1. Stefano Scopel Supersymmetric Dark Matter PPC2010, Torino, 12 July 2010

2. Outline Dark Matter & susy in a nutshell examples of susy scenarios The low mass WIMP conspiracy: DAMA, CDMS2 and CoGeNT the XENON100 exclusion plot light neutralinos in the MSSM

3. Evidence for Dark Matter Spiral galaxies rotation curves Clusters & Superclusters Weak gravitational lensing Strong gravitational lensing Galaxy velocities X rays Large scale structure Structure formation CMB anisotropy: WMAP Ω tot =1 Ω dark energy ~0.7 Ω matter ~ 0.27 Ω baryons ~0.05 Ω visible ~0.005 Ω dark matter ~ 0.22

4. (Incomplete) List of DM candidates Neutrinos Axions Lightest Supersymmetric particle (LSP) – neutralino, sneutrino, axino Lighest Kaluza-Klein Particle (LKP) Heavy photon in Little Higgs Models Solitons (Q-balls, B-balls) Black Hole remnants Hidden-sector tecnipions BEC/scalar field … BEC/scalar field

5. Over-constrained scenario: the concordance model

6. thermal cosmological density of a WIMP X Ω X h 2 ~ 1/ int int = ∫ dx xfxf x0x0 x f =M/T f x 0 =M/T 0 T f =freeze-out temperature T 0 =present (CMB) temperature X f >>1, X non relativistic at decoupling, low temp expansion for : ~a+b/x if σ ann is given by weak-type interactions → Ω X ~0.1-1 …+ cohannihilations with other particle(s) close in mass + resonant annihilations

7. today’s entropy critical density freeze-out temperature # of degrees of freedom m = WIMP mass Y 0 : from Boltzmann equation

8. N.B. Very different scales conjure up to lead to the weak scale! CMB temp. Hubble par. Planck scale the WIMP “miracle”

9. Hierarchy problem of the Standar Model : radiative corrections to the Higgs boson: δm H 2 ~λ 2, where λ is the scale beyond which the low-energy theory no longer applies (λ=cut-off of the SM) a huge cancellation needed unless λ~TeV itself Higgs mass expected to be below a few TeV (on general grounds, perturbativity of the theory)

10. new physics at the electro-weak scale is cool because it kills two birds with one stone: 1.solves the hierarchy problem 2.explains the Dark Matter The bottom line

11. most popular thermal WIMP candidates from particle physics (solve hierarchy problem: M W /M Pl ~ 10 -16 ) susy conserved symmetry DM candidate R-parity K-parity T-parity χ ( neutralino) extra dimensions little Higgs B (1) (KK photon) B H (heavy photon) all thermal candidates, massive, with weak-type interactions (WIMPs) * the most popular

12. suggested by string theory renormalizable solves the hierarchy problem (why m W <<m planck ) compatible to GUT unification of gauge couplings provides a DM candidate (if R-parity is introduced to prevent nucleon decay so that the LSP is stable) Why susy is so appealing:

13. GUT unification of gauge couplings

14. WIMP signal at accelerators: missing energy+new particles produced in pairs dangerous, don’t want it!

16. the sneutrino [Arina, Fornengo, JHEP0711(2007)029

17. the sneutrino allowed due to rescaling

18. [Arina, Fornengo, JHEP0711(2007)029 mixing with a right-handed component makes thing easier 2

19. low see-saw scale M=1 TeV needed inelastic scattering in direct detection! [Arina, Fornengo, JHEP0711(2007)029 relic abundance direct detection Z

20. The neutralino  The neutralino is defined as the lowest-mass linear superposition of bino B, wino W (3) and the two higgsino states H 1 0, H 2 0 :  neutral, colourless, only weak-type interactions  stable if R-parity is conserved, thermal relic  non relativistic at decoupling  Cold Dark Matter (required by CMB data + structure formation models)  relic density can be compatible with cosmological observations: 0.095 ≤ Ω χ h 2 ≤ 0.131  IDEAL CANDIDATE FOR COLD DARK MATTER ~ ~ ~ ~ 3 4

21. SUGRA (a.k.a. CMSSM) focus point [Feng, Machev, Moroi, Wilczek] stau coannihilationHiggs funnel [Ellis, Olive, Santoso, Spanos, 1001.3651] only few regions cosmologically allowed variants (e.g. non-universality of soft masses at the GUT scale or lower unification scale) that increase Higgsino content of the neutralino→ lower relic abundance and higher signals neutralino density tends to be too large is the WIMP “miracle” failing?

22. Many contributions to neutralino annihilation…

23. …but two main classes: fermion diagrams: m f /M W helicity suppression due to Majorana nature of neutralino Gauge boson diagrams: suppressed if neutralino~Bino (this is usually the case when Radiative ElectroWeak Symmetry Breaking is implemented, |μ|>>M 1,M 2 )

24. the WIMP paradigm is fine but the devil is in the details!

25. The Next-to-Minimal MSSM (NMSSM) solves the μ problem, i.e. why μ~M EW superpotential: Higgs soft terms in the NMSSM: NMSSM particle content: MSSM+ 2 Higgs (CP-even, CP-odd) 1 neutralino dof The lightest neutralino: CP-even Higgs:

26. Relic density and direct detection rate in NMSSM [Cerdeño, Hugonie, López-Fogliani, Muñoz, Teixeira] relic abundance direct detection M 1 =160 GeV, M 2 =320, A λ =400 GeV, A k =-200 GeV, μ=130 GeV, tan β=5 (sizeable direct detection ) very light neutral Higgs (mainly singlet) light scalars imply more decay channels and resonant decays neutralino relatively light (< decay thresholds) and mostly singlino high direct detection cross sections (even better for lower M 1 ) tachyons Landau pole unphysical minima W H1H1 H 2 /2 χ,H lighter χ singlino Z

27. Effective MSSM: effective model at the EW scale with a few MSSM parameters which set the most relevant scales M 1 U(1) gaugino soft breaking term M 2 SU(2) gaugino soft breaking term μ Higgs mixing mass parameter tan β ratio of two Higgs v.e.v.’s m A mass of CP odd neutral Higgs boson (the extended Higgs sector of MSSM includes also the neutral scalars h, H, and the charged scalars H ±) m q soft mass common to all squarks m l soft mass common to all sleptons A common dimensionless trilinear parameter for the third family (A b = A t ≡ Am q ; A τ ≡ Am l ) R ≡ M 1 /M 2 ~ ~ ~ ~ ~ ~ ~ SUGRA  R=0.5

28. Cosmological lower bound on m χ upper bound on Ω CDM h 2 scatter plot: full calculation curve: analytical approximation for minimal Ω CDM h 2 A. Bottino, F. Donato, N. Fornengo, S. Scopel, Phys. Rev. D 68, 043506 (2003)

29. The elastic cross section is bounded from below:  “funnel” at low mass Neutralino – nucleon cross section Color code: ● Ω χ h 2 < 0.095  Ω χ h 2 > 0.095 A. Bottino, N. Fornengo, S. Scopel ; Phys.Rev.D67:063519,2003 ; A. Bottino, F. Donato, N. Fornengo, S. Scopel, PRD69:037302,2004

30. The field of Dark Matter searches has been quite active recently… CDMS2 (December 2009) DAMA/Libra (February 2010) CoGeNT (February 2010) XENON100 ( May 2010)

31. two further annual cycles collected, the first with the same setup of previous data, the second after detector upgrade in 2008 corresponds to a further exposure of 0.34 ton year combining DAMA/NaI and DAMA/Libra a total of 13 annual cycles collected (7 DAMA/NaI+6 DAMA/Libra) corresponding to 1.17 ton year 8.9 σ C.L. effect Bernabei at al., arXiv:1002.1028 The DAMA/Libra annual modulation result

32. 6 years of DAMA/Libra (0.87 ton year) Bernabei at al., arXiv:1002.1028

33. Channeling effect in crystals (Dobryshevsky, arXiv:0706.3095, Bernabei et al., arxiv:07100288) anomalous deep penetration of ions into crystalline targets discovered a long time ago (1957, 4 keV 134 CS + observed to penetrate λ~ 1000 Å in Ge, according to Lindhard theory λ~ 44 Å) when the ion recoils along one crystallographic axis it only encounters electrons → long penetration depth and q~1 C 2 ~3, d=interatomic spacing a 0 =0.529 Å (Bohr radius) critical angle:

34. DAMA WIMP interpretation and other direct searches From Savage et al., arXiv:0901.2713 small viable window with M WIMP ≲ 10

35. 14 Ge detectors (out of a total of 30 detectors, 19 Ge and 11 Si) After the timing cut (to remove “surface events”) Efficiency of the cut~25% close to threshold Z. Ahmed at al., arXiv:0912.3592 When signal region is unblinded2 events survived Resulting exposure~194.1 kg-day The CDMS2 result

36. Background estimation due to surface “leakage” : before unblinding: 0.6±0.1 (stat.) after unblinding: 0.8±0.1 (stat.) ±0.2 (stat.) Z. Ahmed at al., arXiv:0912.3592 ~23% probability that the 2 events are just background Final comment from J. Cooly’s talk @ SLAC, 17 December 2009:

37. 90% C.L. interval for 2 observed events: 0.53→5.3 DAMA no channeling DAMA channeling effMSSM including uncertainty on hadronic matrix elements x 0.098<Ω χ h 2 <0.122 Ω χ h 2 <0.098 Scatter plot: reference value for hadronic matrix elements The 2 CDMS events and light relic neutralinos Bottino, Donato, Fornengo, Scopel, PRD81 107302(2010), arXiv:0912.4025

38. 95% C.L. interval using spectral info (maximum likelihood method, no background) DAMA no channeling DAMA channeling effMSSM including uncertainty on hadronic matrix elements x 0.098<Ω χ h 2 <0.122 Ω χ h 2 <0.098 Scatter plot: reference value for hadronic matrix elements The 2 CDMS events and light relic neutralinos

39. Bottino, Donato, Fornengo, Scopel, PRD81 107302(2010), arXiv:0912.4025 85% C.L. interval using spectral info (maximum likelihood method, background included) DAMA no channeling DAMA channeling effMSSM including uncertainty on hadronic matrix elements x 0.098<Ω χ h 2 <0.122 Ω χ h 2 <0.098 Scatter plot: reference value for hadronic matrix elements The 2 CDMS events and light relic neutralinos

40. The CoGeNT experiment Germanium ionization detector with new geometry (P-type point contact, PPC) standard coaxial geometryP-type Point Contact (PPC) Reduction of electronic noise Surface event rejection using rise-time cuts → very low threshold<400 eV

41. The new CoGeNT result (C.E. Aalseth et al., 1002.4703) fit of the observed count rate using 28 bins and 3 components: L/K shell electron-capture peaks from 71 Ge (1 parameter) Exponentially decaying background (2 parameters, amplitude and exponent) Free constant background (1 parameter) DM component (2 parameters) For 7 GeV < m WIMP <11 GeV the chi square probability drops < 10% if the DM component is zero → need additional exponential, WIMP signal indication?

42. The new CoGeNT result (C.E. Aalseth et al., 1002.4703)

43. The XENON10 limit nowadays widely considered the most competitive Dark Matter Search experiment dual-phase Xenon allows to measure ionization and scintillation at the same time Anticorrelation between the prompt scintillation in the liquid and the proportional scintillation in the gas (the latter produced by the charges produced in ionization and taken out by electric field). The sum of ionization and scintillation is proportional to the total deposited energy

44. Discrimination between background (β and γ) and recoils+neutrons ←for a gamma source S2/S1 is larger ←for a neutron source S2/S1 is smaller J. Angle et al., Phys. Rev. Lett. 100 (2008) 021303, arXiv: 0706.0039.

45. N.B.: the XENON100 limit is slightly less constraining than the XENON10 one MAY 2010: the first XENON100 result (1005.0380):

46. A small threshold is crucial to be sensitive to WIMP induced nuclear recoils

47. Two major limitations: The response in the detector is not homogeneous (ionization strongly depends on the position due to different reflection at the liquid-gas surface, impurities, charge recombination, local electric field). However position information is available event by event (89 photomultipliers + vertical drift timing info), so the response can be mapped using internal neutron-activated 131 Xe (emitting 164 keV gammas) and 129 Xe (emitting 236 keV gammas) This map, along with a Monte Carlo, is used to renormalize the events. Aprile et al., arXiv:1001.2834 However no direct map is available at energies below 164 keV. What happens @ 4 keV?

48. Energy calibration only available at 122 keV and 662 kev (the characteristic X-ray peak @ 30 keV from 57 Co is barely visible at the edge of the sensitive volume) The energy scale at lower energy is extrapolated from 122 kev to 4 kev assuming a linear response. However between 122 keV and 662 keV the response is already non linear (the light yield is 2.2 p.e./kev @662 keV and 3.1 p.e./keV @122 keV).

49. DAMA calibration: the 3.2 keV peak from 40 K provides the lowest- energy calibration point Comparison with other experiments CDMS and Edelweiss calibration: Neutrons from 252 Cf source activate 71 Ge that decays to 71 Ga (T 1/2 ~16 days) producing a peak at 10.4 keV Additional calibration points: 133 Ba (γ lines at 303, 356 and 384 keV)

50. 50 Relative intensity..... Am calibration -> ~5 p.e /keV Am241 calibration in KIMS E(keV) 13.9keV Np L  X-ray 17.8keV Np L  X-ray 20.8keV Np L  X-ray 26.35keV gamma Cs, I X –ray escape 59.54 gamma S. C. Kim’s talk, KIMS Coll., Yongpyong, February 2010

51. In short: for the time being, the 4 keV threshold and the linear response of XENON10(0) rely on an extrapolation at the energies where the WIMP signal is expected People in XENON are aware of the problem and plan to use a lower calibration point from E. Aprile’s talk, SJTU workshop, june 2009

52. This was supposed to be the “easy” part (gammas calibration). What about nuclear recoils?

53. The efficiency factor (quenching) of xenon From: Aprile et al., PRC79,045807(2009) Defined as the scintillation yield of nuclear recoils relative to that of 122-keV γ rays Crucial in determining the energy scale of WIMP recoils starting from the gamma calibration directly measured using a fixed-energy neutron flux

54. The XENON10 efficiency factor saga in the 2007 paper (arXiv:0706.0039) the XENON10 limit widely used in the literature was derived assuming a constant L eff =0.19 in 2008 a part of the Collaboration measured again the efficiency, finding a lower value, depending on the energy. The exclusion plot weakened accordingly. in 2009 another (smaller) part of the Collaboration repeated the measurement, finding an even lower value of L eff : N.B. larger effect (~1 order of magnitude) at low WIMP masses. Large error bars, the limit corrected using the central value of L eff. What is the conservative exclusion plot? Aprile et al., PRC79,045807(2009) Manzur et al., arXiv: 0909.1063 0.19 MC

55. For the moment it would be safe to take XENON10 n with a grain of salt, although improvements are likely in the future

57. Conclusions susy still the most popular solution to the dark matter problem (soon checked @ LHC? see next talk by A. Polesello) several scenarios on the market: SUGRA, NMSSM, Light Neutralinos,… The low-mass WIMP connection: DAMA/Libra, CDMS 2, Cogent XENON100 claims to exclude these effects but for the moment take it with a grain of salt light WIMPs (~10 GeV) are fashionable these days. First dicussed in connection to experimental results as early as 2003 (Bottino et al., Phys.Rev.D67:063519,2003 ; PRD69:037302,2004)Neutralino