)Kim; Shifman, Vainshtein, Zakharov (KSVZ)

Dine, Fischler, Srednicki; Zhitnitsky (DFSZ)

• pseudo-Goldstone boson (SSB of a global U(1) at scale fa)

• produced “cold” (from a condensate |~p| ≃ 0 << ma)

• axion DM could soon be detected or ruled out experimentally!

• “Invisible axion” models have two Higgs doublets (plus a singlet but ata higher scale) whose components should be found at the LHC.



AXION

Good CDMcandidate for

1µeV ≤ m ≤ 1meV



AXION

ADMX (Axion DM eXperiment)

Microwave cavity: gaγγMany experimental searches (L. Rosenberg 2010)

ADMX Phase II is starting- “definitive” search



Axions: best present bounds(Duffy et al 2006)

Axion Dark Matter eXperiment

(ADMX) uses a Sikivie microwave

cavity detector to search for aγγ

“Medium Resolution” (MR) assumes

velocity dispersion is ≤ 10−3c (axion

escape velocity is 2 × 10−3c.)

“High Resolution” (HR) uses the

possible existence of discrete flows, or

streams (smaller velocity dispersion)

in Sikivie Halo Model 97.7% CL limits

ADMX Phase II is starting- “definitive” search


Lecture 3: Direct Dark Matter Detection

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