Symmetries and the Spin Praha, July 28th, 2005 On the Direct Detection of SUSY Dark Matter On the...

Symmetries and the Spin PrSymmetries and the Spin Praha, July 28th, 2005aha, July 28th, 2005

On the Direct Detection On the Direct Detection of SUSY Dark Matterof SUSY Dark Matter

J.D. VergadosJ.D. VergadosUniversity of Ioannina, GreeceUniversity of Ioannina, Greece


KINDS OF MATTER AND KINDS OF MATTER AND ENERGYENERGY• Dark MatterDark Matter Matter which cannot Matter which cannot

radiate radiate Interacts only gravitationally Interacts only gravitationally and perhaps very-very weaklyand perhaps very-very weakly

• Dark EnergyDark Energy Cosmological Constant Cosmological Constant ΛΛ

• Baryonic matterBaryonic matter Non exotic Non exotic Standard Model matterStandard Model matter


Gravitational Evidence for Dark Gravitational Evidence for Dark MatterMatterI. I. The Rotational VelocitiesThe Rotational Velocities ((υυ22 does not vary as 1/r outside the does not vary as 1/r outside the galaxy)galaxy)


II: Cosmological EvidenceII: Cosmological Evidence for dark matter for dark matter 3 Reasons for the Big Bang Scenario:3 Reasons for the Big Bang Scenario:• The The receding of Galaxiesreceding of Galaxies (red shift) (Hubble (red shift) (Hubble

1929)1929)• The The Microwave Background RadiationMicrowave Background Radiation

(CMBR –Penzias and Wilson 1964)(CMBR –Penzias and Wilson 1964)• The The Big Bang NucleosynthesisBig Bang Nucleosynthesis (BBN) (BBN) All have put a signature on dark matterAll have put a signature on dark matter(BBN also gave the first argument for CMBR, (BBN also gave the first argument for CMBR,

but nobody paid attention)but nobody paid attention)


IIa: IIa: Light curvesLight curves : :ddL L vs red shift z vs red shift z (Generalization of Hubble’s (Generalization of Hubble’s Law for Large Distances)Law for Large 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


Anisotropy in the CMBR Anisotropy in the CMBR


IIa. Relative abundance IIa. Relative abundance • RelativeRelative (with respect(with respect hydrogen)hydrogen) abundanceabundance of some of some elementselements vs the baryonvs the baryon densitydensity• The criticalThe critical density isdensity is 20 times larger20 times largerFrom BBNFrom BBND/H=(2-5)x10D/H=(2-5)x10-5-5

From WMAPFrom WMAPD/H=2.5x10D/H=2.5x10-5-5


Relative abundance of elements in Relative abundance of elements in BBNBBN• The relativeThe relative• ((With respectWith respect• To hydrogen)To hydrogen)• abundance abundance • of elementsof elements• BBN (left)BBN (left)• D/H=(2-5)x10D/H=(2-5)x10-5-5

• 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


Slicing the Pie of the Slicing the Pie of the CosmosCosmos


DARK MATTER CANDIDATESDARK MATTER CANDIDATES• The axionThe axion:: 1010-6 -6 eVeV<<mma a <10<10-3 -3 eVeV• The neutrinoThe neutrino: : It is rejected, since it is not cold. Not It is rejected, since it is not cold. Not

CDM.CDM.• Supersymmetric particlesSupersymmetric particles.. Three possibilitiesThree 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 thecombination of the 2 neutral gauginos and the 2 2 neutral gauginos and the 2 neutral Higgsinos. neutral Higgsinos. OUR CANDIDATEOUR CANDIDATE


The kinematics of the LSP-The kinematics of the LSP-nucleus collisionnucleus collision


Conversion of the energy of Conversion of the energy of the recoiling nucleus into light, the recoiling nucleus into light, heat, ionization etc.heat, ionization etc.• The neutralino (LSP) is non relativistic.The neutralino (LSP) is non relativistic.

• With few exceptions, it cannot excite the nucleusWith few exceptions, it cannot excite the nucleusιι::

• 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 30 per Kg of target per year) (much less than 30 per Kg of target per year).. -Bothersome backgrounds-Bothersome backgrounds (the signal is not very characteristic) (the signal is not very characteristic).. --Threshold effectsThreshold effects.. --Quenching factorsQuenching factors..


Novel approachesNovel approaches: : Exploitation Exploitation of of other signaturesother signatures of the of the reactionreaction• The modulation effectThe modulation effect): The seasonal ): The seasonal

dependence of the rate due to the motion of dependence of the rate due to the motion of the Earth.the Earth.

• The excitationThe excitation of the nucleus (in some rare of the nucleus (in some rare cases that this is realistic) andcases that this is realistic) and detection of the detection of the subsequently emitted de-excitationsubsequently emitted de-excitation γ γ rays.rays.

• Asymmetry measurements in directional Asymmetry measurements in directional experiments experiments (the direction of the recoiling (the direction of the recoiling nucleus is also measured).nucleus is also measured).

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


The SUSY INPUTThe SUSY INPUT • Allowed parameter space: Allowed parameter space: Univerality at GUT scale: Univerality 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

• Constrain these parameters via the Constrain these parameters via the renormalization renormalization group equationgroup equation from the observable low energy from the observable low energy quantities (all related to the above five parameters).quantities (all related to the above five parameters).

• (see: Ellis, Arnowitt, Nath, Bottino and collaborators)(see: Ellis, Arnowitt, Nath, Bottino and collaborators)


From the quark level to the From the quark level to the nucleon level (coherent: nucleon level (coherent: amplitude amplitude ~m~mqq))


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 (from weak interactions): (from weak interactions): f f11

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

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

AA =0.1=0.1


The Differential cross section The Differential cross section at 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) ο ο 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==σσpp

ss((μμrr/m/mpp))22AA2 2 for the scalar for the scalar contributioncontribution

• With With σσpps s the the scalar proton LSP cross sectionscalar proton LSP cross section

• μμrr is is the LSP-nucleus reduced massthe LSP-nucleus reduced mass• A is the nuclear massA is the nuclear mass• ΣΣSpin Spin is the expression for the spin inducedis the expression for the spin induced• cross section, which will be discussed latercross section, which will be discussed later


LSP Velocity DistributionsLSP Velocity Distributions• Conventional: Conventional: • Maxwell-BoltzmannMaxwell-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 galaxy varound the galaxy v0 0 =220 km/s=220 km/s and escape velocity and escape velocity

• vvesc esc =2.84v=2.84v00 put in by hand. put in by hand.• Isothermal models employing Isothermal models employing Eddington’s theoryEddington’s theory: : • ρρ(r)->(r)->ΦΦ(r) ->(r) -> f(r,v) (JDV-Owen)f(r,v) (JDV-Owen)• Non-thermal modelsNon-thermal models::• Caustic rings, wimps in bound orbits etcCaustic rings, wimps in bound orbits etc• Sgr Dwarf galaxySgr Dwarf galaxy, anisotropic flux, (Green and , anisotropic flux, (Green and

Spooner)Spooner)


The The event rateevent rate for the coherent for the coherent modemode• Can be cast in the formCan be cast in the form::

• Where:Where: ρ(0) ρ(0) the local neutralino densitythe local neutralino density≈0.3GeV/cm≈0.3GeV/cm33.. σσSS

pp,χ,χ the neutralino-nucleon cross section. the neutralino-nucleon cross section. It can be extractedIt can be extracted from from the data the data once once ffcoh coh (A,m(A,mχχ)) , which will be plotted below, , which will be plotted below, is knownis known..


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


Current Limits on coherent Current Limits on coherent proton cross sectionproton cross section


A typical Scatter Plot: A typical Scatter Plot: Universal Universal SUSY parametersSUSY parameters (Ceredeno, (Ceredeno, Gabrielli, Gomez and Munoz)Gabrielli, Gomez and Munoz)


A Scatter Plot: A Scatter Plot: Non Universal Non Universal SUSY parametersSUSY parameters (Ceredeno, (Ceredeno, Gabrielli, Gomez and Munoz)Gabrielli, Gomez and Munoz)


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

• WhereWhere ff00A A ((isoscalarisoscalar) ) and and ff11

AA ((isovectorisovector) ) couplings at the couplings at the nucleon level and nucleon level and ΩΩ00(0), Ω(0), Ω11(0)(0) the corresponding the corresponding static spin static spin matrix elementsmatrix 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 for A=127 A=127 (I)(I)(The Dashed for threshold (The Dashed for threshold 10keV)10keV)


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


The The constrained amplitude planeconstrained amplitude plane (f(fpp,χ,χ,f,fnn,χ,χ) for the) for the Α=127 Α=127 systemsystem ((arbitrary unitsarbitrary units))


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 MOFULATION EFFECTTHE MOFULATION EFFECT

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


THE THE MODULATION EFFECTMODULATION EFFECT(continued)(continued)

• α=α=phase of the Earthphase of the Earth ((αα=0 around June 3nd) =0 around June 3nd) • γ=π/3γ=π/3 is the angle between the axis of is the angle between the axis of

galagalaχχy and the axis of the ecliptic. y and the axis of the ecliptic. • h=modulation amplitudeh=modulation amplitude..• RR00 =average rate =average rate..

)cos1()cossin1( 00 hRbRR


The The Modulation AmplitudeModulation Amplitude h h for for II On the On the left zero energyleft zero energy cut cut off.off. On the On the right a cut off of 10keVright a cut off of 10keV


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 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)


The The modulation vs the LSP modulation vs the LSP massmass::oppositeopposite the sun’s velocity the sun’s velocity ((leftleft)) and and perpendicularperpendicular to it ( to it (rightright))



BR for transitions to the BR for transitions to the first first excited stateexcited state at 50 keV for Iat 50 keV for I vs vs LSP mass (quenching of recoil LSP mass (quenching of recoil ignored)ignored)


The relative differential Rate, The relative differential Rate, (dR(dRee/dT/dTe e )/R)/Rrecoilrecoil, vs electron , vs electron energy T for energy T for electron electron productionproduction in LSP-nucleus in LSP-nucleus (Moustakides, JDV, Ejiri).(Moustakides, JDV, Ejiri).


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


There are Z electrons in an There are Z electrons in an atom!atom!


Detection of Detection of hard X-rayshard X-rays• After the ionization there is a After the ionization there is a K or L holeK or L hole• This hole de-excites via emitting X-rays or This hole de-excites via emitting X-rays or

Auger electronAuger electron. Indicate with . Indicate with bbnnℓℓ the the relative ratio (determined experimentally)relative ratio (determined experimentally)

• Then the Then 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 discussed above discussed above


Detection of Detection of hard X-rayshard X-rays (continued)(continued)• nnℓℓshell shell εεnnℓℓ(keV)(keV) σσnnℓℓ//σσr r σσX(nX(nℓℓ) ) //σσr r

• isis 34.5634.56 0.220.22 ??• 2s 5.45 2s 5.45 1.461.46 ? ?• 2p 4.89 4.51 ?2p 4.89 4.51 ?


Conclusions: Experimental Conclusions: Experimental ambitionsambitions


Projected exclusion curve for 3He detector

Background = 0.01 day-1

Energy threshold = 1 keV

CRESST SaphireELEGANT V NaIUKDMC NaINAIAD projection


Projected exclusion curvefor scalar detectors

2003 Edelweiss and CDMS projections


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

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

• The other uncertainties (The other uncertainties (nuclear form nuclear form factor, structure of the nucleon, quenching factor, structure of the nucleon, quenching factor, energy thresholdfactor, energy threshold) could affect the ) could affect the results by an results 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 due to the scalar interaction is the scalar 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 than

2%2% and depends on the LSP mass. Its and depends on the LSP mass. Its signsign is is also also uncertainuncertain for intermediate and heavy for intermediate and heavy nuclei.nuclei.

• It may It may increaseincrease as the energy cut off remains as the energy cut off remains big (as in the DAMA experiment), but big (as in the DAMA experiment), but at the at the expense of the number of countsexpense of the number of counts. The DAMA . The DAMA experiment maybe consistent with the other experiment maybe consistent with the other experiments, if the spin interaction experiments, if the spin interaction dominates. dominates.


CONCLUSIONS-CONCLUSIONS-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


CONCLUSIONS- CONCLUSIONS- 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,

parallel to the sun’s motion, the parallel 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)


CONCLUSIONS-CONCLUSIONS-Transitions to Transitions to excited statesexcited states• Transitions to excited states are possible Transitions to excited states are possible in in

few odd A nucleifew 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


CONCLUSIONS: CONCLUSIONS: 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 (Low threshold (Low threshold ~0.25keV ~0.25keV TPC detectors)TPC detectors)• The branching ratio for this process depends The branching ratio for this process depends

on the threshold energies and the LSP mass.on the threshold energies and the LSP mass.• For a threshold energy of 0.25 keV the For a threshold energy of 0.25 keV the

ionization event rate in the case of a heavy ionization event rate in the case of a heavy target can exceed the rate for recoils target can exceed the rate for recoils by an by an order of 10order of 10..

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


•THE ENDTHE END


3He- cross-section

• SI cross-section : SI(AX) SI(p)×A4

• SD cross-section : SD(AX) SD(p)×A2

For 3He : SD SI only SD considered

For AX nucleus:

(3He) mr2 (J+1)/J (ap<Sp>+an<Sn>)2

with 3He spin content: <Sp>=-0.05 <Sn>=0.49

scattering on the unpaired neutron

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