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

Symmetries and the Spin Praha, July 28th, 2005 On the Direct Detection of SUSY Dark Matter On the Direct Detection of SUSY Dark Matter J.D. Vergados University of Ioannina, Greece

Symmetries and the Spin Praha, July 28th, 2005 KINDS OF MATTER AND ENERGY Dark Matter  Matter which cannot radiate  Interacts only gravitationally and perhaps very-very weakly Dark Matter  Matter which cannot radiate  Interacts only gravitationally and perhaps very-very weakly Dark Energy  Cosmological Constant Λ Dark Energy  Cosmological Constant Λ Baryonic matter  Non exotic  Standard Model matter Baryonic matter  Non exotic  Standard Model matter

Symmetries and the Spin Praha, July 28th, 2005 Gravitational Evidence for Dark Matter I. The Rotational Velocities (υ 2 does not vary as 1/r outside the galaxy) Gravitational Evidence for Dark Matter I. The Rotational Velocities (υ 2 does not vary as 1/r outside the galaxy)

Symmetries and the Spin Praha, July 28th, 2005 II: Cosmological Evidence for dark matter 3 Reasons for the Big Bang Scenario: 3 Reasons for the Big Bang Scenario: The receding of Galaxies (red shift) (Hubble 1929) The receding of Galaxies (red shift) (Hubble 1929) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Big Bang Nucleosynthesis (BBN) The Big Bang Nucleosynthesis (BBN) All have put a signature on dark matter All have put a signature on dark matter (BBN also gave the first argument for CMBR, but nobody paid attention)

Symmetries and the Spin Praha, July 28th, 2005 IIa: Light curves : d L vs red shift z (Generalization of Hubble’s Law for Large Distances) Upper continuous Upper continuous Middle continuous Middle continuous Lower continuous Lower continuous Dashed- Dashed- Non accelerating Non accelerating universe universe

Symmetries and the Spin Praha, July 28th, 2005 Anisotropy in the CMBR

Symmetries and the Spin Praha, July 28th, 2005 IIa. Relative abundance Relative Relative (with respect (with respect hydrogen) hydrogen) abundance abundance of some of some elements elements vs the baryon vs the baryon density density The critical The critical density is density is 20 times larger 20 times larger From BBN D/H=(2-5)x10 -5 From WMAP From WMAP D/H=2.5x10 -5

Symmetries and the Spin Praha, July 28th, 2005 Relative abundance of elements in BBN The relative The relative ( With respect ( With respect To hydrogen) To hydrogen) abundance abundance of elements of elements BBN (left) BBN (left) D/H=(2-5)x10 -5 D/H=(2-5)x10 -5 WMAP (right ) WMAP (right ) D/H=2.5x10 -5 D/H=2.5x10 -5 Notice the Notice the Ratio with Ratio with Respect Respect To the To the Critical Critical Density Density

Symmetries and the Spin Praha, July 28th, 2005 Slicing the Pie of the Cosmos

Symmetries and the Spin Praha, July 28th, 2005 DARK MATTER CANDIDATES The axion: 10 -6 eV<m a <10 -3 eV The axion: 10 -6 eV<m a <10 -3 eV The neutrino: It is rejected, since it is not cold. Not CDM. The neutrino: It is rejected, since it is not cold. Not CDM. Supersymmetric particles. Supersymmetric particles. Three possibilities: Three possibilities: i) s-νετρίνο: Excluded on the basis of results of underground experiments and accelerator experiments (LEP) i) s-νετρίνο: Excluded on the basis of results of underground experiments and accelerator experiments (LEP) ii) Gravitino: Not directly detectable ii) Gravitino: Not directly detectable iii) Αxino: Not directly detectable iii) Αxino: Not directly detectable iv) A Majorana fermion, the neutralino or LSP iv) A Majorana fermion, the neutralino or LSP (The lightest supersymmetric particle): A linear (The lightest supersymmetric particle): A linear combination of the 2 neutral gauginos and the 2 combination of the 2 neutral gauginos and the 2 neutral Higgsinos. OUR CANDIDATE neutral Higgsinos. OUR CANDIDATE

Symmetries and the Spin Praha, July 28th, 2005 The kinematics of the LSP-nucleus collision

Symmetries and the Spin Praha, July 28th, 2005 Conversion of the energy of the recoiling nucleus into light, heat, ionization etc. The neutralino (LSP) is non relativistic. The neutralino (LSP) is non relativistic. With few exceptions, it cannot excite the nucleusι : With few exceptions, it cannot excite the nucleusι : Measuring the energy of the recoiling nucleus is extremely hard: Measuring the energy of the recoiling nucleus is extremely hard: -Low event rate (much less than 30 per Kg of target per year). -Low event rate (much less than 30 per Kg of target per year). -Bothersome backgrounds (the signal is not very characteristic). -Bothersome backgrounds (the signal is not very characteristic). -Threshold effects. -Threshold effects. -Quenching factors. -Quenching factors.

Symmetries and the Spin Praha, July 28th, 2005 Novel approaches: Exploitation of other signatures of the reaction The modulation effect): The seasonal dependence of the rate due to the motion of the Earth. The modulation effect): The seasonal dependence of the rate due to the motion of the Earth. The excitation of the nucleus (in some rare cases that this is realistic) and detection of the subsequently emitted de-excitation γ rays. The excitation of the nucleus (in some rare cases that this is realistic) and detection of the subsequently emitted de-excitation γ rays. Asymmetry measurements in directional experiments (the direction of the recoiling nucleus is also measured). Asymmetry measurements in directional experiments (the direction of the recoiling nucleus is also measured). Detection of other particles (electrons, X-rays), produced during the LSP-nucleus collision Detection of other particles (electrons, X-rays), produced during the LSP-nucleus collision

Symmetries and the Spin Praha, July 28th, 2005 The SUSY INPUT Allowed parameter space: Univerality at GUT scale: - One mass m 0 for the scalars -One mass m 1/2 for the fermions -Tanβ, the ratio of vacuum expectation values of the Allowed parameter space: Univerality at GUT scale: - One mass m 0 for the scalars -One mass m 1/2 for the fermions -Tanβ, the ratio of vacuum expectation values of the Higss H u,H d, i.e. / -The cubic coupling A 0 (or m t ) -The sign of μ, in μH u H d Higss H u,H d, i.e. / -The cubic coupling A 0 (or m t ) -The sign of μ, in μH u H d Constrain these parameters via the renormalization group equation from the observable low energy quantities (all related to the above five parameters). Constrain these parameters via the renormalization group equation from the observable low energy quantities (all related to the above five parameters). (see: Ellis, Arnowitt, Nath, Bottino and collaborators) (see: Ellis, Arnowitt, Nath, Bottino and collaborators)

Symmetries and the Spin Praha, July 28th, 2005 From the quark level to the nucleon level (coherent: amplitude ~m q )

Symmetries and the Spin Praha, July 28th, 2005 Spin Contribution  Axial Current Going from quark to the nucleon level for the isovector component is standard (from weak interactions): f 1 A (q) -> f 1 A = g A f 1 A (q), g A =1.24 Going from quark to the nucleon level for the isovector component is standard (from weak interactions): f 1 A (q) -> f 1 A = g A f 1 A (q), g A =1.24 For the isoscalar this is not trivial. The naïve quark model fails badly (the proton spin crisis) f 0 A (q) -> f 0 A = g 0 A f 0 A (q), g 0 A =0.1 For the isoscalar this is not trivial. The naïve quark model fails badly (the proton spin crisis) f 0 A (q) -> f 0 A = g 0 A f 0 A (q), g 0 A =0.1

Symmetries and the Spin Praha, July 28th, 2005 The Differential cross section at the nuclear level. υ is the neutralino velocity and u stands essentially for the energy transfer Q: υ is the neutralino velocity and u stands essentially for the energy transfer Q: u=Q/Q 0, Q 0 =40A -4/3 MeV u=Q/Q 0, Q 0 =40A -4/3 MeV F(u) ο The nuclear form factor F(u) ο The nuclear form factor F 11 (u) the isovector spin response function F 11 (u) the isovector spin response function

Symmetries and the Spin Praha, July 28th, 2005 Expressions for the nuclear cross section (continued) With With Σ S =σ p s (μ r /m p ) 2 A 2 for the scalar contribution Σ S =σ p s (μ r /m p ) 2 A 2 for the scalar contribution With σ p s the scalar proton LSP cross section With σ p s the scalar proton LSP cross section μ r is the LSP-nucleus reduced mass μ r is the LSP-nucleus reduced mass A is the nuclear mass A is the nuclear mass Σ Spin is the expression for the spin induced Σ Spin is the expression for the spin induced cross section, which will be discussed later cross section, which will be discussed later

Symmetries and the Spin Praha, July 28th, 2005 LSP Velocity Distributions Conventional: Conventional: Maxwell-Boltzmann (symmetric or axially symmetric) with characteristic velocity equal to the sun’s velocity around the galaxy v 0 =220 km/s and escape velocity Maxwell-Boltzmann (symmetric or axially symmetric) with characteristic velocity equal to the sun’s velocity around the galaxy v 0 =220 km/s and escape velocity v esc =2.84v 0 put in by hand. v esc =2.84v 0 put in by hand. Isothermal models employing Eddington’s theory: Isothermal models employing Eddington’s theory: ρ(r)->Φ(r) -> f(r,v) (JDV-Owen) ρ(r)->Φ(r) -> f(r,v) (JDV-Owen) Non-thermal models: Non-thermal models: Caustic rings, wimps in bound orbits etc Caustic rings, wimps in bound orbits etc Sgr Dwarf galaxy, anisotropic flux, (Green and Spooner) Sgr Dwarf galaxy, anisotropic flux, (Green and Spooner)

Symmetries and the Spin Praha, July 28th, 2005 The event rate for the coherent mode Can be cast in the form: Can be cast in the form: Where: Where: ρ(0) the local neutralino density≈0.3GeV/cm 3. ρ(0) the local neutralino density≈0.3GeV/cm 3. σ S p,χ the neutralino-nucleon cross section. It can be extracted from σ S p,χ the neutralino-nucleon cross section. It can be extracted from the data once f coh (A,m χ ), which will be plotted below, is known. the data once f coh (A,m χ ), which will be plotted below, is known.

Symmetries and the Spin Praha, July 28th, 2005 The factor f coh (A,m χ ) for A=127 (I) (The Dashed for threshold 10keV)

Symmetries and the Spin Praha, July 28th, 2005 The factor f coh (A,m χ ) for A=19 (F) (The Dashed for threshold 10keV)

Symmetries and the Spin Praha, July 28th, 2005 Current Limits on coherent proton cross section

Symmetries and the Spin Praha, July 28th, 2005 A typical Scatter Plot: Universal SUSY parameters (Ceredeno, Gabrielli, Gomez and Munoz)

Symmetries and the Spin Praha, July 28th, 2005 A Scatter Plot: Non Universal SUSY parameters (Ceredeno, Gabrielli, Gomez and Munoz)

Symmetries and the Spin Praha, July 28th, 2005 The event rate due to the spin Where f 0 A (isoscalar) and f 1 A (isovector) couplings at the nucleon level and Ω 0 (0), Ω 1 (0) the corresponding static spin matrix elements Where f 0 A (isoscalar) and f 1 A (isovector) couplings at the nucleon level and Ω 0 (0), Ω 1 (0) the corresponding static spin matrix elements The event rate is cast in the form: The event rate is cast in the form:

Symmetries and the Spin Praha, July 28th, 2005 The factor f spin (A,m χ ) for A=127 (I) (The Dashed for threshold 10keV)

Symmetries and the Spin Praha, July 28th, 2005 The factor f spin (A,m χ ) for A=19 (F) (The Dashed for threshold 10keV)

Symmetries and the Spin Praha, July 28th, 2005 The constrained amplitude plane (f p,χ,f n,χ ) for the Α=127 system (arbitrary units)

Symmetries and the Spin Praha, July 28th, 2005 The constrained (σ p,χ,σ n,χ ) plane for the Α=127 system (arbitrary units). Under the curve on the left, if the amplitudes have the same sign and between the curves on the right for opposite sign.

Symmetries and the Spin Praha, July 28th, 2005 THE MOFULATION EFFECT v June =235+15=250km/s v Dec =235-15=220km/s

Symmetries and the Spin Praha, July 28th, 2005 THE MODULATION EFFECT (continued) α=phase of the Earth α=phase of the Earth (α=0 around June 3nd) (α=0 around June 3nd) γ=π/3 is the angle between the axis of galaχy and the axis of the ecliptic. γ=π/3 is the angle between the axis of galaχy and the axis of the ecliptic. h=modulation amplitude. h=modulation amplitude. R 0 =average rate. R 0 =average rate.

Symmetries and the Spin Praha, July 28th, 2005 The Modulation Amplitude h for I On the left zero energy cut off. On the right a cut off of 10keV

Symmetries and the Spin Praha, July 28th, 2005 The directional event rate The event rate in directional experiments is: The event rate in directional experiments is: R dir =(κ/2π)R 0 [1+cos(α-α m π)] R dir =(κ/2π)R 0 [1+cos(α-α m π)] R 0 is the average usual (non-dir) rate R 0 is the average usual (non-dir) rate α the phase of the Earth (as usual) α the phase of the Earth (as usual) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ and α m depend only slightly on SUSY κ and α m depend only slightly on SUSY

Symmetries and the Spin Praha, July 28th, 2005 The event rate vs the polar angle (A=19, left), (A=127, right) for m χ =100 GeV and M-B distribution

Symmetries and the Spin Praha, July 28th, 2005 The parameter κ vs the LSP mass: perpendicular to the sun’s velocity (left) and opposite to it (right)

Symmetries and the Spin Praha, July 28th, 2005 The modulation vs the LSP mass: opposite the sun’s velocity (left) and perpendicular to it (right)

Symmetries and the Spin Praha, July 28th, 2005

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

Symmetries and the Spin Praha, July 28th, 2005 The relative differential Rate, (dR e /dT e )/R recoil, vs electron energy T for electron production in LSP- nucleus (Moustakides, JDV, Ejiri). The relative differential Rate, (dR e /dT e )/R recoil, vs electron energy T for electron production in LSP- nucleus (Moustakides, JDV, Ejiri).

Symmetries and the Spin Praha, July 28th, 2005 The Relative (with respect to recoil) rate of ionization per atom vs: a) E threshold for m χ =100Gev (left) and b) m χ for E threshold = 0.2 keV (right)

Symmetries and the Spin Praha, July 28th, 2005 There are Z electrons in an atom!

Symmetries and the Spin Praha, July 28th, 2005 Detection of hard X-rays After the ionization there is a K or L hole After the ionization there is a K or L hole This hole de-excites via emitting X-rays or Auger electron. Indicate with b n ℓ the relative ratio (determined experimentally) This hole de-excites via emitting X-rays or Auger electron. Indicate with b n ℓ the relative ratio (determined experimentally) Then the fraction of X-rays per recoil is: σ X(n ℓ ) /σ r = b nl (σ n ℓ /σ r ) with σ n ℓ /σ r the relative ionization rate discussed above Then the fraction of X-rays per recoil is: σ X(n ℓ ) /σ r = b nl (σ n ℓ /σ r ) with σ n ℓ /σ r the relative ionization rate discussed above

Symmetries and the Spin Praha, July 28th, 2005 Detection of hard X-rays (continued) n ℓ shell ε n ℓ (keV) σ n ℓ /σ r σ X(n ℓ ) /σ r n ℓ shell ε n ℓ (keV) σ n ℓ /σ r σ X(n ℓ ) /σ r is 34.56 0.22 ? is 34.56 0.22 ? 2s 5.45 1.46 ? 2s 5.45 1.46 ? 2p 4.89 4.51 ? 2p 4.89 4.51 ?

Symmetries and the Spin Praha, July 28th, 2005 Conclusions: Experimental ambitions

Symmetries and the Spin Praha, July 28th, 2005 Projected exclusion curve for 3 He detector Background = 0.01 day -1 Energy threshold = 1 keV CRESST Saphire ELEGANT V NaI UKDMC NaI NAIAD projection

Symmetries and the Spin Praha, July 28th, 2005 Projected exclusion curve for scalar detectors 2003 Edelweiss and CDMS projections

Symmetries and the Spin Praha, July 28th, 2005 CONCLUSIONS-Standard Rates (theory) Most of the uncertainties come the fact that the allowed SUSY parameter space has not been sufficiently sharpened. Most of the uncertainties come the fact that the allowed SUSY parameter space has not been sufficiently sharpened. The other uncertainties (nuclear form factor, structure of the nucleon, quenching factor, energy threshold) could affect the results by an order of magnitude. The other uncertainties (nuclear form factor, structure of the nucleon, quenching factor, energy threshold) could affect the results by an order of magnitude. Most of the parameter space yields undetectable rates. Most of the parameter space yields undetectable rates. The coherent contribution due to the scalar interaction is the most dominant. The coherent contribution due to the scalar interaction is the most dominant.

Symmetries and the Spin Praha, July 28th, 2005 CONCLUSIONS-Modulation (theory) The modulation amplitude h is small less than 2% and depends on the LSP mass. Its sign is also uncertain for intermediate and heavy nuclei. The modulation amplitude h is small less than 2% and depends on the LSP mass. Its sign is also uncertain for intermediate and heavy nuclei. It may increase as the energy cut off remains big (as in the DAMA experiment), but at the expense of the number of counts. The DAMA experiment maybe consistent with the other experiments, if the spin interaction dominates. It may increase as the energy cut off remains big (as in the DAMA experiment), but at the expense of the number of counts. The DAMA experiment maybe consistent with the other experiments, if the spin interaction dominates.

Symmetries and the Spin Praha, July 28th, 2005 CONCLUSIONS-Directional Rates Good signatures, but the experiments are hard (the DRIFT experiment cannot tell the sense of direction of recoil) Good signatures, but the experiments are hard (the DRIFT experiment cannot tell the sense of direction of recoil) Large asymmetries are predicted Large asymmetries are predicted The rates are suppressed by a factor κ/2π, κ<0.6 The rates are suppressed by a factor κ/2π, κ<0.6 For a given LSP velocity distribution, κ depends on the direction of observation For a given LSP velocity distribution, κ depends on the direction of observation In the most favored direction κ is approximately 0.6 In the most favored direction κ is approximately 0.6 In the plane perpendicular to the sun’s velocity κ is approximately equal to 0.2 In the plane perpendicular to the sun’s velocity κ is approximately equal to 0.2

Symmetries and the Spin Praha, July 28th, 2005 CONCLUSIONS- Modulation in Directional Experiments The Directional rates also exhibit modulation The Directional rates also exhibit modulation In the most favored direction of observation, parallel to the sun’s motion, the modulation is now twice as large. (Maximum in June, Minimum in December) In the most favored direction of observation, parallel to the sun’s motion, the modulation is now twice as large. (Maximum in June, Minimum in December) In the plane perpendicular to the sun’s motion the modulation is much larger. The difference between the maximum and the minimum can be as high as 50%. It also shows a direction characteristic pattern (for observation directions on the galactic plane the maximum may occur in September or March, while normal behavior for directions perpendicular to the galaxy) In the plane perpendicular to the sun’s motion the modulation is much larger. The difference between the maximum and the minimum can be as high as 50%. It also shows a direction characteristic pattern (for observation directions on the galactic plane the maximum may occur in September or March, while normal behavior for directions perpendicular to the galaxy)

Symmetries and the Spin Praha, July 28th, 2005 CONCLUSIONS-Transitions to excited states Transitions to excited states are possible in few odd A nuclei. Transitions to excited states are possible in few odd A nuclei. When allowed, are kinematically suppressed When allowed, are kinematically suppressed The branching ratio depends on the structure of the nucleus and the LSP mass The branching ratio depends on the structure of the nucleus and the LSP mass In the case of Iodine, a popular target for recoils, it can be as high as 7% for LSP mass higher than 200 GeV In the case of Iodine, a popular target for recoils, it can be as high as 7% for LSP mass higher than 200 GeV

Symmetries and the Spin Praha, July 28th, 2005 CONCLUSIONS: Electron production during LSP-nucleus collisions During the neutralino-nucleus collisions, electrons may be kicked off the atom During the neutralino-nucleus collisions, electrons may be kicked off the atom Electrons can be identified easier than nuclear recoils (Low threshold ~0.25keV TPC detectors) Electrons can be identified easier than nuclear recoils (Low threshold ~0.25keV TPC detectors) The branching ratio for this process depends on the threshold energies and the LSP mass. The branching ratio for this process depends on the threshold energies and the LSP mass. For a threshold energy of 0.25 keV the ionization event rate in the case of a heavy target can exceed the rate for recoils by an order of 10. For a threshold energy of 0.25 keV the ionization event rate in the case of a heavy target can exceed the rate for recoils by an order of 10. Detection of hard X-rays also seams feasible Detection of hard X-rays also seams feasible

Symmetries and the Spin Praha, July 28th, 2005 THE END THE END

Symmetries and the Spin Praha, July 28th, 2005 3 He-  cross-section SI cross-section :  SI ( A X)   SI (p)×A 4 SD cross-section :  SD ( A X)   SD (p)×A 2 For 3 He :  SD   SI  only  SD considered For A X nucleus:  ( 3 He)  m r 2 (J+1)/J (a p +a n ) 2 with 3 He spin content: =-0.05 =0.49  scattering on the unpaired neutron

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

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

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Presentation on theme: "Symmetries and the Spin Praha, July 28th, 2005 On the Direct Detection of SUSY Dark Matter On the Direct Detection of SUSY Dark Matter J.D. Vergados University."— Presentation transcript:

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