Physics of Masssive Neutrinos Milos 20-24/05/08 Direct Dark Matter Searches- Can Solar neutrinos be a background? J.D. Vergados* J.D. Vergados* Cyprus

Physics of Masssive Neutrinos Physics of Masssive Neutrinos Milos 20-24/05/08 Milos 20-24/05/08

Direct Dark Matter Searches-Direct Dark Matter Searches-Can Solar neutrinos be a Can Solar neutrinos be a background?background?

J.D. Vergados*J.D. Vergados*

Cyprus Technical University (CUT), Cyprus Technical University (CUT), CyprusCyprus

* In collaboration with H. Ejiri* In collaboration with H. Ejiri


Motivation for consideringMotivation for considering Solar Neutrino Solar Neutrino backgroundbackground

• The low counting rate expected for WIMP detectionThe low counting rate expected for WIMP detection• The large number of neutrino events expected in The large number of neutrino events expected in

Supernova Neutrino Detectors.Supernova Neutrino Detectors.We have found:We have found:• For p=10 Atm, R=4m, D=10 kpc, UFor p=10 Atm, R=4m, D=10 kpc, Uν ν =0.5=0.5x10x1053 53 ergsergs• ## of eventsof events (no quenching, (no quenching, zero thresholdzero threshold)) He Ne He Ne Ar Ar Kr Kr XeXe 1.25 31.6 1.25 31.6 153153 614614 1880 1880


EVIDENCE FOR EVIDENCE FOR THE EXISTENCE OF THE EXISTENCE OF DARK MATTERDARK MATTER• Gravitational effects around galaxiesGravitational effects around galaxies• Extended X-ray sources.Extended X-ray sources.• The recent observation of the collision of The recent observation of the collision of

two galaxy clusters (to-day 3.5two galaxy clusters (to-day 3.5101099 ly ly away from us, 2away from us, 2101066 ly apart) ly apart)

• Cosmological Observations (confirmed by Cosmological Observations (confirmed by the recent WMAP3 &WMAP05) : Dark the recent WMAP3 &WMAP05) : Dark matter and dark energy dominance matter and dark energy dominance


Ia: Weighing a Galaxy!Ia: Weighing a Galaxy!• ScaleScale10 10 kpc=kpc=1000010000pc=pc=30000 30000 lyly• The rotational velocity does not fall outside the visible The rotational velocity does not fall outside the visible

galaxygalaxy!!


If we could see Dark MatterIf we could see Dark Matter


Ib: Collision of the Galaxy Clusters: 1E Ib: Collision of the Galaxy Clusters: 1E

0657-56;0657-56; OpticalOptical ((orange-orange-whitewhite)), Χ, Χ-rays-rays ((magenta, magenta, with the bullet on the with the bullet on the rightright)), , & & microlensingmicrolensing ( (blueblue >> Dark MatterDark Matter))


II: Cosmological EvidenceII: Cosmological Evidence for dark for dark mattermatter

The 3 main reasons for the Big Bang The 3 main reasons for the Big Bang Scenario:Scenario:

• The receding of GalaxiesThe receding of Galaxies (red shift) (red shift) (Hubble 1929)(Hubble 1929)

• The Microwave Background RadiationThe Microwave Background Radiation (CMBR –Penzias and Wilson 1964)(CMBR –Penzias and Wilson 1964)

• The Big Bang NucleosynthesisThe Big Bang Nucleosynthesis (BBN, 1946) (BBN, 1946)

All bear a signature of dark matterAll bear a signature of 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


Cosmological Constraints in the Cosmological Constraints in the (Ω(ΩΛΛ,Ω,Ωmm) ) Plane Plane (From M. Kowalski et (From M. Kowalski et al, asrto-ph/08)al, asrto-ph/08)


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 from the

rotation curves)rotation 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 (if it did, it should have

already been detected)already 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 for its direct

detectiondetection• The smallness of the strength of such an interaction The smallness of the strength of such an interaction

and its low energyand its low energy makes its makes its direct detection extremely direct detection extremely difficultdifficult. .


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: : Excluded on the basis of results of Excluded on the basis of results of

underground experiments and accelerator experimentsunderground experiments and accelerator experiments (LEP)(LEP)

ii) ii) GravitinoGravitino: : Not directly detectableNot directly detectable iiiiii) ) ΑΑxinoxino: : Not directly detectableNot 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-The Lightest Technibaryon, LTB (Gudnason-Kouvaris-

Sannino)Sannino)


A: SUSY MODELSA: SUSY MODELS

• The most favorable candidate is the The most favorable candidate is the neutralino neutralino (a Majorana Fermion)(a Majorana Fermion)

• The rates predicted depend on The rates predicted depend on the choice the choice of the parametersof the parameters in the SUSY allowed in the SUSY allowed parameter space.parameter space.

• Detectable ratesDetectable rates near the present near the present experimental goals are predicted to be experimental goals are predicted to be possible, but unlikely.possible, but unlikely.

• One may use the available limits to One may use the available limits to constrain the nucleon cross section.constrain the nucleon cross section.


A SUSY CADIDATE- the LSPA SUSY CADIDATE- the LSP(R-parity conservation)(R-parity conservation)

• Allowed parameter space: Allowed parameter space: Universality at GUT scaleUniversality at GUT scale: : - One mass - One mass mm00 for the scalarsfor the scalars

-One mass -One mass mm1/2 1/2 for the fermions for the fermions - -TanTanββ, , the ratio of vacuum the ratio of vacuum expectation values of the expectation values of the

Higss HHigss Hu u ,H,Hd d ,, i.e. <vi.e. <vuu>/ <v>/ <vdd> > -The cubic coupling -The cubic coupling AA0 0 (or m (or mtt)) -The -The sign of sign of μμ, , in in μμHHu u HHdd

• These parameters are constrained via the These parameters are constrained via the renormalization group equationsrenormalization group equations from the observable from the observable low energy quantities (all are related to the above five low energy quantities (all are related to the above five parameters). (see, parameters). (see, e.g.,: Ellis, Arnowitt, Nath, Bottino, Lazarides, Munoz, e.g.,: Ellis, Arnowitt, Nath, Bottino, Lazarides, Munoz, Gomez and their collaborators)Gomez and their collaborators)


B. Universal Extra Dimension B. Universal Extra Dimension TheoriesTheories (e.g. Servant et al) (e.g. Servant et al)

• Kaluza-Klein Theories: Kaluza-Klein Theories: A tower of new A tower of new particlesparticles

• Postulate a discreet symmetry: Postulate a discreet symmetry: K-K parityK-K parity• The even modes (ordinaryThe even modes (ordinary particles) have particles) have

K-K parity +1 K-K parity +1 • The odd modes (exotic) have K-K parity -1The odd modes (exotic) have K-K parity -1• The lightest odd mode is absolutely stableThe lightest odd mode is absolutely stable• The interactions of the new particles are The interactions of the new particles are the the

same with those of SMsame with those of SM• Essentially only the particle’s mass is unknown Essentially only the particle’s mass is unknown

parameterparameter


LSP Velocity DistributionsLSP Velocity Distributions• Conventional:Conventional: Isothermal models Isothermal models• (1) Maxwell-Boltzmann(1) Maxwell-Boltzmann (symmetric or axially symmetric) (symmetric or axially symmetric) with characteristic velocity equal to the sun’s velocity with characteristic velocity equal to the sun’s velocity

around the center of the galaxy, around the center of the galaxy, υυ ΜΒΜΒ= = υυ0 0 = 220 km/s, = 220 km/s,

and escape velocity and escape velocity υυesc esc =2.84=2.84υυ00 put in by hand. put in by hand.• (2)(2) Modification of M-B characteristic velocityModification of M-B characteristic velocity υ υΜΒ ΜΒ following following

thethe interaction of dark matter with dark energy:interaction of dark matter with dark energy: υυΜΒΜΒ == nnυυ0 0 , , υυesc esc =n2.84 =n2.84 υυ00 ,, n>1n>1 (Tetradis, Feassler and JDV )(Tetradis, Feassler and JDV )• Adiabatic models employingAdiabatic models employing Eddington’s approachEddington’s approach: : ρρ((rr))ΦΦ((rr) ) f(f(r,vr,v) (JDV-Owen)) (JDV-Owen)• Realistic axially symmetric velocity distributions obtained via Realistic axially symmetric velocity distributions obtained via

simulations simulations Tsallis type functions (Host, Hansen and JDV) Tsallis type functions (Host, Hansen and JDV)• Other non-thermal modelsOther non-thermal models:: Caustic ringsCaustic rings (Sikivie , JDV), WIMP’s in bound orbits etc (Sikivie , JDV), WIMP’s in bound orbits etc Sgr Dwarf galaxySgr Dwarf galaxy, anisotropic flux, (Green & Spooner), anisotropic flux, (Green & Spooner)


Principles of WIMP Detection Principles of WIMP Detection (WIMP: Weakly Interacting massive (WIMP: Weakly Interacting massive particle)particle)


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..


TheThe event rateevent rate for the coherent for the coherent modemode

• The number of events during time t is given byThe number of events during time t is given by::

Where:Where:• t depends on nuclear physics, the WIMP mass and the velocity distributiont depends 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..• μμr r is the WIMP-Nucleus reduced massis the WIMP-Nucleus reduced mass• 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


The coherent differential rateThe coherent differential rate kg- kg-y/keV y/keV for mfor mχ χ =100 =100 GeV (intermediate GeV (intermediate target (target (131131Xe))Xe))


The coherent differential rateThe coherent differential rate kg- kg-y/keV y/keV for mfor mχ χ =100 =100 GeV (light target GeV (light target ((3232S))S))


The coherent total rateThe coherent total rate kg-y kg-y as a as a function of the WIMP mass (intermediate function of the WIMP mass (intermediate target (target (131131Xe))Xe))


The coherent total rateThe coherent total rate kg-y for kg-y for σ=10σ=10-9 -9

pbpb top intermediate target (top intermediate target (131131Xe), Bottom: light Xe), Bottom: light target target 3232SS


Novel approachesNovel approaches: : Exploitation Exploitation ofof other signaturesother signatures of the of the reactionreaction• The modulation effectThe modulation effect: The seasonal, due to : The seasonal, due to

the motion of the Earth, dependence of the the motion of the Earth, dependence of the rate.rate.

• The excitationThe excitation of the nucleus (in some cases , of the nucleus (in some cases , heavy WIMP etc, that this is realistic) andheavy WIMP etc, that this is realistic) and detection of the subsequently emitted de-detection of the subsequently emitted de-excitationexcitation γ γ rays.rays.

• Asymmetry measurements in directional Asymmetry measurements in directional experiments experiments (the (the direction of the recoilingdirection of the recoiling nucleusnucleus must also be measured). must also be measured).

• Detection of other particles (electrons, X-rays), Detection of other particles (electrons, X-rays), produced during the LSP-nucleus collisionproduced during the LSP-nucleus collision


The bothersome backgroundsThe bothersome backgrounds

• Anyway it will be necessary to detect nuclear Anyway it will be necessary to detect nuclear recoilsrecoils

• At this level, processes which are ordinarily At this level, processes which are ordinarily harmless can become a serious background, harmless can become a serious background, since since they have the same signature with the good they have the same signature with the good eventsevents. .

• One must see some recoil events. The One must see some recoil events. The background is minimized but still there.background is minimized but still there.

• One such background may come from solar One such background may come from solar neutrinos.neutrinos.


The differential elastic The differential elastic neutrino-nucleus cross sectionneutrino-nucleus cross section

• MMV V and Mand MA A are the nuclear matrix elements are the nuclear matrix elements associated with the vector and axial current associated with the vector and axial current and Tand TA A is the nuclear recoil energy.is the nuclear recoil energy.


The coherent (due to neutrons) The coherent (due to neutrons) neutrino nucleus elastic scattering neutrino nucleus elastic scattering


Kinematical relations Kinematical relations (for any target) (for any target)


The maximum nuclear recoil The maximum nuclear recoil energy energy as a function of Eas a function of Eνν


The maximum nuclear recoil The maximum nuclear recoil energy as a function of the WIMP energy as a function of the WIMP velocity velocity for the indicated values for the indicated values of (A, mof (A, mχχ))


The average nuclear recoil energy The average nuclear recoil energy as a function of the WIMP mass as a function of the WIMP mass for for the indicated values of Athe indicated values of A


The Solar neutrino spectrumThe Solar neutrino spectrum


The Boron solar neutrinoThe Boron solar neutrino spectrum spectrum (top) and flux (bottom, Log-log (top) and flux (bottom, Log-log plot)plot)


The elastic neutrino-nucleus cross section (cmThe elastic neutrino-nucleus cross section (cm2 2

keVkeV-1-1)) for an intermediate target (top) and a light for an intermediate target (top) and a light target (bottom)target (bottom)


Event rates for nuclear recoils:Event rates for nuclear recoils: (a) for WIMP induced and(a) for WIMP induced and (b) Boron solar neutrino (b) Boron solar neutrino inducedinduced


The Quenching factor:The Quenching factor:

• The quenching factor for a given detector The quenching factor for a given detector is the ratio of the signal height of a nuclear is the ratio of the signal height of a nuclear recoil event divided by the corresponding recoil event divided by the corresponding one of an electron with the same energy.one of an electron with the same energy.

• The quenching factor must be determined The quenching factor must be determined experimentally for a given detector.experimentally for a given detector.

• In our calculation it was adequate to In our calculation it was adequate to multiply the energy by an energy multiply the energy by an energy dependent dependent quenching factor given by a quenching factor given by a Lidhard type theory.Lidhard type theory.


The Quenching factor:The Quenching factor: A=131 (top)A=131 (top) and and A=32 A=32 (bottom)(bottom)


Due to quenching the rate is not Due to quenching the rate is not affected but the energy is shifted affected but the energy is shifted downwards (thick line). Target downwards (thick line). Target A=131A=131


Due to quenching the rate is not Due to quenching the rate is not affected but the energy is shifted affected but the energy is shifted downwards (thick line). Target downwards (thick line). Target A=32A=32


The solar neutrino differential rate: The solar neutrino differential rate: A=32 target.A=32 target. For threshold energy 1 keV For threshold energy 1 keV the detectable portion is above the thin line the detectable portion is above the thin line (no quenching) and the thick line (no quenching) and the thick line (quenching)(quenching)


The solar neutrino differential rate: The solar neutrino differential rate: A=131 target.A=131 target. For threshold energy 1 keV For threshold energy 1 keV the detectable portion is above the thin line the detectable portion is above the thin line (no quenching) and the thick line (no quenching) and the thick line (quenching)(quenching)


The WIMP differential rate: The WIMP differential rate: WIMP mass 100 GeV & A=131 target.WIMP mass 100 GeV & A=131 target. For threshold energy 2 keV the detectable For threshold energy 2 keV the detectable portion is above the thin line (no portion is above the thin line (no quenching) and the thick line (quenching)quenching) and the thick line (quenching)


The ratio of the event rates The ratio of the event rates R(QR(Qthth)/R(Q)/R(Qthth=0)=0) as a function of Q as a function of Qth th ((in kev)in kev) for for

WIMP mass of 100 GeV and A=131WIMP mass of 100 GeV and A=131. . No No quenching (thin line)quenching (thin line) Quenching (thick line)Quenching (thick line)



WIMP mass of 100 GeV and A=32WIMP mass of 100 GeV and A=32. . No No quenching (thin line)quenching (thin line) Quenching (thick line)Quenching (thick line)



boron solar neutrinos and A=131boron solar neutrinos and A=131. . No No quenching (thin line)quenching (thin line) Quenching (thick line)Quenching (thick line)



boron solar neutrinos and A=32boron solar neutrinos and A=32. . No No quenching (thin line)quenching (thin line) Quenching (thick line)Quenching (thick line)


Conclusions: Conclusions: No experiment has No experiment has directly seen any WIMP events. directly seen any WIMP events. The expected event rate is very The expected event rate is very low. So..low. So..• The coherent WIMP event rate for a target of 1 Kg of The coherent WIMP event rate for a target of 1 Kg of

mass in the case of a heavy WIMP increases with A.mass in the case of a heavy WIMP increases with A.• The coherent neutrino event rate for a target of 1 Kg of The coherent neutrino event rate for a target of 1 Kg of

mass varies as Nmass varies as N22/A. The recoil energy decreases with A./A. The recoil energy decreases with A.• Both rates decrease as the threshold energy increases, Both rates decrease as the threshold energy increases,

but the solar neutrino event rate does much more so.but the solar neutrino event rate does much more so.• Both are sensitive to quenching, but its effect on the Both are sensitive to quenching, but its effect on the

solar neutrino event rate is much more dramatic.solar neutrino event rate is much more dramatic.• The WIMP event rate is sensitive to the nuclear form The WIMP event rate is sensitive to the nuclear form

factor, but the solar neutrino event rate is not.factor, but the solar neutrino event rate is not.


ConclusionsConclusions

• The boron neutrinos are not a serious The boron neutrinos are not a serious background to WIMP detection, unless the background to WIMP detection, unless the event rate turns out to be event rate turns out to be

less than 1 event per ton per less than 1 event per ton per yearyear

• Even below this level one can minimize the Even below this level one can minimize the neutrino background by a judicious choice of neutrino background by a judicious choice of the target and exploiting the energy cut offthe target and exploiting the energy cut off


Conclusions: Directional Conclusions: Directional experimentsexperiments

• The neutrino background gives an The neutrino background gives an entirely different signature compared to entirely different signature compared to the WIMP signal in Directional the WIMP signal in Directional Experiments*. In such experiments this Experiments*. In such experiments this background can be discarded at any levelbackground can be discarded at any level

* Experiments in which the direction of the * Experiments in which the direction of the recoiling nucleus is also observed.recoiling nucleus is also observed.


•THE ENDTHE END


Techniques for direct WIMP Techniques for direct WIMP detectiondetection


Techniques for direct WIMP Techniques for direct WIMP detectiondetection


World StatusWorld Status (BUS 2006)(BUS 2006)


THE MODULATION EFFECTTHE MODULATION EFFECT

vvJuneJune==235+15=235+15=250km/s250km/s vvDecDec=235-15==235-15=220km/s220km/s


THETHE MODULATION EFFECT*MODULATION EFFECT*(continued)(continued)

• R=RR=R0 0 (1+b(1+b sinsinγγ cos cosαα)=R)=R0 0 (1+h(1+h coscosαα))

((αα=0 around June 3nd) =0 around June 3nd)

• γ=γ= π/ π/2-2-γγ’’, γ, γ’ ’ ≈ ≈ π/π/3 is the angle between the 3 is the angle between the axis of galaaxis of galaχχy and the axis of the ecliptic. y and the axis of the ecliptic.

• h=modulation amplitudeh=modulation amplitude..

• RR00 =average rate =average rate..

• *n=2 corresponds to calculations with non *n=2 corresponds to calculations with non standard M-B (Tetradis, Faeesler and JDV)standard M-B (Tetradis, Faeesler and JDV)


TheThe Modulation AmplitudeModulation Amplitude h h for for 127127II QQthth=0=0,, 10 10 keV, Isothermal model (M-B),keV, Isothermal model (M-B),

On topOn top n=1, at the bottom n=2 n=1, at the bottom n=2


TheThe Modulation AmplitudeModulation Amplitude h (h (light light target)target) QQthth=0=0,, Isothermal model (M-B), Isothermal model (M-B),

n=1 (Left), n=2 (right) n=1 (Left), n=2 (right)


TheThe Modulation AmplitudeModulation Amplitude h (light h (light target) target) QQthth=10 keV=10 keV, , Isothermal model Isothermal model (M-B),(M-B),



The directional event rate* The directional event rate* (The direction of recoil is (The direction of recoil is observed)observed)• The event rate in The event rate in directional experimentsdirectional experiments is: is: RRdirdir=(=(κ/2π)κ/2π)RR00[1+h[1+hmmcos(cos(α-αα-αmmππ))]]• 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)• α α mm is the is the shift in the phase of the Earthshift in the phase of the Earth (it (it

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

the the direction of observationdirection of observation))• κ κ and and ααm m depend only slightly on SUSY parametersdepend only slightly on SUSY parameters

• * Calculations by Faessler and JDV* Calculations by Faessler and JDV


The The parameter parameter κκ vs the polar vs the polar angleanglein the case of in the case of A=32A=32; ; mmχχ=100 =100 GeV GeV definite sense (Left), Both senses definite sense (Left), Both senses (Right)(Right)


The The parameter parameter κκ vs the polar vs the polar angleanglein the case of in the case of A=127A=127; ; mmχχ=100 =100 GeV GeV

definite sense (Left), definite sense (Left), Both senses Both senses (Right)(Right)


The The parameter hparameter hmm vs the polar vs the polar angleanglein 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)


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)


NON RECOIL MEASUREMENTSNON RECOIL MEASUREMENTS

• (a) Measurement of ionization electrons (a) Measurement of ionization electrons produced directly during the WIMP-produced directly during the WIMP-nucleus collisionsnucleus collisions (Moustakidis, Ejiri and (Moustakidis, Ejiri and JDV)JDV)

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

(Ejiri, Moustakidis and JDV)(Ejiri, Moustakidis and JDV)

• (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(Ejiri, Moustakidis , and J.D.V)(Ejiri, Moustakidis , and J.D.V)

• After the ionization there is a probability for a After the ionization there is a probability for a K or L holeK or 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 (determined experimentally)experimentally)


K X-ray BR in WIMP interactions in K X-ray BR in WIMP interactions in 132 132 XeXe vs vs masse:masse: L<->30GeVL<->30GeV, , M<->100GeVM<->100GeV, , H<->300GeVH<->300GeV


Excitation of the nucleus:Excitation of the nucleus:Appears possible in the exotic Appears possible in the exotic modelsmodels

•<T<Tχχ>>≈≈40 40 keV nkeV n2 2 (m(mχχ/100GeV)/100GeV)

•TTχχ,max,max≈≈ 215215 keV nkeV n2 2 (m(mχχ/100GeV)./100GeV). ThusThus

• mmχχ =500GeV, n=2 =500GeV, n=2 <T<Tχχ>>≈≈0.8 MeV, 0.8 MeV, TTχχ,max,max≈≈ 4 MeV4 MeV


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

• Sharply peaked at Sharply peaked at ξ=1ξ=1


The recoil energy The recoil energy in keVin keV for A=127 for A=127 and and ΔΔ=50 keV.=50 keV. MMχ χ =3=300 GeV, GeV, MMχ χ ==100100 GeV, GeV, MMχ χ ==200200 GeV, GeV, MMχ χ ==200200 GeV, GeV, MMχ χ ==400400 GeVGeV..


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 vs LSP massLSP mass (Ejiri; Quentin, Strottman (Ejiri; Quentin, Strottman and JDV) and JDV) Relative to nucleon recoilRelative to nucleon recoil i) i) no quenching no quenching ii) ii) Left Left E Eth th =0 keV, Right =0 keV, Right E Eth th =10 keV=10 keV


CONCLUSIONS A: K-K WIMPSCONCLUSIONS A: K-K WIMPS

• Theoretical advantages: Theoretical advantages: Only the masses Only the masses are unknownare unknown parameters. parameters. The couplings The couplings are S.Mare S.M

• Experimental advantagesExperimental advantages: The WIMP : The WIMP energy is an order of magnitude biggerenergy is an order of magnitude bigger

The energy transfer to the nucleus is a bit The energy transfer to the nucleus is a bit higher. higher. One has a better chance to excite One has a better chance to excite the nucleusthe nucleus

• Limits Limits K-K Nucleon cross sectionsK-K Nucleon cross sections can be can be extracted fromextracted from current limitscurrent limits via: via:

• σσ(K-K)(K-K) (coh) (coh) ≈(A/Z)≈(A/Z)221010(-6)(-6) pbpb [[mm(K-K)(K-K)/200GeV]/200GeV]

• σσ(K-K)(K-K) (spin) (spin) ≈≈1010(-2)(-2) pbpb [[mm(K-K)(K-K)/200GeV]/200GeV]


CONCLUSIONS- SUSY WIMPS CONCLUSIONS- SUSY WIMPS Standard Rates (theory)Standard Rates (theory)• Most of the uncertainties come from the fact Most of the uncertainties come from the fact

that the that the allowed SUSY parameter space has not allowed SUSY parameter space has not been sufficiently sharpened.been sufficiently sharpened.

• The other uncertainties (The other uncertainties (nuclear form factor, nuclear form factor, structure of the nucleon, quenching factor, structure of the nucleon, quenching factor, energy thresholdenergy threshold) could also affect the results ) could also affect the results by an by an order of magnitudeorder of magnitude..

• Most of the parameter space yields Most of the parameter space yields undetectable ratesundetectable rates..

• The The coherent contributioncoherent contribution due to the scalar due to the scalar interaction is the interaction is the most dominantmost dominant..


CONCLUSIONS-Modulation CONCLUSIONS-Modulation (theory)(theory)• The The modulation amplitude hmodulation amplitude h is small, less is small, less

than 2%than 2% and depends on the LSP mass. and depends on the LSP mass. • It crucially It crucially depends on the velocity depends on the velocity

distributiondistribution• Unfortunately even its Unfortunately even its signsign is is uncertainuncertain for for

intermediate and heavy nuclei.intermediate and heavy nuclei.• It may It may increaseincrease as the energy cut off as the energy cut off

remains big (as in the DAMA experiment), remains big (as in the DAMA experiment), but but at the expense of the number of counts.at the expense of the number of counts. The DAMA experiment The DAMA experiment maybe consistentmaybe consistent with the other experiments, with the other experiments, if the spin if the spin interaction dominatesinteraction dominates. .

• The modulation is reduced further in the The modulation is reduced further in the case of exotic WIMP velocity distributionscase of exotic WIMP velocity distributions


CONCLUSIONSCONCLUSIONS-Directional -Directional ExperimentsExperiments

• The predicted rates are The predicted rates are downdown by at least by at least a a factor of 4factor of 4ππ compared to those of the compared to those of the standard experiments. standard experiments. However:However:

• Strong Strong correlations of the event rates with correlations of the event rates with the sun’s direction of motionthe sun’s direction of motion are expected. are expected. Thus large asymmetries are expected.Thus large asymmetries are expected.

• The modulation now is much larger.The modulation now is much larger. The The location of its maximum depends on the location of its maximum depends on the direction of observation. Thus direction of observation. Thus it cannot be it cannot be mimicked by seasonal variations of the mimicked by seasonal variations of the background.background.


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

electrons may be kicked off the atomelectrons may 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 for this process depends on the the threshold energies and the LSP mass.threshold energies and the LSP 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 10by an order of 10..

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


Conclusions: Conclusions: Experimental ambitions for Experimental ambitions for RecoilsRecoils


COMMON WISDOM!COMMON WISDOM!


nucleon cross sections extracted nucleon cross sections extracted from the data. R<2.3 events for from the data. R<2.3 events for 52.5 Kg-d52.5 Kg-dDottedDotted EEth th =10 keV, thick =10 keV, thick E Eth th =0 keV=0 keV 127127I (left) I (left) 73 73 Ge (right) Ge (right) (light WIMP)(light WIMP)


nucleon cross sections extracted nucleon cross sections extracted from the data. from the data. R<16 events per R<16 events per Kg-yKg-yDottedDotted EEthth=10 keV, thick =10 keV, thick E Ethth=0 keV =0 keV ((1919FF))


CONCLUSIONS: CONCLUSIONS: Excitation of the Excitation of the nucleus:nucleus:

Appears possible in the exotic Appears possible in the exotic modelsmodels


Unfortunately,Unfortunately,Not all available energy is Not all available energy is exploitableexploitable!!• For ground to ground transitionsFor ground to ground transitions

• For Transitions to excited statesFor Transitions to excited states

• Sharply peaked at Sharply peaked at ξ=1ξ=1


The recoil energy in keV for A=127 The recoil energy in keV for A=127 and and ΔΔ=50 keV.=50 keV. MMχ χ =3=300 GeV, GeV, MMχ χ ==100100 GeV, GeV, MMχ χ ==200200 GeV, GeV, MMχ χ ==200200 GeV, GeV, MMχ χ ==400400 GeVGeV..


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


The directional event rateThe directional event rate

• The event rate in The event rate in directional experimentsdirectional experiments is: is:

RRdirdir=(=(κ/2π)κ/2π)RR00[1+cos([1+cos(α-αα-αmmππ))]]• 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)• α α mm is the is the shift in the phase of the Earthshift in the phase of the Earth (it (it

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

and the and the direction of observationdirection of observation))• κ κ and and ααm m depend only slightly on SUSYdepend only slightly on SUSY


The Directional rate tThe Directional rate tdir dir in the in the case of case of 127127I for wimp mass of I for wimp mass of 100 GeV100 GeV M-B distribution M-B distribution m=1)m=1)




The The parameter parameter κκ vs the polar vs the polar angleanglein the case of in the case of A=127, rightA=127, right for for mmχχ=100 =100 GeV(M-B distribution GeV(M-B distribution m=1)m=1)


The The parameter parameter κκvs the polar vs the polar angleanglein the case of in the case of A=127, rightA=127, right for for mmχχ=100 =100 GeV(M-B distribution GeV(M-B distribution m=2)m=2)


Directional Rate: ModulationDirectional Rate: Modulation vs vs ΘΘmmwimpwimp=100 GeV,=100 GeV,dotteddottedΦ=πΦ=π, , fine fine Φ=0Φ=0, , thickthickΦΦ==π/2,3π/2π/2,3π/2 ((m=1m=1))




The The event rateevent rate vs the polar vs the polar angleangle((A=19, left) A=19, left) , (, (A=127, rightA=127, right) ) for mfor mχχ=100 =100 GeV and M-B GeV and M-B distributiondistribution


The parameter The parameter κκ vs the LSP vs the LSP massmass::perpendicular to the sun’s perpendicular to the sun’s velocity (left)velocity (left) and and opposite to it opposite to it (right) (right)


A. SUSY MODELS WITH R-A. SUSY MODELS WITH R-PARITY: PARITY: The neutralinoThe neutralino χ χ

• Standard model particles have R-Standard model particles have R-parity=1parity=1

• All SUSY particles have R-parity -1All SUSY particles have R-parity -1

• Lightest SUSY particle absolutely Lightest SUSY particle absolutely stablestable

• A linear combination of the 4 neutral A linear combination of the 4 neutral fermions fermions (two gauginos and two Higgsinos) i.e.(two gauginos and two Higgsinos) i.e.


From the quark level From the quark level to the nucleon level (coherent)to the nucleon level (coherent)


The Differential cross section at The Differential cross section at the nuclear level.the nuclear level.

• υ υ is the neutralino velocityis the neutralino velocity and and uu stands stands essentially for essentially for the energy transfer Qthe energy transfer Q::

• u=Q/Qu=Q/Q0 0 , Q, Q00=40A=40A-4/3-4/3 MeVMeV

• F(u): F(u): The nuclear form factorThe nuclear form factor• FF11 11 (u):(u): The isovector spin response The isovector spin response

functionfunction


Expressions for the nuclear Expressions for the nuclear cross section (continued)cross section (continued)

WithWith

• ΣΣSS==σσppss((μμrr/m/mpp))22AA2 2 (scalar interaction) (scalar interaction)

• σσppss is the scalar proton-LSP cross section is the scalar proton-LSP cross section

• μμrr is is the LSP-nucleus reduced massthe LSP-nucleus reduced mass

• AA is the nuclear mass is the nuclear mass

• ΣΣSpin Spin is the expression for the spin inducedis the expression for the spin induced

cross section (to be discussed later).cross section (to be discussed later).


The The RelativeRelative (with respect to recoil) (with respect to recoil) rate of ionization per electron rate of ionization per electron vs: vs: a) a) EEthresholdthreshold for m for mχ χ =100=100Gev (left)Gev (left) and b) mand b) mχχ for E for Ethreshold threshold = = 0.2 keV (right)0.2 keV (right)


Relative rate forRelative rate for inner electron inner electron hole productionhole production in the case of in the case of 132132XeXe. . • nnℓℓ εεnnℓℓ(keV) ((keV) (σσnnℓℓ//σσrr))L L ((σσnnℓℓ//σσrr))M M ((σσnnℓℓ//σσrr))HH

• isis 34.5634.56 0.0340.034 0.2210.221 0.2550.255

• 2s 5.45 2s 5.45 1.2111.211 1.4611.461 1.4631.463

• 2p 4.89 3.796 4.506 4.513 2p 4.89 3.796 4.506 4.513

• WIMP masses indicated by subscript:WIMP masses indicated by subscript:

LL30GeV, M30GeV, M100GeV, H100GeV, H300GeV300GeV


CONCLUSIONSCONCLUSIONS--Transitions to Transitions to excited statesexcited states

• For neutralino transitions to excited states For neutralino transitions to excited states are possible are possible in few odd A nuclei*in few odd A nuclei*..

• When allowed, are When allowed, are kinematically kinematically suppressedsuppressed

• The branching ratio depends on the The branching ratio depends on the structure of the nucleus and the LSP massstructure of the nucleus and the LSP mass

• In the case of In the case of IodineIodine, a popular target for , a popular target for recoils, it can be as high as recoils, it can be as high as 7% for LSP 7% for LSP mass higher than 200 GeVmass higher than 200 GeV

• * For K-K WIMPS it is quite easy* For K-K WIMPS it is quite easy


II: Cosmological EvidenceII: Cosmological Evidence for dark for dark mattermatter The 3 main reasons for the Big Bang The 3 main reasons for the Big Bang

Scenario:Scenario:• The receding of GalaxiesThe receding of Galaxies (red shift) (red shift)

(Hubble 1929)(Hubble 1929)• The Microwave Background RadiationThe Microwave Background Radiation

(CMBR –Penzias and Wilson 1964)(CMBR –Penzias and Wilson 1964)• The Big Bang NucleosynthesisThe Big Bang Nucleosynthesis (BBN, 1946) (BBN, 1946)

All bear a signature of dark matterAll bear a signature of dark matter(BBN also gave the first argument for CMBR, (BBN also gave the first argument for CMBR,

but nobody paid any attention)but nobody paid any attention)


Anisotropy in the CMBR Anisotropy in the CMBR (cont.)(cont.)


IIc: Light curves : IIc: Light curves : ddLL vs red vs red shift z shift z (Generalization of (Generalization of Hubble’s Law to Large Hubble’s Law to Large Distances)Distances)• Upper continuousUpper continuous

• Middle continuousMiddle continuous

• Lower continuousLower continuous

• DashedDashed-- Non accelerating Non accelerating universeuniverse

3.0,7.0 M

3.0,0.0 M

0.1,0.0 M


B1 Kaluza-Klein theories B1 Kaluza-Klein theories WIMP:BWIMP:B(1)(1) K-K qK-K q(1)(1)exchange-exchange-The axial current.The axial current.


BB22 WIMP is WIMP is the the νν(1)(1)..

(continued)(continued)ΖΖ-Exchange Dominates.-Exchange Dominates.


Spin Contribution Spin Contribution Axial Axial CurrentCurrent

• Going from quark to the nucleon level Going from quark to the nucleon level for the for the isovector component is standardisovector component is standard (as in weak interactions): (as in weak interactions): f f11

A A (q) (q) f f11A A == ggAA ff11

A A (q) , (q) , ggA A =1.24=1.24

• For the For the isoscalar this is not trivialisoscalar this is not trivial. The . The naïve quark model fails badly (naïve quark model fails badly (the the proton spin crisisproton spin crisis) ) f f00

A A (q) (q) f f00A A == gg00

AA ff00A A (q) , (q) , gg00

AA =0.1=0.1


The relative differential Rate, The relative differential Rate, (dR(dRee/dT/dTe e )/R)/Rrecoilrecoil, , vs the electron vs the electron energyenergy TT for for electron electron productionproduction in LSP-nucleus in LSP-nucleus (Moustakidis, Ejiri, JDV).(Moustakidis, Ejiri, JDV).


Detection of Detection of hard X-rayshard X-rays (events relative to recoil) (events relative to recoil) (continued)(continued)• The interesting quantity is:The interesting quantity is:

• ((σσK K (K(Kijij)/)/σσrr)=()=(σσ1s1s//σσrr)) bb1s 1s B(KB(Kijij))

• Where:Where:

• bbnnℓℓ==Fluorecence ratio, KFluorecence ratio, Kij ij =K-ij branch=K-ij branch


CONCLUSIONSCONCLUSIONS--Directional Directional RatesRates• Good signaturesGood signatures, but the , but the experiments are hardexperiments are hard

(the DRIFT experiment cannot tell the sense of (the DRIFT experiment cannot tell the sense of direction of recoil)direction of recoil)

• Large asymmetriesLarge asymmetries are predicted are predicted• The The rates are suppressedrates are suppressed by a factor by a factor κ/2πκ/2π, , κκ<0.6<0.6• For a given LSP velocity distribution, For a given LSP velocity distribution, κκ depends depends

on the direction of observationon the direction of observation• In the most favored direction In the most favored direction κ κ is approximately is approximately

0.60.6• In the plane perpendicular to the sun’s velocity In the plane perpendicular to the sun’s velocity κκ

is approximately equal to 0.2is approximately equal to 0.2


CONCLUSIONSCONCLUSIONS- - Modulation in Modulation in Directional ExperimentsDirectional Experiments• The The Directional ratesDirectional rates also also exhibit modulationexhibit modulation• In the In the most favored directionmost favored direction of observation, of observation,

opposite to the sun’s motion, the opposite to the sun’s motion, the modulation is modulation is now twice as largenow twice as large. (Maximum in June, Minimum . (Maximum in June, Minimum in December)in December)

• In the plane In the plane perpendicular to the sun’s motionperpendicular to the sun’s motion the the modulation is modulation is much largermuch larger. The difference . The difference between the maximum and the minimum can be between the maximum and the minimum can be as high as high as 50%.as 50%. It also shows a It also shows a direction direction characteristic patterncharacteristic pattern (for observation directions (for observation directions on the galactic plane the maximum may occur in on the galactic plane the maximum may occur in September or March, while normal behavior for September or March, while normal behavior for directions perpendicular to the galaxy)directions perpendicular to the galaxy)


A Scatter Plot (A Scatter Plot (Non UniversalNon Universal) ) (Ceredeno, Gabrielli, Gomez (Ceredeno, Gabrielli, Gomez and Munoz)and Munoz)


The event rate due to the spinThe event rate due to the spin

• WhereWhere ff00AA== aapp+a+ann ((isoscalarisoscalar) ) and and ff11

AA== aapp-a-ann ((isovectorisovector) ) couplings at the nucleon level and couplings at the nucleon level and ΩΩ00(0), Ω(0), Ω11(0)(0) the the corresponding corresponding static spin matrix elementsstatic spin matrix elements

• The event rate is cast in the formThe event rate is cast in the form::


The factorThe factor ffspinspin(A,m(A,mχχ)) for A=127 for A=127 (I)(I)(The Dashed for threshold (The Dashed for threshold 10keV)10keV)


The factorThe factor ffspinspin(A,m(A,mχχ)) for A=19 for A=19 (F)(F)(The Dashed for threshold (The Dashed for threshold 10keV)10keV)


The The constrained amplitude planeconstrained amplitude plane (a(app,χ,χ,a,ann,χ,χ) for the) for the Α=127 Α=127 systemsystem ((arbitrary unitsarbitrary units), ), when they are when they are relatively real.relatively real.


The constrained (aThe constrained (app,χ,χ,a,ann,χ,χ) plane: relative ) plane: relative phase of the amplitudes phase of the amplitudes δ=π/6δ=π/6 ( (--)), δ=π/3 , δ=π/3 ((--)and )and δ=π/δ=π/2 (-)2 (-)


The The constrainedconstrained ((σσpp,χ,χ,,σσnn,χ,χ) plane) plane for the for the Α=127 Α=127 system system ((arbitrary unitsarbitrary units)). Under the . Under the curve on the curve on the leftleft, if the amplitudes have , if the amplitudes have the the same signsame sign and between the curves on the and between the curves on the right for opposite signright for opposite sign..


The constrained (The constrained (σσp,p,χχ,,σσnn,χ,χ)) plane: relative plane: relative phase of amplitudes phase of amplitudes δ=π/6δ=π/6 ( (--)), δ=π/3 , δ=π/3 ((--)and )and δ=π/δ=π/2 (-)2 (-)


The directional event rateThe directional event rate

• The event rate in The event rate in directional experimentsdirectional experiments is: is:

RRdirdir=(=(κ/2π)κ/2π)RR00[1+cos([1+cos(α-αα-αmmππ))]]• 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)• α α mm is the is the shift in the phase of the Earthshift in the phase of the Earth (it (it

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

and the and the direction of observationdirection of observation))• κ κ and and ααm m depend only slightly on SUSYdepend only slightly on SUSY






The The parameter parameter κκ vs the polar vs the polar angleanglein the case of in the case of A=127, rightA=127, right for for mmχχ=100 =100 GeV(M-B distribution GeV(M-B distribution n=1)n=1)


The The parameter parameter κκvs the polar vs the polar angleanglein the case of in the case of A=127, rightA=127, right for for mmχχ=100 =100 GeV(M-B distribution GeV(M-B distribution m=2)m=2)






The Differential RateThe Differential Rate (Reminders)(Reminders)


The differential rate is The differential rate is proportional to the Function proportional to the Function ΨΨ0 0

((xx)); here n=1; here n=1(dotted (dotted mmWIMP WIMP 30GeV, thick 30GeV, thick mmWIMP WIMP 200GeV)200GeV)


The differential rate is The differential rate is proportional to the Function proportional to the Function ΨΨ0 0

((xx)); here n=2; here n=2(dotted (dotted mmWIMP WIMP 30GeV, thick 30GeV, thick mmWIMP WIMP 200GeV)200GeV) (dotted(dottedmmWIMP WIMP 30GeV, thick 30GeV, thick mmWIMP WIMP 200GeV)200GeV)


The Differential Modulation The Differential Modulation Amplitude is proportional to H(x); Amplitude is proportional to H(x); Here n=1Here n=1


The Modulation Amplitude H(x), The Modulation Amplitude H(x), n=2n=2Note a decrease by almost a Note a decrease by almost a factor of 5factor of 5


Effect on Total RatesEffect on Total Rates


Coupling of Dark Matter and Coupling of Dark Matter and Dark EnergyDark Energy (N. Tetradis, P.L. B 632 (N. Tetradis, P.L. B 632 (2006) 463(2006) 463• Energy momentum tensor for DM Energy momentum tensor for DM diag(-diag(-ρ,ρ,p,p,p) with Eq. of state: p(r)=p,p,p) with Eq. of state: p(r)=ρρ(r)(r) <υ <υ22>>• Solution of Einstein EqsSolution of Einstein Eqs gravitational Potentialgravitational Potential such that: such that: ΦΦ’ ’ =(2/=(2/3)3)(1+κ(1+κ22)<υ)<υ22>1/>1/rr matter rotational velocity:matter rotational velocity:(υ(υ00))22==((22//33(1+κ(1+κ22))<υ))<υ22>> DM: MBDM: MB ~~ Exp[-Exp[-υυ22 / / ((n n υυ00))22]] ; ; nn2 2 ==(1+κ(1+κ22))• And escape velocity:And escape velocity:• υυesc esc =2.84=2.84υυ0 0 (matter)(matter) υυesc esc =2.84n=2.84nυυ0 0 (DM)(DM)

• BEFORE WE EXPLOIT THIS EFFECTBEFORE WE EXPLOIT THIS EFFECT

SOME REMINDERS ARE NEEDEDSOME REMINDERS ARE NEEDED


Expression for the event Expression for the event raterate

• Where:Where:• m is the target massm is the target mass• ρ(0)ρ(0):: the local WIMP density≈0.3 GeV/cmthe local WIMP density≈0.3 GeV/cm33..• σσSS

pp,χ,χ ((σσspinspinpp,χ,χ): the scalar (spin) WIMP-nucleon cross section. ): the scalar (spin) WIMP-nucleon cross section.

It can be computed in a particle model.It can be computed in a particle model. •


TheThe Modulation AmplitudeModulation Amplitude h h for for 127127II QQthth=0=0thick, Qthick, Qthth=5keV=5keVfine fine QQthth=10=10dash; dash; Eddington TheoryEddington Theory


Conclusions: Conclusions: Experimental ambitions for Experimental ambitions for RecoilsRecoils


nucleon cross sections extracted nucleon cross sections extracted from the data. R<2.3 events for from the data. R<2.3 events for 52.5 Kg-d52.5 Kg-dDottedDotted EEthth=10 keV, thick =10 keV, thick E Ethth=0 keV =0 keV ((1919FF) )


nucleon cross sections extracted nucleon cross sections extracted from the data. R<2.3 events for from the data. R<2.3 events for 52.5 Kg-d52.5 Kg-dDottedDotted EEth th =10 keV, thick =10 keV, thick E Eth th =0 keV=0 keV 127127I (left) I (left) 73 73 Ge (right)Ge (right)


TheThe factor t factor t for for 127127II (coherent (coherent mode)mode) QQthth=0=0, 10 , 10 keV, Isothermal keV, Isothermal model (M-B),model (M-B),

On topOn top n=1, at the bottom n=1, at the bottom n=2n=2


TheThe parameter tparameter t for for 3232SS QQthth=0=0, , Isothermal model (M-B), Isothermal model (M-B),



TheThe parameter t parameter t for for 3232SS QQthth=10 keV=10 keV, , Isothermal model (M-B), Isothermal model (M-B),



IIc: The angular power spectrumIIc: The angular power spectrum; ; θθ =π=π//ℓℓ blackblackWMAP3 WMAP3 ΛΛCDMCDM redredWMAP1WMAP1, , orangeorangeWMAP1+CBIWMAP1+CBI


The dif. Rate;The dif. Rate; ξ=ξ=the cosine of the the cosine of the angle between the line of angle between the line of observation and the line of recoilobservation and the line of recoil (for the indicated polar angles).(for the indicated polar angles).


Nuclear Recoil is after the Nuclear Recoil is after the WIMP-nucleus collision WIMP-nucleus collision (WIMP: (WIMP: Weakly Interacting massive Weakly Interacting massive particle)particle)


Cosmological Constraints Cosmological Constraints in the in the (Ω,Λ) (Ω,Λ) Plane (from S. Plane (from S. Perlmutter)Perlmutter)


Cosmological Constraints in the Cosmological Constraints in the (Ω,Λ) (Ω,Λ) Plane Plane (From M. Kowalski et al, (From M. Kowalski et al, asrto-ph/08)asrto-ph/08)


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±±0.00.00303Confirming earlier data (Supernovae, WMAP1 Confirming earlier data (Supernovae, WMAP1 etc):etc):


Direct WIMP DETECTION - Direct WIMP DETECTION - RECOILRECOIL


Current Limits on coherent Current Limits on coherent proton cross sectionproton cross section (astro- (astro-ph/0509259)ph/0509259)


I:Measure vI:Measure vrsrs(r) and I(r); Assume (r) and I(r); Assume

ρρ(r)=bI(r)(r)=bI(r) ΦΦ(r,b)(r,b)vv22

lumlum(r,b)=r d(r,b)=r dΦΦ/dr/drvv22lumlum# # vv22

rsrs


At still larger scales…At still larger scales…


IIa: Luminosity-distance red IIa: Luminosity-distance red shiftshiftBlue region: Blue region: ΛΛCDM model CDM model WMAP3 WMAP3 prediction (prediction (68% CL68% CL) ) vs datavs data


IIb: Relative abundance of elements in IIb: Relative abundance of elements in BBNBBN η=10η=10-10 -10

0.70.7 1010-31-31 g/cmg/cm-3 -3

• The relativeThe relative• ((With respectWith respect• To hydrogen)To hydrogen)• abundance abundance • of elementsof elements• BBN (left)BBN (left)• D/H=2.5x10D/H=2.5x10-5-5

• WMAP (rightWMAP (right) ) D/H=2.5x10D/H=2.5x10-5-5

• Notice theNotice the• Ratio withRatio with• Respect Respect • To theTo the• CriticalCritical• DensityDensity


IIc: Anisotropy in CMBR with IIc: Anisotropy in CMBR with WMAP3: WMAP3: astro-ph/0603449astro-ph/0603449


IIc: The angular power spectrumIIc: The angular power spectrum Red lineRed linebest fit to best fit to ΛΛCDM; CDM; θθ =π=π//ℓℓ


The harmonic indexThe harmonic indexℓℓas function of as function of ΩΩmm (Sanders, astro-ph/0402065)(Sanders, astro-ph/0402065) . . The dashed line The dashed line to WMAP data. to WMAP data. ΩΩ=1 is favored =1 is favored ΩΩmm≈0.3≈0.3


A typical Scatter Plot (A typical Scatter Plot (Universal Universal set of parametersset of parameters) (Ceredeno, ) (Ceredeno, Gabrielli, Gomez and Munoz)Gabrielli, Gomez and Munoz)


PRESENT VIEW OF THE PRESENT VIEW OF THE COSMOSCOSMOS


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


nucleon cross sections extracted nucleon cross sections extracted from the data. from the data. R<16 events per R<16 events per Kg-yKg-yDottedDotted EEth th =10 keV, thick =10 keV, thick E Eth th =0 keV=0 keV 127127I (left) I (left) 73 73 Ge (right) Ge (right) (mass: Log (mass: Log scale)scale)


B1: K-B BOSON AS A WIMP B1: K-B BOSON AS A WIMP for for ΔΔ=(m=(m2 2 /m/m1 1 )-1)-1=0.8=0.8


B2:B2:R for K-K MAJORANA NEUTRINOR for K-K MAJORANA NEUTRINO(Higgs exchange, m(Higgs exchange, mh h =500 GeV, =500 GeV, Optimistic Structure of nucleon: Optimistic Structure of nucleon: ΣΣq q ffq q

=0.67)=0.67)


B2: R for K-K MAJORANA B2: R for K-K MAJORANA NEUTRINONEUTRINO(Z-exchange) spin induced; (Z-exchange) spin induced; 1919FF


B2B2: R for K-K MAJORANA : R for K-K MAJORANA NEUTRINONEUTRINO(Z-exchange) spin induced; (Z-exchange) spin induced; 127127II

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