Introduction to Direct Dark Matter Detection Phenomenology

Transcription

1 Introduction to Direct Dark Matter Detection Phenomenology Chung-Lin Shan Institute of Physics, Academia Sinica College of Applied Sciences, Beijing University of Technology Beijing, China September 19, 2012

2 Outline Introduction Direct Dark Matter detection Model-independent data analyses Motivation Reconstruction of the WIMP velocity distribution Determination of the WIMP mass Estimation of the SI WIMP-nucleon coupling Determinations of ratios of WIMP-nucleon cross sections Effects of residue background events AMIDAS package and website Summary C.-L. Shan, AS IoP BUT, September 19, 2012, p. 1

3 References References: Dark Matter (detection) Cosmology M. S. Turner, arxiv:astro-ph/ (1999). J. Beringer et al., "The Review of Particle Physics", Phys. Rev. D 86, (2012): K. A. Olive and J. A. Peacock, 21. Big-Bang Cosmology; B. D. Fields and S. Sarkar, 22. Big-Bang Nucleosynthesis; O. Lahav and A. R. Liddle, 23. The Cosmological Parameters; M. Drees and G. Gerbier, 24. Dark Matter; D. Scott and G. F. Smoot, 25. Cosmic Microwave Background. C.-L. Shan, AS IoP BUT, September 19, 2012, p. 2

4 References References: Dark Matter (detection) Dark Matter evidence, candidates and detection (astrophysics) G. Jungman, M. Kamionkowski and K. Griest, "Supersymmetric Dark Matter", Phys. Rep. 267, 195 (1996). G. Bertone, D. Hooper and J. Silk, "Particle Dark Matter: Candidates and Constraints", Phys. Rep. 405, 279 (2005). Evidence, D. Hooper, "TASI 2008 Lectures on Dark Matter", arxiv: [hep-ph] (2009). L. Bergström, "Dark Matter Evidence, Particle Physics Candidates and Detection Methods", arxiv: [astro-ph.he] (2012). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 3

5 References References: Dark Matter (detection) Dark Matter candidates (particle physics) F. D. Steffen, "Dark Matter Candidates: Axions, Neutralinos, Gravitinos, and Axinos", Eur. Phys. J. C 59, 557 (2009). L. Bergström, "Dark Matter Candidates", New J. Phys. 11, (2009). J. Ellis and K. A. Olive, "Supersymmetric Dark Matter Candidates", contribution to "Particle Dark Matter: Observations, Models and Searches", edited by G. Bertone, Cambridge University Press (2010), arxiv: [astro-ph.co]. M. Drees and G. Gerbier, "Mini-Review of Dark Matter: 2012", updated minireview for "The Review of Particle Physics 2012", arxiv: [hep-ph] (2012). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 4

6 References References: Dark Matter (detection) Direct Dark Matter detection (theory) C.-L. Shan, Ph.D. Thesis, "Theoretical Interpretation of Experimental Data from Direct Dark Matter Detection", arxiv: (2007). D. G. Cerde~no and A. M. Green, "Direct Detection of WIMPs", contribution to "Particle Dark Matter: Observations, Models and Searches", edited by G. Bertone, Cambridge University Press (2010), arxiv: [astro-ph.co]. K. Freese, M. Lisanti and C. Savage, Annual Modulation of Dark Matter: A Review, arxiv: [astro-ph.co] (2012). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 5

7 References References: Dark Matter (detection) Direct Dark Matter detection (experiments) L. Baudis, "Direct Detection of Cold Dark Matter", arxiv: (2007). E. Armengaud, "Gif Lectures on Direct Detection of Dark Matter", arxiv: [hep-ex] (2010). E. Aprile and T. Doke, "Liquid Xenon Detectors for Particle Physics and Astrophysics", Rev. Mod. Phys. 82, 2053 (2010). S. Ahlen et al., "The Case for a Directional Dark Matter Detector and the Status of Current Experimental Efforts", Int. J. Mod. Phys. A 25, 1 (2010). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 6

8 References References: direct Dark Matter detection phenomenology Velocity distribution A. H. G. Peter and S. Tremaine, "Dynamics of WIMPs in the Solar System and Implications for Detection", PoS IDM2008, 061 (2008). A. H. G. Peter, "Getting the Astrophysics and Particle Physics of Dark Matter Out of Next-Generation Direct Detection Experiments", PRD 81, (2010). A. H. G. Peter, "WIMP Astronomy with Liquid-Noble and Cryogenic Direct-Detection Experiments", PRD 83, (2011). L. E. Strigari and R. Trotta, "Reconstructing WIMP Properties in Direct Detection Experiments Including Galactic Dark Matter Distribution Uncertainties", JCAP 0911, 019 (2009). A. Natarajan, C. Savage and K. Freese, "Probing Dark Matter Streams with CoGeNT", PRD 84, (2011). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 7

9 References References: direct Dark Matter detection phenomenology Mass/SI cross section (maximum likelihood analysis) A. M. Green, "Determining the WIMP Mass Using Direct Detection Experiments", JCAP 0708, 022 (2007). A. M. Green, "Determining the WIMP Mass from a Single Direct Detection Experiment, a More Detailed Study", JCAP 0807, 005 (2008). A. M. Green, "Extracting Information about WIMP Properties from Direct Detection Experiments: Astrophysical Uncertainties", arxiv: [astro-ph.co] (2010). B. J. Kavanagh and A. M. Green, "Improved Determination of the WIMP Mass from Direct Detection Data", arxiv: [astro-ph.co] (2012). M. Pato et al., "Complementarity of Dark Matter Direct Detection Targets", PRD (2011). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 8

10 References References: direct Dark Matter detection phenomenology SD cross sections/couplings D. R. Tovey et al., "A New Model-Independent Method for Extracting Spin-Dependent Cross Section Limits from Dark Matter Searches", PLB 488, 17 (2000). F. Giuliani, "Model-Independent Assessment of Current Direct Searches for Spin-Dependent Dark Matter", PRL 93, (2004). F. Giuliani and T. A. Girard, "Model-Independent Limits from Spin-Dependent WIMP Dark Matter Experiments", PRD 71, (2005). T. A. Girard and F. Giuliani, "On the Direct Search for Spin-Dependent WIMP Interactions", PRD 75, (2007). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 9

11 References References: direct Dark Matter detection phenomenology SI and SD cross sections M. Cannoni, J. D. Vergados and M. E. Gomez, "Extraction of Neutralino-Nucleon Scattering Cross Sections from Total Rates", PRD 83, (2011). P. J. Fox, G. D. Kribs and T. M. P. Tait, "Interpreting Dark Matter Direct Detection Independently of the Local Velocity and Density Distribution", PRD 83, (2011). P. J. Fox, J. Liu and N. Weiner, "Integrating Out Astrophysical Uncertainties", PRD 83, (2011). M. Pato, "What Can(not) be Measured with Ton-Scale Dark Matter Direct Detection Experiments", JCAP 1110, 035 (2011). S. D. McDermott, H. B. Yu and K. M. Zurek, "The Dark Matter Inverse Problem: Extracting Particle Physics from Scattering Events", PRD 85, (2012). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 10

12 References References: direct Dark Matter detection phenomenology Directional information J. Billard, F. Mayet and D. Santos, "Exclusion Limits from Data of Directional Dark Matter Detectors", PRD 82, (2010). J. Billard, F. Mayet and D. Santos, "A Markov Chain Monte Carlo Analysis to Constrain Dark Matter Properties with Directional Detection", PRD 83, (2011). S. K. Lee and A. H. G. Peter, "Probing the Local Velocity Distribution of WIMP Dark Matter with Directional Detectors", JCAP 1204, 029 (2012). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 11

13 References References: our works Model-independent data analyses M. Drees and C.-L. Shan, "Reconstructing the Velocity Distribution of Weakly Interacting Massive Particles from Direct Dark Matter Detection Data", JCAP 0706, 011 (2007). M. Drees and C.-L. Shan, "Model-Independent Determination of the WIMP Mass from Direct Dark Matter Detection Data", JCAP 0806, 012 (2008). C.-L. Shan, "Estimating the Spin-Independent WIMP-Nucleon Coupling from Direct Dark Matter Detection Data", arxiv: [hep-ph] (2011). C.-L. Shan, "Determining Ratios of WIMP-Nucleon Cross Sections from Direct Dark Matter Detection Data", JCAP 1107, 005 (2011). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 12

14 References References: our works Effects of residue background events Y.-T. Chou and C.-L. Shan, "Effects of Residue Background Events in Direct Dark Matter Detection Experiments on the Determination of the WIMP Mass", JCAP 1008, 014 (2010). C.-L. Shan, "Effects of Residue Background Events in Direct Dark Matter Detection Experiments on the Reconstruction of the Velocity Distribution Function of Halo WIMPs", JCAP 1006, 029 (2010). C.-L. Shan, "Effects of Residue Background Events in Direct Dark Matter Detection Experiments on the Estimation of the Spin-Independent WIMP-Nucleon Coupling", arxiv: [hep-ph] (2011). C.-L. Shan, "Effects of Residue Background Events in Direct Dark Matter Detection Experiments on the Determinations of Ratios of WIMP-Nucleon Cross Sections", arxiv: [hep-ph] (2011). C.-L. Shan, AS IoP BUT, September 19, 2012, p. 13

15 Preface Some words about simulations and phenomenology Some words about simulations and phenomenology C.-L. Shan, AS IoP BUT, September 19, 2012, p. 14

16 Preface Some words about simulations and phenomenology Some words about simulations and phenomenology In the 1930s Enrico Fermi made some numerical experiments that would now be called Monte Carlo calculations. [Monte Carlo Methods, M. H. Kalos and P. A. Whitlock, Chap. 1, p. 3] The name Monte Carlo was applied to a class of mathematical methods first by scientists working on the development of nuclear weapons in Los Alamos in the 1940s. [Monte Carlo Methods, M. H. Kalos and P. A. Whitlock, Chap. 1, p. 1] Relationship between theory, experiment, and numerical simulation: each is distinct, but each is strongly connected to the other two. Experiment Theory Simulation [A Guide to M. C. Simu. in Stat. Phys., D. P. Landau and K. Binder, Sec. 1.5, p. 5] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 15

17 Preface Some words about simulations and phenomenology Some words about simulations and phenomenology Research "triangle" Theory: model building, phenomenon predicting Phenomenology: data analyzing, model constraining/distinguishing 6 7 Experiment: Simulation: detection techniques, data analyzing techniques, data taking/analyzing numerical programming C.-L. Shan, AS IoP BUT, September 19, 2012, p. 16

18 Introduction Dark Matter searches C.-L. Shan, AS IoP BUT, September 19, 2012, p. 17

19 Introduction Dark Matter searches DM should have small, but non-zero interactions with SM matter. = Three different ways to detect DM particles p, e DM DM e, ν µ, γ DM DM (, ) p, e + DM ( ) DM e +, p, D q q Colliders Indirect detection Direct detection C.-L. Shan, AS IoP BUT, September 19, 2012, p. 18

20 Introduction Direct DM detection Direct Dark Matter detection C.-L. Shan, AS IoP BUT, September 19, 2012, p. 19

21 Introduction Direct DM detection We start with... the existence of Dark Matter (DM) Clusters of galaxies Galactic rotation curves [Coma cluster of galaxies; F. Zwicky (1933)] Bullet Cluster CMBR anisotropy [Rubin and Ford, ApJ 159, 379 (1970)] [ Abundances of D, 3 HE, 4 He [NASA/WMAP Science Team, WMAP5 (2008)] SNe Ia observations at high-z [Review of Particle Physics 2006] [Supernova Cosmology Project 2010]] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 20

22 Introduction Direct DM detection We start with... the majority of Cold Dark Matter (CDM) moved non-relativistically when galaxies could just start to form (matter-radiation decoupling time). would form some small galactic scale structures due to their relatively slower velocities (botton-up). Hot Dark Matter (HDM) moved relativistically would cover great(er) distances and form some very large scale structures (top-down). Warm Dark Matter (WDM) Dark baryons C.-L. Shan, AS IoP BUT, September 19, 2012, p. 21

23 Introduction Direct DM detection We start with... Weakly Interacting Massive Particles (WIMPs) χ Dark Matter relic density Ω χh cm 3 /s σ anniv = σ anni v cm 3 /s = weak interaction = ± EM, gravitational, strong interactions have masses roughly between 10 GeV and a few TeV. ( ) v χ 10 3 c = Q m χ Gravitino, axion, axino C.-L. Shan, AS IoP BUT, September 19, 2012, p. 22

24 Introduction Direct DM detection We start with... the lightest SUSY neutralino χ 0 1 the lightest SUSY particle (LSP). are linear combinations of photino, Z-ino and neutral higgsinos. The lightest Kaluza-Klein (KK) particle (LKP) in Universal Extra Dimensions (UED) models The lightest T-odd particle in Little-Higgs (LH) models Sneutrinos Other candidates: Asymmetric DM, CHAMPs, dynamical DM, fermionic DM, FIMP, inelastic DM, inert-doublet DM, isospin-violating DM, itimp, kev DM, leptophilic DM, light DM, MeV DM, mirror DM, heavy fourth-generation Dirac and Majorana/massive/sterile neutrinos, (singlet) scalar DM, WIMPless DM,... C.-L. Shan, AS IoP BUT, September 19, 2012, p. 23

25 Introduction Direct DM detection We start with... elastic WIMP-nucleus scattering The event rate depends on the WIMP density near the Earth ρ 0 the WIMP-nucleus cross sections σ0 SI and σ0 SD the WIMP mass m χ the velocity distribution of incident WIMPs f 1(v) The WIMP-nucleus cross section is about pb the optimistic expected event rate is 10 3 events/kg-day but could be < 1 event/ton-yr An exponential-like recoil energy spectrum Most events would be with energies less than 50 kev. Typical background events due to cosmic rays and ambient radioactivity : signals O(10 6 ) : 1 C.-L. Shan, AS IoP BUT, September 19, 2012, p. 24

26 Introduction Direct DM detection We start with... direct detection signals Ionization (charges) Scintillation (light) Heat (phonons) Quenching factor Nuclear recoil relative efficiency Measured (electron equivalent) recoil energy kev ee true nuclear recoil energy kev r Raw/total mass/exposure fiducial mass/exposure Combinations of two signals: = event-by-event background rejection C.-L. Shan, AS IoP BUT, September 19, 2012, p. 25

27 Introduction Direct DM detection We start with... direct detection detectors Semi-conductor detectors Cryogenic Ge, Si, NaI, CsI, CaWO 4, TeO 2 Liquid noble gas detectors Single-phase (liquid) Dual-phase (gas-liquid) Xe, Ar, Ne Superheated droplet/gas detectors Time-projection chamber (TPC) Directional (head-tail) information Xe-CS 2, CF 4, C 3F 8, C 4F 10, CF 3I, C 2ClF 5 For nuclei with A 30, the SI interaction ( A 2 ) almost always dominates over the SD interaction. C.-L. Shan, AS IoP BUT, September 19, 2012, p. 26

28 2 ] Introduction to Direct Dark Matter Detection Phenomenology Introduction Direct DM detection We start with... direct detection experiments Minimal and maximal cut-off energies: Q (min,max), Q max,kin Quenching factor: kev ee /kev r = q(q), energy smearing and resolution Detector materials: Ge Si, Xe Ar, F I Background (discrimination) Excluded/constrained areas on σ SI/SD χ(p/n) vs. m χ planes WIMP-Nucleon Cross Section [cm DAMA/Na CoGeNT XENON10 (2011) DAMA/I CRESST-II (2012) SIMPLE (2012) EDELWEISS (2011/12) XENON100 (2012) observed limit (90% CL) Expected limit of this run: ± 1 σ expected ± 2 σ expected CDMS (2010/11) COUPP (2012) ZEPLIN-III (2012) XENON100 (2011) WIMP Mass [GeV/c ] [XENON100 Collab., arxiv: (2012); CRESST Collab., EPJ C 72, 1971 (2012)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 27

29 Introduction Direct DM detection We start with... direct detection theory/phenomenology (One-dimensional) velocity distribution function f(v) of f 1 (v) Local DM density ρ 0 Escape and the 1-D maximal cut-off velocity v esc and v max WIMP-nucleon(proton/neutron) couplings: SI scalar couplings f (p,n) SD axial-vector couplings a (p,n) SI vector couplings b (p,n) (WIMP-nucleus) nuclear scattering form factors F 2 SI(Q) and F 2 SD(Q) WIMP mass and mass splitting m χ and δ C.-L. Shan, AS IoP BUT, September 19, 2012, p. 28

30 Introduction Direct DM detection We start with... direct detection theory/phenomenology/experiments Time-dependence of the velocity distribution Annual modulation of the event rate [Y. Ramachers, Nucl. Phys. Proc. Suppl. 118, 341 (2003)] Diurnal modulation of the event rate Directionality of the WIMP wind Shielding of the incident WIMP flux by the Earth [Y. Ramachers (2003); M. de Jesus, Int. J. Mod. Phys. A19, 1142 (2004)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 29

31 Introduction Direct DM detection We start with... DD theory (particle/astronomical halo model building) Predicting WIMP-nucleon couplings/cross sections [V. Barger, W. Y. Keung, and G. Shaughnessy, PRD 78, (2008)] Exclusion limits on the (predicted) SI WIMP-nucleon cross section [ ZEPLIN Collab., PRL 103, (2009)] Predicting Velocity distribution function C.-L. Shan, AS IoP BUT, September 19, 2012, p. 30

32 Introduction Direct DM detection We start with... direct detection phenomenology Developing data analysis procedures Constraining/distinguishing particle/astronomical halo models Reconstructing WIMP properties Being combination with and complementarity of indirect DM detection and collider experiments. Packages for Monte-Carlo simulations and/or (real) data analysis C.-L. Shan, AS IoP BUT, September 19, 2012, p. 31

33 Introduction Direct DM detection We start with... direct detection phenomenology Exclusion limits on σ SI/SD χ(p/n) vs. m χ planes S. Yellin Constraints on SD WIMP-nucleon couplings D. R. Tovey et al. T. A. Girard and F. Giuliani Velocity distribution A. H. G. Peter L. E. Strigari et al. Maximum likelihood (ML) analysis A. M. Green and B. Moore Bayesian + ML analysis M. Pato et al. J. Billard, F. Mayet, D. Santos et al. (MIMAC Collab.) Model-independent analysis using the total event rate P. J. Fox et al. C.-L. Shan, AS IoP BUT, September 19, 2012, p. 32

34 Model-independent data analyses Model-independent data analyses C.-L. Shan, AS IoP BUT, September 19, 2012, p. 33

35 Model-independent data analyses Motivation Motivation Differential event rate for elastic WIMP-nucleus scattering dr vmax [ ] f1(v) dq = AF2 (Q) dv v min v Here v min = α Astrophysics Q is the minimal incoming velocity of incident WIMPs that can deposit the recoil energy Q in the detector, A ρ0σ0 6 mn α m 2m χm 2 r,n 2m 2 r,n = mχmn r,n m χ + m N Particle physics ρ 0 : WIMP density near the Earth σ 0 : total cross section ignoring the form factor suppression F(Q): elastic nuclear form factor f 1 (v): one-dimensional velocity distribution of halo WIMPs C.-L. Shan, AS IoP BUT, September 19, 2012, p. 34

36 Model-independent data analyses Motivation Motivation Differential event rate for elastic WIMP-nucleus scattering dr vmax [ ] f1(v) dq = AF2 (Q) dv v min v Here v min = α Q is the minimal incoming velocity of incident WIMPs that can deposit the recoil energy Q in the detector, ρ0σ0 A 2m χm 2 r,n α mn 2m 2 r,n mχmn m r,n = m χ + m N ρ 0 : WIMP density near the Earth σ 0 : total cross section ignoring the form factor suppression F(Q): elastic nuclear form factor f 1 (v): one-dimensional velocity distribution of halo WIMPs C.-L. Shan, AS IoP BUT, September 19, 2012, p. 35

37 Model-independent data analyses Reconstruction of the WIMP velocity distribution Reconstruction of the WIMP velocity distribution Normalized one-dimensional WIMP velocity distribution function { [ ( )]} d 1 dr f 1(v) = N 2Q dq F 2 (Q) dq N = 2 α { 0 1 Q [ 1 F 2 (Q) ( )] } dr 1 dq dq Q=v 2 /α 2 Moments of the velocity distribution function ( α v n n+1 = N (Q thre) 2 [ N (Q thre) = 2 2Q 1/2 thre α F 2 (Q thre) ) [ 2Q (n+1)/2 thre F 2 (Q thre) [ 1 I n(q thre) = Q (n 1)/2 Q thre F 2 (Q) ( ) dr dq ( ) dr + I 0(Q thre) dq Q=Q thre ( )] dr dq dq + (n + 1)I n(q thre) Q=Q thre ] 1 [M. Drees and CLS, JCAP 0706, 011 (2007)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 36 ]

38 Model-independent data analyses Reconstruction of the WIMP velocity distribution Reconstruction of the WIMP velocity distribution Ansatz: the measured recoil spectrum in the nth Q-bin ( ) dr r n e kn(q Qs,n) r n Nn dq expt, Q Q n b n Logarithmic slope and shifted point in the nth Q-bin Q Q n n 1 N n ( ) bn (Q n,i Q n) = coth N n 2 i=1 Q s,n = Q n + 1 [ ] sinh(knbn/2) ln k n k nb n/2 ( knb n 2 ) 1 k n Reconstructing the one-dimensional WIMP velocity distribution [ ] [ 2Qs,nrn d ] f 1(v s,n) = N F 2 (Q s,n) dq ln F2 (Q) k n Q=Qs,n [ ] N = α Qa F 2 v s,n = α Q s,n (Q a) a [M. Drees and CLS, JCAP 0706, 011 (2007)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 37

39 Model-independent data analyses Reconstruction of the WIMP velocity distribution Reconstruction of the WIMP velocity distribution Reconstructed f 1,rec (v s,n ) ( 76 Ge, 500 events, 5 bins, up to 3 bins per window) [M. Drees and CLS, JCAP 0706, 011 (2007)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 38

40 Model-independent data analyses Determination of the WIMP mass Determination of the WIMP mass Estimating the moments of the WIMP velocity distribution v n = α n 2Q1/2 min rmin F 2 (Q min) 1 + I 0 2Q(n+1)/2 min r min F 2 + (n + 1)I n (Q min) I n = a Q (n 1)/2 a F 2 (Q a) Determining the WIMP mass ( ) dr r min = dq = r 1 e k 1 (Q min Q s,1 ) expt, Q=Q min [M. Drees and CLS, JCAP 0706, 011 (2007)] mxm m v Y m XR n χ n = R n m X/m Y R n = 2Q(n+1)/2 min,x r min,x/f 2 X (Qmin,X) + (n + 1)In,X (X ) 1/n 1 Y 2Q 1/2 (n 0) min,x rmin,x/f2 X (Qmin,X) + I0,X [CLS and M. Drees, arxiv: ] Assuming a dominant SI WIMP-nucleus interaction m χ σ = (mx/my)5/2 m Y m XR σ R σ (m X/m Y) 5/2 R σ = EY E X 2Q1/2 min,x rmin,x/f2 X 2Q 1/2 min,y rmin,x/f2 Y (Qmin,X) + I0,X (Qmin,Y) + I0,Y [M. Drees and CLS, JCAP 0806, 012 (2008)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 39

41 Model-independent data analyses Determination of the WIMP mass Determination of the WIMP mass χ 2 -fitting χ 2 (m χ) = i,j where f i,x = α i 2Q(i+1)/2 min,x r min,x/f 2 ( X (Qmin,X) + (i + 1)Ii,X X 2Q 1/2 min,x rmin,x/f2 X (Qmin,X) + I0,X (f i,x f i,y) Cij 1 (fj,x fj,y) f nmax+1,x = E X A 2 X 2Q 1/2 min,x rmin,x/f2 X (Qmin,X) + I0,X C ij = cov (f i,x, f j,x) + cov (f i,y, f j,y) km/s ( ) mx m χ + m X ) i Algorithmic Q max matching ( ) 2 αx Q max,y = Q max,x α Y ( vcut = α Q max ) [M. Drees and CLS, JCAP 0806, 012 (2008)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 40

42 Model-independent data analyses Determination of the WIMP mass Determination of the WIMP mass Reconstructed m χ,rec ( 28 Si + 76 Ge, Q max < 100 kev, 2 50 events) [M. Drees and CLS, JCAP 0806, 012 (2008)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 41

43 Model-independent data analyses Estimation of the SI WIMP-nucleon coupling Estimation of the SI WIMP-nucleon coupling Spin-independent (SI) WIMP-nucleus cross section ( ) ( ) ( 4 σ0 SI = m 2 [ ] 2 4 r,n Zfp + (A Z)f n m 2 r,n π π A2 f p 2 = A 2 mr,n m r,p ( ) 4 σχp SI = m 2 r,p π fp 2 f (p,n) : effective SI WIMP-proton/neutron couplings Rewriting the integral of f 1 (v)/v over v ) 2 σ SI χp ( ) dr = Eρ0A 2 [( ] 4 )m 2r,p dq expt, Q=Q min 2m χm 2 r,p π fp 2 F 2 1[ ] 2 (Q min) mr,n 2Q1/2 min rmin 2 rmin m N F 2 + I 0 (Q min) F 2 (Q min) Estimating the SI WIMP-nucleon coupling f p 2 = 1 [ ( )] π ρ E ZA 2 2Q1/2 min,z rmin,z Z mz F 2 Z (Qmin,Z) + I 0,Z (m χ + m Z) [M. Drees and CLS, PoS IDM2008, 110 (2008)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 42

44 Model-independent data analyses Estimation of the SI WIMP-nucleon coupling Estimation of the SI WIMP-nucleon coupling Estimating the SI WIMP-nucleon coupling f p 2 = 1 [ ( )] π ρ E ZA 2 2Q1/2 min,z rmin,z Z mz F 2 Z (Qmin,Z) + I 0,Z (m χ + m Z) f p 2 ( 76 Ge (+ 28 Si+ 76 Ge), Q max < 100 kev, σ SI χp = 10 8 [M. Drees and CLS, PoS IDM2008, 110 (2008)] pb, 1(3) 50 events) [CLS, arxiv: ] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 43

45 Model-independent data analyses Estimation of the SI WIMP-nucleon coupling Estimation of the SI WIMP-nucleon coupling Estimating the SI WIMP-nucleon coupling f p 2 = 1 [ ( )] π ρ E ZA 2 2Q1/2 min,z rmin,z Z mz F 2 Z (Qmin,Z) + I 0,Z (m χ + m Z) f p 2 vs. m χ ( 76 Ge (+ 28 Si+ 76 Ge), Q max < 100 kev, σ SI χp = 10 8 [M. Drees and CLS, PoS IDM2008, 110 (2008)] pb, 1(3) 50 events) [CLS, arxiv: ] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 44

46 Model-independent data analyses Determinations of ratios of WIMP-nucleon cross sections Determination of the ratio of SD WIMP-nucleon couplings Spin-dependent (SD) WIMP-nucleus cross section ( ) ( ) 32 J + 1 [ Sp a σ0 SD = G 2 ] 2 F π m2 r,n p + S n a n J σ SD χp/n = ( 32 π ) G 2 F m2 r,p/n ( ) 3 a 2 p/n 4 J: total nuclear spin S (p,n) : expectation values of the proton/neutron group spin a (p,n) : effective SD WIMP-proton/neutron couplings Determining the ratio of two SD WIMP-nucleon couplings ( ) SD an Sp X ± Sp YRJ,n = S n X ± S n YR J,n a p ±,n [( ) ( ) ] JX JY + 1 1/2 Rσ R J,n (n 0) J X + 1 J Y R n [M. Drees and CLS, arxiv: ] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 45

47 Model-independent data analyses Determinations of ratios of WIMP-nucleon cross sections Determination of the ratio of SD WIMP-nucleon couplings Reconstructed (a n /a p ) SD rec,1 ( 73 Ge + 37 Cl, Q min > 5 kev, Q max < 100 kev, 2 50 events, m χ = 100 GeV or a n/a p = 0.7) [CLS, JCAP 1107, 005 (2011)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 46

48 Model-independent data analyses Determinations of ratios of WIMP-nucleon cross sections Determination of the ratio of SD WIMP-nucleon couplings Reconstructed (a n /a p ) SD rec,1 ( 19 F I, Q min > 5 kev, Q max < 100 kev, 2 50 events, m χ = 100 GeV or a n/a p = 0.7) [CLS, JCAP 1107, 005 (2011)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 47

49 Model-independent data analyses Determinations of ratios of WIMP-nucleon cross sections Determinations of ratios of WIMP-nucleon cross sections Differential rate for combined SI and SD cross sections ( ) dr dq expt, Q=Q min = E ( ρ0σ SI 0 2m χm 2 r,n ( ) [ ] J + 1 Sp + (a 2 n/a p) S n ) ( σ SD ) ] [F 2SI (Q) + χp vmax [ σχp SI C pf 2 f1(v) SD (Q) v min v ] dv C p 4 3 J A Determining the ratio of two WIMP-proton cross sections σχp SD = F 2 SI,Y (Qmin,Y)Rm,XY F2 SI,X (Qmin,X) σχp SI C p,xf 2 SD,X (Qmin,X) Cp,YF2 SD,Y (Qmin,Y)Rm,XY ( ) ( rmin,x R m,xy E Y ) ( ) my 2 E X r min,y m X Determining the ratio of two SD WIMP-nucleon couplings ( ) SI+SD an = a p ± c p,x 4 ( )[ JX + 1 Sp X 3 J X A X (c p,xs n/p,x c p,ys n/p,y ) ± c p,xc p,y sn/p,x s n/p,y c p,xs 2 n/p,x cp,ys2 n/p,y ] 2[ F 2 SI,Z (Qmin,Z)Rm,YZ F2 SI,Y (Qmin,Y) ]F 2 SD,X (Qmin,X) [M. Drees and CLS, arxiv: ] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 48

50 Model-independent data analyses Determinations of ratios of WIMP-nucleon cross sections Determinations of ratios of WIMP-nucleon cross sections Reconstructed (a n /a p ) SI+SD rec vs. (a n /a p ) SD rec,1 ( 19 F I + 28 Si, Q min > 5 kev, Q max < 100 kev, 3 50 events, σχp SI = 10 8 /10 10 pb, a p = 0.1, m χ = 100 GeV) [CLS, JCAP 1107, 005 (2011)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 49

51 Model-independent data analyses Determinations of ratios of WIMP-nucleon cross sections Determinations of ratios of WIMP-nucleon cross sections Reconstructed ( ) σχp/σ SD χp SI and ( ) σχn/σ SD χp SI rec rec ( 19 F I + 28 Si vs. 23 Na/ 131 Xe + 76 Ge, Q min > 5 kev, Q max < 100 kev, σχp SI = 10 8 pb, a p = 0.1, m χ = 100 GeV, 3/2 50 events) [CLS, JCAP 1107, 005 (2011)] C.-L. Shan, AS IoP BUT, September 19, 2012, p. 50

52 Effects of residue background events Effects of residue background events C.-L. Shan, AS IoP BUT, September 19, 2012, p. 51

53 Effects of residue background events Effects of residue background events Background spectrum Target-dependent exponential background spectrum ( ) ( dr = exp Q/keV ) dq bg,ex A 0.6 Constant background spectrum Background window Entire experimental possible energy range (0-100 kev) Low energy range (0-50 kev) High energy range ( kev) (Naively) simulate only a few residue background events induced by two or more different sources C.-L. Shan, AS IoP BUT, September 19, 2012, p. 52

54 AMIDAS package and website AMIDAS package and website C.-L. Shan, AS IoP BUT, September 19, 2012, p. 53

55 AMIDAS package and website AMIDAS package and website A Model-Independent Data Analysis System for direct Dark Matter detection experiments DAMNED Dark Matter Web Tool (ILIAS Project) [CLS, arxiv: , ] TiResearch (Taiwan interactive Research) Online interactive simulation/data analysis system Full Monte Carlo simulations Theoretical estimations Real/user-uploaded data analyses C.-L. Shan, AS IoP BUT, September 19, 2012, p. 54

56 AMIDAS package and website Currently running and further projects Planned improvements (AMIDAS-II) More well-motivated velocity distributions More more-realistic form factors for each single target Connection to other simulation/data analysis packages for (in)direct detections Dark Matter Les Houches Accord (DLHA) [G. Brooijmans et al., arxiv: ] User account/setup database system Currently running and further projects Data analysis in the inelastic scattering framework Reconstructing modeled velocity distribution functions Analyzing data with directional information C.-L. Shan, AS IoP BUT, September 19, 2012, p. 55

57 Summary Summary C.-L. Shan, AS IoP BUT, September 19, 2012, p. 56

58 Summary Summary Direct Dark Matter detection searches for WIMP particles. Direct detection experiments aim to observe WIMP-nucleus scattering signals. Theoretical models predict WIMP candidates. Phenomenological data analyses would exclude/constrain the parameter space and even extract WIMP properties. Our data analysis procedures could extract WIMP properties model-independently by combining data sets with different detector materials. C.-L. Shan, AS IoP BUT, September 19, 2012, p. 57

59 Summary Summary These information will help us to distinguish the (neutralino) LSP from the LKP [G. Bertone et al., PRL 99, (2007); V. Barger et al., PRD 78, (2008); G. Belanger et al., PRD 79, (2009); R. C. Cotta et al., NJP 11, (2009)] identify the particle produced at colliders to be indeed halo WIMPs predict the WIMP annihilation cross section σ anni v Furthermore, we could determine the local WIMP density ρ 0 predict the indirect detection event rate dφ/de test our understanding of the early Universe... C.-L. Shan, AS IoP BUT, September 19, 2012, p. 58

60 Summary Thank you very much for your attention! C.-L. Shan, AS IoP BUT, September 19, 2012, p. 59