J.D. Vergados University of Ioannina , Ioannina , Greece

H-D seminar June 10, H-D seminar June 10, 11 11

Direct Dark Matter Direct Dark Matter Detection-Detection- Directional Experiments Directional Experiments Asymmetries andAsymmetries and the Diurnal the Diurnal Variation* Variation* J.D. VergadosJ.D. Vergados University of Ioannina, Ioannina, Greece.University of Ioannina, Ioannina, Greece.

• *In collaboration with Ch. Moustakidis. *In collaboration with Ch. Moustakidis.


EVIDENCE FOR EVIDENCE FOR THE EXISTENCE OF THE EXISTENCE OF DARK MATTERDARK MATTER• Gravitational effects around galaxiesGravitational effects around galaxies•Gravitational Lensing. Gravitational Lensing.

The observation of the collision of two The observation of the collision of two galaxy clusters (to-day 3.5galaxy clusters (to-day 3.5101099 ly ly away from us, 2away from us, 2101066 ly apart) ly apart)

•Cosmological Observations (confirmed Cosmological Observations (confirmed by the recent WMAP5 ; together with by the recent WMAP5 ; together with dark energy) dark energy)

Slicing the Pie of the CosmosSlicing the Pie of the Cosmos WMAP3:WMAP3: ΩΩCDM CDM ==0.240.24±±0.02,0.02, ΩΩΛΛ ==0.720.72±±0.040.04,, ΩΩb b ==0.0.040422±±0.00.00303To-day (T=13.6 billion y old)To-day (T=13.6 billion y old) T=380000 y oldT=380000 y old



Dark Matter exists! Dark Matter exists! What is the nature of dark matter?What is the nature of dark matter? It is not known. However:It is not known. However:• It possesses gravitational interactions It possesses gravitational interactions ( (from the rotation from the rotation

curves)curves)• No other long range interaction is allowed. Otherwise it No other long range interaction is allowed. Otherwise it

would have formed “would have formed “atomsatoms” and , hence, stars etc. So ” and , hence, stars etc. So It isIt is electrically neutral electrically neutral • It does not interactIt does not interact strongly strongly (if it did, it should have already (if it did, it should have already

been detected)been detected)• It may (hopefully!) posses some very weak interactionIt may (hopefully!) posses some very weak interaction This will depend on the assumed theory This will depend on the assumed theory WIMPs (Weakly Interacting Massive Particles)WIMPs (Weakly Interacting Massive Particles)• Such an interaction may be exploited Such an interaction may be exploited for its direct detectionfor its direct detection• The smallness of the strength of such an interaction and its The smallness of the strength of such an interaction and its

low energylow energy makes its makes its direct detection extremely difficultdirect detection extremely difficult. . So we have to seek for its special signatures, if any.So we have to seek for its special signatures, if any.


DARK MATTER (WIMP) DARK MATTER (WIMP) CANDIDATESCANDIDATES• The axionThe axion:: 1010-6 -6 eVeV<<mma a <10<10-3 -3 eVeV• The neutrinoThe neutrino: : It is not dominant. It is not cold, not It is not dominant. It is not cold, not CDMCDM..• Supersymmetric particlesSupersymmetric particles.. Four possibilitiesFour possibilities:: ii) ) s-s-νετρίνονετρίνο: : Not favored on the basis of results of Not favored on the basis of results of

underground experiments and accelerator experimentsunderground experiments and accelerator experiments (LEP)(LEP) ii) ii) GravitinoGravitino: : Interesting possibility, but not directly detectableInteresting possibility, but not directly detectable iiiiii) ) ΑΑxinoxino: : Interesting, but not directly detectableInteresting, but not directly detectable iv)iv) AA Majorana fermionMajorana fermion, , the the neutralino neutralino oror LSP LSP ((The lightest supersymmetric particleThe lightest supersymmetric particle):): A linear A linear combination of the 2 neutral gauginos and the 2 combination of the 2 neutral gauginos and the 2 neutral Higgsinos. neutral Higgsinos. MOST FAVORITE CANDIDATE!MOST FAVORITE CANDIDATE!• Particles from Universal Extra Dimension Theories (e.g. Particles from Universal Extra Dimension Theories (e.g.

Kaluza-Klein WIMPs)Kaluza-Klein WIMPs)• The Lightest Technibaryon, LTB (Gudnason-Kouvaris-Sannino)The Lightest Technibaryon, LTB (Gudnason-Kouvaris-Sannino)• Secluded Dark matter (to explain excess eSecluded Dark matter (to explain excess e++,e,e-- in cosmic in cosmic

rays), Ioannina group (2009), T. Schwetz (2009)) rays), Ioannina group (2009), T. Schwetz (2009))

WIMP-Nucleus Elastic WIMP-Nucleus Elastic scatteringscattering



AI. The standard AI. The standard (non directional)(non directional) event rateevent rate for the coherent modefor the coherent mode• The number of events during time t is given byThe number of events during time t is given by::

Where:Where:• ttcoh ,coh , h hcoh coh (modulation)(modulation) depend on nuclear physics, the WIMP mass and the velocity depend on nuclear physics, the WIMP mass and the velocity

distributiondistribution• ρ(0)ρ(0):: the local WIMP density≈0.3 GeV/cmthe local WIMP density≈0.3 GeV/cm33.. σσSS

pp,χ,χ : the WIMP-nucleon cross section. : the WIMP-nucleon cross section. It is computed in a particle model.It is computed in a particle model. It can be extractedIt can be extracted from the data from the data once once ffcoh coh (A,m(A,mχχ)) is knownis known

AI1:The coherent differential rate forAI1:The coherent differential rate for σσNN ==1010-7-7 pb and medium target (I or pb and medium target (I or Ar)Ar)Q in keVQ in keV


AI2:The total Coherent Event RateAI2:The total Coherent Event Rate ( (σσpp,χ,χ=10=10-7 -7

pb)pb)(As a function of WIMP mass in GeV)(As a function of WIMP mass in GeV)Light System (F,S etc)Light System (F,S etc)

Heavy System ( A=I, Xe etc)Heavy System ( A=I, Xe etc)


EDELEEISS (Dr Eitel) EDELEEISS (Dr Eitel) XENON100 XENON100 (prl/2010(prl/2010


AI3:Threshold effect on event AI3:Threshold effect on event rates for a medium-heavy target rates for a medium-heavy target vs WIMP massvs WIMP massEEthth=10 keV (no quenching)=10 keV (no quenching)

EEthth=10 keV (quenching)=10 keV (quenching)


AI3:Threshold effect on event AI3:Threshold effect on event rates for a light target target vs rates for a light target target vs WIMP massWIMP massEEthth=10 keV (no quenching)=10 keV (no quenching)



AII.WIMP-Nucleus scattering AII.WIMP-Nucleus scattering (both SI and SD); Modulation (both SI and SD); Modulation ignoredignored



Cross sections extracted from the Cross sections extracted from the ratesratesR(127)=R(73)=1(kg-y)R(127)=R(73)=1(kg-y)-1-1 Cannoni, Gomez and JDV, PRD Cannoni, Gomez and JDV, PRD 83(2011)07501083(2011)075010


Cross sections in a constrained Cross sections in a constrained MSSM MSSM Cannoni, Gomez and JDV, PRD Cannoni, Gomez and JDV, PRD 83(2011)07501083(2011)075010


• AA00=0, =0, μ>0μ>0• mm00 <4000 GeV <4000 GeV• mm1/21/2 <1500 GeV <1500 GeV• Blue<->tanBlue<->tanββ =10 =10• turquoise<->tan turquoise<->tan

ββ=50=50• Red: XENON100 Red: XENON100

limitlimit

Comparison of the cross Comparison of the cross sectionssections ExtractedExtracted Constrained MSSMConstrained MSSM



B: Novel approachesB: Novel approaches: : Exploitation ofExploitation of other signaturesother signatures of the reactionof the reaction• The modulation effectThe modulation effect: The seasonal, due to the : The seasonal, due to the

motion of the Earth, dependence of the rate.motion of the Earth, dependence of the rate.• Detection of other particles (electrons, X-rays), Detection of other particles (electrons, X-rays),

produced produced during the LSP-nucleus collision during the LSP-nucleus collision (it will not (it will not be discussed to-day).be discussed to-day).

• The excitationThe excitation of the nucleus (in some cases : heavy of the nucleus (in some cases : heavy WIMP, low excitation energy etc.) andWIMP, low excitation energy etc.) and detection of detection of the subsequently emitted de-excitationthe subsequently emitted de-excitation γ γ rays.rays. (it will (it will not be discussed to-day).not be discussed to-day).

•Asymmetry measurements in directional Asymmetry measurements in directional experiments experiments (the (the direction of the recoiling direction of the recoiling nucleus nucleus must also be measured)-->must also be measured)-->

• DIURNAL VARIATION.DIURNAL VARIATION.


BI: THEBI: THE MODULATION EFFECTMODULATION EFFECT(standard recoil experiments)(standard recoil experiments)• R=RR=R0 0 (1+h(1+h coscosαα) (total rate)) (total rate)• dR/dQ=(dR/dQ)dR/dQ=(dR/dQ)00+dh/dQ cos+dh/dQ cosα α or or dR/dQ=(dR/dQ)dR/dQ=(dR/dQ)00 (1+H cos (1+H cosα α ) (dif. Rate)) (dif. Rate) ((α α is the phase of the Earth; is the phase of the Earth; αα=0 around June 3nd) =0 around June 3nd) h=modulation amplitudeh=modulation amplitude.. RR00 =average rate =average rate..• The difference between the minimum and the The difference between the minimum and the

maximum is 2h or 2Hmaximum is 2h or 2H• The location of the maximum The location of the maximum depends on the sign of hdepends on the sign of h

BIa:The total modulation BIa:The total modulation amplitudeamplitude(As a function of WIMP mass in (As a function of WIMP mass in GeV)GeV)Light System (e.g. A=32, A=19)Light System (e.g. A=32, A=19) Heavy system (e.g. A=127)Heavy system (e.g. A=127)


BIb: The coherent differential mod. BIb: The coherent differential mod. rate forrate for σσNN ==1010-7-7 pb and medium target (I or pb and medium target (I or Ar)Ar)Q in keVQ in keV


BIc: The relative (differential) Modulation BIc: The relative (differential) Modulation amplitudeamplitude(As a function of (As a function of α α for various WIMP mass in for various WIMP mass in GeV) From left to right top to bottom: Q=2,4.6,8 GeV) From left to right top to bottom: Q=2,4.6,8 keV keV Heavy System (e.g. A=127, 131)Heavy System (e.g. A=127, 131) Light system (e.g. A=F, Na) Light system (e.g. A=F, Na) It is It is

a bit smallera bit smaller


BIc: The (differential) Modulation BIc: The (differential) Modulation amplitudeamplitude(As a function of (As a function of α α for various WIMP masses) for for various WIMP masses) for NaINaIFrom left to right top to bottom : Q=2,4.6,8 keVFrom left to right top to bottom : Q=2,4.6,8 keV


BII: Directional Experiments* BII: Directional Experiments* (Measuring both the energy and direction of the (Measuring both the energy and direction of the recoiling nucleus)recoiling nucleus)• We will show that the observed eventsWe will show that the observed events• will exhibit will exhibit asymmetryasymmetry due to the motion of due to the motion of

the Sunthe Sun• On top of this they will exhibit On top of this they will exhibit characteristiccharacteristic

annual modulationannual modulation due to the annual motion due to the annual motion of the Earthof the Earth

• Both of these will manifest themselves as Both of these will manifest themselves as periodicperiodic diurnal variation diurnal variation due to the rotation due to the rotation of the Earth.of the Earth.

• * DM-TPC, NEWAGE, DRIFT, MIMAC * DM-TPC, NEWAGE, DRIFT, MIMAC (Review: (Review: S. Ahlen et al, S. Ahlen et al, arXiv:0911.0323)arXiv:0911.0323)

• *Also gaseous TPC detectors (3-D reconstruction arXiv:1001.2983 (atro-ph.CO)*Also gaseous TPC detectors (3-D reconstruction arXiv:1001.2983 (atro-ph.CO)H-D seminar June 10, H-D seminar June 10, 11 11

WIMP flux,“WIMP flux,“The solar wind” (towards the The solar wind” (towards the Cygnus constellation),Cygnus constellation), Spergel (88), Spergel (88), vergados (02), Morgan-Green-Spooner (04).vergados (02), Morgan-Green-Spooner (04). Flux variatioFlux variationn


Morgan-Green-Spooner (04).Morgan-Green-Spooner (04).

BII: The directional event rate BII: The directional event rate (The direction of recoil is (The direction of recoil is observed)observed)• The calculation will proceed in two steps:The calculation will proceed in two steps:• A) Evaluation of the event rate as a function of (A) Evaluation of the event rate as a function of (Θ,Φ) Θ,Φ) taking taking

the sun’s direction of motion as polar axis (polar angle the sun’s direction of motion as polar axis (polar angle Θ Θ)) Φ Φ is measured on a plane perpendicular to the sun’s velocity is measured on a plane perpendicular to the sun’s velocity

from x (radially out of the galaxyfrom x (radially out of the galaxy. The direction of recoil is. The direction of recoil is

- - due to the Sun’s motion due to the Sun’s motion the rate dependsthe rate depends only on only on Θ Θ --> --> Asymmetry.Asymmetry.

-due to the Earth’s annual motion it will show a -due to the Earth’s annual motion it will show a modulation, modulation, dependent on (dependent on (Θ,Φ)Θ,Φ) with very characteristic signature. with very characteristic signature.

• B) The direction of observation fixed in the labB) The direction of observation fixed in the lab.. --ThenThen Diurnal variation Diurnal variation due to the rotation of the Earthdue to the rotation of the Earth


Comparison of the usual (R) and Comparison of the usual (R) and directional directional (dR/d(dR/dΩΩ) ) total rates total rates


BNL Seminar June 15/2009BNL Seminar June 15/2009

Signatures in Directional Signatures in Directional ExperimentsExperiments -These experiments will attempt to measure both -These experiments will attempt to measure both

the energy and the direction of recoiling nucleus.the energy and the direction of recoiling nucleus.- To simplify our discussion we will consider the To simplify our discussion we will consider the

rate in a given direction divided by the Standard rate in a given direction divided by the Standard raterate

- This will depend onThis will depend on• The WIMP Mass (the only particle parameter The WIMP Mass (the only particle parameter

left). This will be treated as a free parameterleft). This will be treated as a free parameter• The velocity distribution of WIMP’s in our galaxyThe velocity distribution of WIMP’s in our galaxy• The nuclear form factorThe nuclear form factor


The directional event rateThe directional event rate(The direction of recoil is (The direction of recoil is observed)observed)• The event rate as a function of the The event rate as a function of the direction angles (direction angles (Θ,Φ)Θ,Φ) iis:s: ddRR/d/dΩΩ=(=(κ/2π)κ/2π)RR00[1+h[1+hmmcos(cos(αα++αα00))]], , κ=κ=t /tt /tdirdir• RR00 is the average usual (is the average usual (non-dirnon-dir) rate) rate• αα the phase of the Earth the phase of the Earth (as usual)(as usual)• hh mm is the is the total total modulation amplitudemodulation amplitude (it strongly depends on (it strongly depends on

the direction of observation):the direction of observation): h hmmcos(cos(αα++αα00)=h)=hcccoscosαα +h +hsssinsinαα• αα00 is the is the shift in the phase of the Earthshift in the phase of the Earth (it strongly depends (it strongly depends

on the direction of observation)on the direction of observation)• κ/2πκ/2π is the is the reduction factorreduction factor (it depends on the direction of (it depends on the direction of

observation , but it is independent of the angle observation , but it is independent of the angle ΦΦ). This factor ). This factor becomesbecomes κκ,, after integrating over after integrating over ΦΦ. . ddR/dR/dΩ->Ω-> d dR/d(cosR/d(cosΘΘ))

• κκ,, hhm m and and ααm m depend only slightly on the particle (e.g. SUSY) depend only slightly on the particle (e.g. SUSY) parameters and the reduced mass parameters and the reduced mass μμrr

The parameter The parameter κ κ vs vs ΘΘ (Directional rates with Ch. (Directional rates with Ch. Moustakidis)Moustakidis)


The modulation amplitudes vs The modulation amplitudes vs ΦΦ for mfor mχχ = =10 10 GeV for a light GeV for a light targettarget For For 1919FF


For For 112727ΙΙ

The total modulation amplitude vs The total modulation amplitude vs ΦΦ for mfor mχχ = =10 10 GeV for a light GeV for a light targettargetThe amplitudeThe amplitude The shift in the locationThe shift in the location


Modulation vs the phase of the Modulation vs the phase of the earth.earth.


The modulation amplitudes vs The modulation amplitudes vs ΦΦ for mfor mχχ = =10 10 GeV for a heavy GeV for a heavy targettarget For For 1919FF


For For 112727ΙΙ

The total modulation amplitude vs The total modulation amplitude vs ΦΦ for mfor mχχ = =10 10 GeV for a heavy GeV for a heavy targettargetThe amplitudeThe amplitude The shift in phaseThe shift in phase




The Diurnal variation of the The Diurnal variation of the rate in Directional Experimentsrate in Directional Experiments• We have seen that:We have seen that:• the parameters the parameters κκ and h and hm m depend on the direction of depend on the direction of

observation relative to the sun’s velocityobservation relative to the sun’s velocity• In a directional experiment the In a directional experiment the direction of direction of

observation is fixed with respect to the earthobservation is fixed with respect to the earth..• Due to the rotation of the Earth during the day this Due to the rotation of the Earth during the day this

direction points direction points in different parts of the galactic sky.in different parts of the galactic sky. So the angles So the angles (Θ,Φ) (Θ,Φ) change and change and the rate becomes the rate becomes time dependenttime dependent. . It will thus show a periodic behaviorIt will thus show a periodic behavior..


Schematic time dependence of the Schematic time dependence of the raterateas may be seen in a directional as may be seen in a directional experiment.experiment. Battat et al (IJMP A, 2009)Battat et al (IJMP A, 2009)


From the celestial From the celestial ((αα=ascention=ascention,δ,δ=inclination=inclination)) to galactic to galactic coordinatescoordinates


Diurnal Variation of the rate (Diurnal Variation of the rate (κκ)) 1919F Target & Fully DirectionalF Target & Fully Directional WIMP MASS 10 GeVWIMP MASS 10 GeV WIMP MASS 50 GeVWIMP MASS 50 GeV


Diurnal Variation of the rate Diurnal Variation of the rate ((κκ)) Iodine Target & Fully Iodine Target & Fully DirectionalDirectional WIMP MASS 10 GeVWIMP MASS 10 GeV WIMP MASS 100 GeVWIMP MASS 100 GeV


Diurnal Variation of the rate Diurnal Variation of the rate ((κκ))CSCS22 Target& partly Target& partly DirectionalDirectionalWIMP MASS 10 GeVWIMP MASS 10 GeV WIMP MASS 100 GeVWIMP MASS 100 GeV



CONCLUSIONS: Non-directionalCONCLUSIONS: Non-directional The The modulation amplitude hmodulation amplitude h : :• is small, less is small, less than 3%,than 3%, and depends on the LSP mass. and depends on the LSP mass. • ItIt depends on the velocity distributiondepends on the velocity distribution• Its Its signsign is also is also uncertain. it is positive for light systems, but uncertain. it is positive for light systems, but

it may become negative it may become negative for intermediate and heavy nuclei for intermediate and heavy nuclei and heavy WIMPsand heavy WIMPs (for both M-B and Realistic velocity (for both M-B and Realistic velocity distributions in the case of heavy WIMPS). distributions in the case of heavy WIMPS). Can this be Can this be exploited to extract the WIMP mass?exploited to extract the WIMP mass?

• It may It may increaseincrease as the energy threshold increases , but as the energy threshold increases , but at at the expense of the number of counts.the expense of the number of counts.

• It shows similar behavior in the case of the spin cross It shows similar behavior in the case of the spin cross section.section.

• The DAMA experiment The DAMA experiment maybe consistentmaybe consistent with the other with the other experiments if the WIMP is very light or experiments if the WIMP is very light or if the spin if the spin interaction dominatesinteraction dominates. Then their contour plot should . Then their contour plot should move to larger nucleon cross sections (the spin proton move to larger nucleon cross sections (the spin proton cross section).cross section).

Prospects for exclusion plots Prospects for exclusion plots (WIMP mass (WIMP mass in GeV)in GeV)



CONCLUSIONS: Non modulated CONCLUSIONS: Non modulated rate in directionalrate in directional ExperimentsExperiments• A useful parameter is A useful parameter is κ κ the reduction factor the reduction factor relative to the relative to the

non directional ratenon directional rate• κκ strongly depends on the polar angle strongly depends on the polar angle Θ Θ (( the angle between the angle between

the direction of observation and the sun’s velocity) the direction of observation and the sun’s velocity) • κκ≈≈1 in the most favored direction (1 in the most favored direction (Θ≈π Θ≈π in in ΜΒ)ΜΒ)• As the Earth rotates the detector samples a different angle As the Earth rotates the detector samples a different angle ΘΘ--

>>• The The event rateevent rate ((κκ ) exhibits a periodic variation with a period ) exhibits a periodic variation with a period

of 24 hours.of 24 hours.• The form of the variation depends on the WIMP massThe form of the variation depends on the WIMP mass• The amplitude of The amplitude of this variation depends on the inclination of this variation depends on the inclination of

the line of observation.the line of observation. It can be quite large. It can be quite large.• The variation persists, even if the sense of direction is not The variation persists, even if the sense of direction is not

known. Then, however, the effect is smaller known. Then, however, the effect is smaller


CONCLUSIONS : The CONCLUSIONS : The modulation in directionalmodulation in directional Experiments Experiments (preliminary)(preliminary)• The modulation amplitude in the most favored directionThe modulation amplitude in the most favored direction

((κκ≈≈1 1 ) is ) is 0.05<h0.05<hmm<0.15<0.15 (bigger than in non- directional (bigger than in non- directional case) depending on the WIMP mass.case) depending on the WIMP mass.

• In plane perpendicularIn plane perpendicular to the sun’s velocity (to the sun’s velocity (κκ≈≈0.3) h0.3) hmm is is much bigger: much bigger:

• | h| hmm| | ≈≈0.250.25 (50% difference between maximum and (50% difference between maximum and minimum).minimum).

• Both its magnitude and its sign depend on the azymouthal Both its magnitude and its sign depend on the azymouthal angle angle ΦΦ

• We are currently computing its time variation. Preliminary We are currently computing its time variation. Preliminary results show results show a weak but spectacular signal a weak but spectacular signal (it cannot be (it cannot be mimicked by other seasonal effects)mimicked by other seasonal effects)

..


COMMON WISDOM!COMMON WISDOM!


•THE ENDTHE END



Slicing the Pie of the CosmosSlicing the Pie of the Cosmos WMAP3:WMAP3: ΩΩCDM CDM ==0.240.24±±0.02,0.02, ΩΩΛΛ ==0.720.72±±0.040.04,, ΩΩb b ==0.0.040422±±0.00.00303


What I will say applies to:What I will say applies to:ALL DARK MATTER (WIMP) ALL DARK MATTER (WIMP) CANDIDATESCANDIDATES• The axionThe axion:: 1010-6 -6 eVeV<<mma a <10<10-3 -3 eVeV• The neutrinoThe neutrino: : It is not dominant. It is not cold, not It is not dominant. It is not cold, not CDMCDM..• Supersymmetric particlesSupersymmetric particles.. Four possibilitiesFour possibilities:: ii) ) s-s-νετρίνονετρίνο: : Excluded on the basis of results of underground Excluded on the basis of results of underground

experiments and accelerator experimentsexperiments and accelerator experiments (LEP)(LEP) ii) ii) GravitinoGravitino: : Interesting possibility, but not directly detectableInteresting possibility, but not directly detectable iiiiii) ) ΑΑxinoxino: : Intersting, but not directly detectableIntersting, but not directly detectable iv)iv) AA Majorana fermionMajorana fermion, , the the neutralino neutralino oror LSP LSP ((The lightest supersymmetric particleThe lightest supersymmetric particle):): A linear A linear combination of the 2 neutral gauginos and the 2 combination of the 2 neutral gauginos and the 2 neutral Higgsinos. neutral Higgsinos. MOST FAVORITE CANDIDATE!MOST FAVORITE CANDIDATE!• Particles from Universal Extra Dimension Theories (e.g. Particles from Universal Extra Dimension Theories (e.g.

Kaluza-Klein WIMPs)Kaluza-Klein WIMPs)• The Lightest Technibaryon, LTB (Gudnason-Kouvaris-Sannino)The Lightest Technibaryon, LTB (Gudnason-Kouvaris-Sannino) • Secluded Dark matter (to explain excess eSecluded Dark matter (to explain excess e++,e- in cosmic rays) ,e- in cosmic rays)


Dark Matter exists! Dark Matter exists! What is the nature of dark matter?What is the nature of dark matter? It is not known. However:It is not known. However:• It possesses gravitational interactions It possesses gravitational interactions ( (from the rotation from the rotation

curves)curves)• No other long range interaction is allowed. Otherwise it No other long range interaction is allowed. Otherwise it

would have formed “would have formed “atomsatoms” and , hence, stars etc. So ” and , hence, stars etc. So It isIt is electrically neutral electrically neutral • It does not interactIt does not interact strongly strongly (if it did, it should have already (if it did, it should have already

been detected)been detected)• It may (hopefully!) posses some very weak interactionIt may (hopefully!) posses some very weak interaction This will depend on the assumed theory This will depend on the assumed theory WIMPs (Weakly Interacting Massive Particles)WIMPs (Weakly Interacting Massive Particles)• Such an interaction may be exploited Such an interaction may be exploited for its direct detectionfor its direct detection• The smallness of the strength of such an interaction and its The smallness of the strength of such an interaction and its

low energylow energy makes its makes its direct detection extremely difficultdirect detection extremely difficult. . So we have to seek for its special signatures, if any.So we have to seek for its special signatures, if any.


NON RECOIL NON RECOIL MEASUREMENTSMEASUREMENTS• (a) Measurement of ionization (a) Measurement of ionization

electrons produced directly during the electrons produced directly during the WIMP-nucleus collisionsWIMP-nucleus collisions

• (b) Measurement of hard X-rays (b) Measurement of hard X-rays following the de-excitation of the atom following the de-excitation of the atom in (a)in (a)

• (c) Excitation of the Nucleus and (c) Excitation of the Nucleus and observation of the de-excitation observation of the de-excitation γγ rays rays


Relative rate for electron Relative rate for electron ionizationionization (there are (there are Z electronsZ electrons in an in an atom!)atom!)


Detection ofDetection of hard X-rayshard X-rays• After the ionization there is a probability for a After the ionization there is a probability for a K K

or L holeor L hole• This hole de-excites via This hole de-excites via emitting X-raysemitting X-rays or or

Auger electronsAuger electrons..• the the fraction of X-rays per recoilfraction of X-rays per recoil is: is: σσX(nX(nℓℓ) ) //σσr r = b= bnlnl((σσnnℓℓ//σσrr)) with with σσnnℓℓ//σσr r the relative the relative ionization rateionization rate per orbit and per orbit and bbnnℓℓ the the

fluorescence ratiofluorescence ratio (determined experimentally)(determined experimentally)


The K X-ray BR in WIMP interactions in The K X-ray BR in WIMP interactions in 132 132 XeXe for masses: for masses: LL30GeV30GeV, , MM100GeV100GeV, , HH300GeV300GeV


Excitation of the nucleus:Excitation of the nucleus:The average WIMP energy is:The average WIMP energy is:•<T<Tχχ>>≈≈40 40 keV nkeV n2 2 (m(mχχ/100GeV)/100GeV)•TTχχ,max,max≈≈ 215215 keV nkeV n2 2 (m(mχχ/100GeV)./100GeV). Thus Thus• mmχχ =500GeV, n=2 =500GeV, n=2

<T<Tχχ>>≈≈0.8 MeV, 0.8 MeV, TTχχ,max,max≈≈ 4 MeV4 MeV•So excitation of the nucleusSo excitation of the nucleus appears appears

possible in exotic models with very heavy possible in exotic models with very heavy WIMPsWIMPs


Unfortunately,Unfortunately,Not all available energy is Not all available energy is exploitableexploitable!!• For ground to ground transitions (qFor ground to ground transitions (qmomentum, Q momentum, Q energy) energy)

• For Transitions to excited statesFor Transitions to excited states

• Both are peaked around Both are peaked around ξ=1ξ=1


The recoil energy in keV as a function of the WIMP The recoil energy in keV as a function of the WIMP velocity, in the case of A=127.velocity, in the case of A=127. Elastic scattering on the Elastic scattering on the left and transitions to the left and transitions to the ΔΔ=50 keV excited state on the =50 keV excited state on the right.right. Shown for WIMP masses in the Shown for WIMP masses in the 100100, , 200, 200, 500, 500, 10001000 and and 15001500 GeV. < GeV. <ξβ>=10ξβ>=10-3-3


The average nuclear recoil energy:The average nuclear recoil energy:A=127;A=127; Δ=Δ=50 keV (left),50 keV (left), Δ=Δ=30 keV 30 keV (right)(right)


BR for transitions to theBR for transitions to the first first excited stateexcited state at 50 keV of Iat 50 keV of I vs LSP vs LSP massmass (Ejiri; Quentin, Strottman and JDV) (Ejiri; Quentin, Strottman and JDV) Relative to nucleon recoil. Relative to nucleon recoil. Quenching not Quenching not included in the recoil included in the recoil i) i) Left Left E Eth th =0 keV ii) Right =0 keV ii) Right E Eth th =10 keV=10 keV


Techniques for direct WIMP Techniques for direct WIMP detectiondetection


Techniques for direct WIMP Techniques for direct WIMP detectiondetection


Another view (ApPEC 19/10/06)Another view (ApPEC 19/10/06)Blue Blue SUSY calculationsSUSY calculations (parameters on (parameters on top)top)


A: Conversion of the energy of A: Conversion of the energy of the recoiling nucleus into the recoiling nucleus into detectable form (light, heat, detectable form (light, heat, ionization etc.)ionization etc.)• The WIMP is non relativisticThe WIMP is non relativistic,< β>,< β>≈10≈10-3-3..

• With few exceptions, it cannot excite the nucleus. It only With few exceptions, it cannot excite the nucleus. It only scatters off elastically:scatters off elastically:

• Measuring the energy of the recoiling nucleus is extremely hardMeasuring the energy of the recoiling nucleus is extremely hard:: --Low event rateLow event rate (much less than 10 per Kg of target per year are expected) (much less than 10 per Kg of target per year are expected).. -Bothersome backgrounds-Bothersome backgrounds (the signal is not very characteristic) (the signal is not very characteristic).. --Threshold effectsThreshold effects.. --Quenching factorsQuenching factors..


If we could see Dark MatterIf we could see Dark Matter


Slicing the Pie of the CosmosSlicing the Pie of the Cosmos WMAP3:WMAP3: ΩΩCDM CDM ==0.240.24±±0.02,0.02, ΩΩΛΛ ==0.720.72±±0.040.04,, ΩΩb b ==0.0.040422±±0.00.00303

The The parameter parameter κκ vs the polar anglevs the polar angle Θ Θin the case of in the case of A=A=3232; ; mmχχ=10 =10 GeV; GeV; Symmetric M-BSymmetric M-Bdefinite sense definite sense Both sensesBoth senses


The The parameter parameter κκ vs the polar anglevs the polar angle Θ Θin the case of in the case of A=A=3232; ; mmχχ=100 =100 GeV GeV definite sense definite sense Both sensesBoth senses


The The parameter parameter κκ vs the polar anglevs the polar angle Θ Θin the case of in the case of A=127A=127; ; mmχχ=10 =10 GeV GeV definite sense definite sense Both sensesBoth senses


The The parameter parameter κκ vs the polar anglevs the polar angle Θ Θin the case of in the case of A=127A=127; ; mmχχ=100 =100 GeV GeV definite sense definite sense Both sensesBoth senses



The The parameter hparameter hmm vs the polar vs the polar angleangle Θ Θin the case of in the case of A=32A=32; ; mmχχ=100 =100 GeV GeV One sense (Left), Both senses One sense (Left), Both senses (Right)(Right)fine,fine, thick,thick, dashed <->dashed <->Φ=(0, π/2, Φ=(0, π/2, π)π)


The The phase phase ααmm vs the polar anglevs the polar anglein the case of in the case of A=32A=32; ; mmχχ=100 =100 GeV GeV One sense (Left), Both senses One sense (Left), Both senses (Right)(Right)


CONCLUSIONSCONCLUSIONS: : Electron Electron productionproduction during LSP-nucleus during LSP-nucleus collisionscollisions• During the neutralino-nucleus collisions, During the neutralino-nucleus collisions, electrons electrons

may be kicked off the atommay be kicked off the atom• Electrons can be identified Electrons can be identified easier than nuclear easier than nuclear

recoils recoils (Needed: low threshold ((Needed: low threshold (~0.25keV) ~0.25keV) TPC TPC detectors)detectors)

• The The branching ratio branching ratio for this process depends on the for this process depends on the atomic number, atomic number, thethe threshold energies threshold energies and the LSP and the LSP mass.mass.

• For a For a threshold energy of 0.25 keVthreshold energy of 0.25 keV the ionization the ionization event rate in the case of a heavy target event rate in the case of a heavy target can can exceed the rate for recoilsexceed the rate for recoils by an order of by an order of magnitudemagnitude..

• Detection of hard X-rays seams more feasibleDetection of hard X-rays seams more feasible


Prelude : Prelude : I. The standard I. The standard (non (non directional)directional) event rateevent rate for the for the coherent modecoherent mode• The number of events during time t is given byThe number of events during time t is given by::

Where:Where:• ttcoh ,coh , h hcoh coh (modulation)(modulation) depend on nuclear physics, the WIMP mass and the velocity distributiondepend on nuclear physics, the WIMP mass and the velocity distribution• ρ(0)ρ(0):: the local WIMP density≈0.3 GeV/cmthe local WIMP density≈0.3 GeV/cm33.. σσSS

pp,χ,χ : the WIMP-nucleon cross section. : the WIMP-nucleon cross section. It is computed in a particle model.It is computed in a particle model. It can be extractedIt can be extracted from the data from the data once once ffcoh coh (A,m(A,mχχ)) is knownis known

Ia:The Coherent Event Rate (Ia:The Coherent Event Rate (σσpp,χ,χ=10=10-7 -7

pb)pb)(As a function of WIMP mass in GeV)(As a function of WIMP mass in GeV)Light System (e.g. A=32)Light System (e.g. A=32)

Heavy System (e.g. A=131)Heavy System (e.g. A=131)


Ib:The time averaged event rate Ib:The time averaged event rate for a medium-heavy target vs for a medium-heavy target vs WIMP massWIMP massEEthth=10 keV (no quenching)=10 keV (no quenching)



Ic:The time averaged event rate Ic:The time averaged event rate for a light target vs WIMP massfor a light target vs WIMP massEEthth=10 keV (no quenching)=10 keV (no quenching)




Directional ExperimentsDirectional Experiments - - To simplify our discussion we will consider To simplify our discussion we will consider

the rate in a given direction divided by the the rate in a given direction divided by the Standard rateStandard rate

- This will depend on- This will depend on• The The WIMPWIMP Mass Mass (the only particle (the only particle

parameter needed). This will be treated as parameter needed). This will be treated as a free parametera free parameter

• The velocity The velocity distribution of WIMP’s distribution of WIMP’s in our in our galaxy. We will employ the MB distribution.galaxy. We will employ the MB distribution.

• The The nuclear form factornuclear form factor

From the celestial From the celestial to galactic to galactic coordinatescoordinates


The circular path in the galactic The circular path in the galactic systemsystem


III: The directional event rate III: The directional event rate (The direction of recoil is (The direction of recoil is observed)observed)• The calculation will proceed in two steps:The calculation will proceed in two steps:• A) Evaluation of the event rate as a function of (A) Evaluation of the event rate as a function of (Θ,Φ) Θ,Φ) taking taking

the sun’s direction of motion as polar axisthe sun’s direction of motion as polar axis

- - due to the Sun’s motion due to the Sun’s motion the rate dependsthe rate depends only on the polar only on the polar angle angle Θ Θ --> Asymmetry.--> Asymmetry.

-due to the Earth’s annual motion it will show a -due to the Earth’s annual motion it will show a modulation modulation dependent on (dependent on (Θ,Φ)Θ,Φ) with very characteristic signature. with very characteristic signature. Φ Φ is is measured on a plane perpendicular to the sun’s velocity from measured on a plane perpendicular to the sun’s velocity from x (radially out of the galaxy)x (radially out of the galaxy)

• B) The direction of observation fixed in the labB) The direction of observation fixed in the lab.. --ThenThen Diurnal variation Diurnal variation due to the rotation of the Earthdue to the rotation of the Earth


The The parameter parameter κκ vs the polar anglevs the polar angle Θ Θ (axial (axial symmetry)symmetry)in the case in the case mmχχ==110 0 GeV; GeV; Red line: sun’s Red line: sun’s velocityvelocity Α=32Α=32 Α=131Α=131


The The parameter parameter κκ vs the polar anglevs the polar angle Θ Θ (axial (axial symmetry)symmetry)in the case in the case mmχχ==330 0 GeV; GeV; Red line: sun’s Red line: sun’s velocityvelocity Α=32Α=32 Α=131Α=131


The The parameter parameter κκ vs the polar anglevs the polar angle Θ Θ (axial (axial symmetry)symmetry)in the case in the case mmχχ==10100 0 GeV; GeV; Red line: sun’s Red line: sun’s velocityvelocity

Α=32Α=32 Α=131Α=131


““The solar wind” The solar wind” (towards the Cygnus (towards the Cygnus constallation)constallation)Spergel (88), vergados (02), Morgan-Green-Spergel (88), vergados (02), Morgan-Green-Spooner (04). Spooner (04). Courtesy of Morgan-Green-Spooner Courtesy of Morgan-Green-Spooner (04).(04).


The parameter The parameter κ κ vs vs ΘΘ for for mmχχ==1010 GeV GeV(Directional rates with (Directional rates with Ch. Moustakidis)Ch. Moustakidis)

For For 3232ss


For For 112727ΙΙ





The rate depends on The rate depends on Θ. Θ. Θ Θ depends on time due to the depends on time due to the earth’s rotationearth’s rotation


Diurnal Variation of the rate Diurnal Variation of the rate ((κκ))Iodine Target& partly Iodine Target& partly DirectionalDirectionalWIMP MASS 10 GeVWIMP MASS 10 GeV WIMP MASS 100 GeVWIMP MASS 100 GeV






The Next step is to use The Next step is to use realisticrealisticAsymmetric Velocity Asymmetric Velocity DistributionDistribution• Obtained from Realistic Density ProfilesObtained from Realistic Density Profiles

In the Eddington Approach In the Eddington Approach • The asymmetry parameter The asymmetry parameter ββ is linked to is linked to

the angular momentum of DM fluidthe angular momentum of DM fluid• It can be fitted to an Axially Symmetric M-It can be fitted to an Axially Symmetric M-

B Velocity DistributionB Velocity Distribution


Velocity distribution obtained Velocity distribution obtained in the Eddington approachin the Eddington approachNFW Halo Density profileNFW Halo Density profile Axially symmetric M-BAxially symmetric M-B


Documents

J.D. Vergados University of Ioannina , Ioannina , Greece