Identification of Dark Matter with Directional Detection Julien Billard, F. Mayet, D. Santos, O. Guillaudin, C. Grignon (MIMAC Collaboration) Laboratoire de Physique Subatomique et de Cosmologie Grenoble - France 1 Identification of Dark Matter 2010 (Montpellier) J. Billard - IDM 2010

2 OUTLINE 1. A brief introduction to Directional Detection 2. Case of a positive detection of Dark Matter 3. Case of a null detection of Dark Matter J. Billard - IDM 2010

3 I.a. directional detection Directional detection is a direct detection of dark matter which is also interested in the recoil direction distribution Gazeous detector and TPC technologies, High background rejection Low threshold Recoil direction Track length Recoil energy Nucleus target Track length Current projects: MIMAC, DRIFT, DM-TPC, NEWAGE and Nuclear Emulsion More details: S. Ahlen et al., International Journal of Modern Physics A25 (2010) J. Billard - IDM 2010

4 l b XGXG YGYG ZGZG Solar System Galactic Center V WIMP V SS Solar System’s orbit Dark matter Halo = gaz of WIMPs Galactic coordinates Considering the standard halo model, isothermal sphere: WIMP flux entering a terrestrial detector represented in Galactic coordinates Cygnus Constellation (l = 90°,b = 0°) I.b WIMP signal WIMP induced recoil distribution After scaterring Expected WIMP signal WIMP velocity distribution in the lab frame J. Billard - IDM 2010

5 I.c Interest of the directional detection Background is supposed to be isotropic WIMP signal Background Background hypothesis should be rejected at high CL even with a low number of WIMP events: Ref: A. Green and B. Morgan, Astropart. Phys. 27 (2007) 142, … L. Krauss and C. J. Copi, Phys. Rev. D 63 (2001) , … Vs Clear and unambiguous difference between WIMP signal (left) and background (right) J. Billard - IDM 2010

6 I.d State of the art: axial interaction ? SUSY : SuperBayes (R. Trotta et al., JHEP 0812 (2008) 024) Directional detection: Gazeous detector Low pressure and light target (Track reconstruction) Spin-Dependent cross section J. Billard - IDM 2010

7 Case of a positive detection J. Billard, F. Mayet, J-F. Macias-Perez, D. Santos, Phys. Lett. B 691 (2010) Observed recoil map J. Billard - IDM 2010

8 II.a A realistic measurement of upcoming directional detectors Characteristics of directional data -Low number of WIMP events -Potentially, a large background fraction -Rather low angular resolution What can we conclude from such a measurement ? A careful data analysis strategy is needed… Realistic simulated data -10 Kg CF 4 - DAQ : 5 months -1.5x10 -3 pb SD WIMP -nucleon - WIMP mass 100 GeV.c WIMP Background (Bckg rate = 0.07 /kg/day) - Angular resolution: 15° (FWHM) J. Billard - IDM 2010

9 II.b Likelihood definition M: Measurement B: Background S: Theoretical WIMP signal A four parameter likelihood: WIMP mass m Χ The WIMP fraction: l and b refers to the galactic coordinates of the peak theoretical WIMP angular distribution J. Billard - IDM 2010

10 II.c A map based likelihood analysis Conclusions of the map analysis: The signal is pointing toward the Cygnus Constellation within 10° (68% CL) N WIMP = 106 ± 15 (68% CL) l [degrees] b [degrees] Probability density functions b Vs l J. Billard - IDM 2010

11 II.d Constraining the WIMP mass and cross-section Constraint on λ implies a constraint on the WIMP-nucleon cross-section: Allowed regions deduced from the likelihood analysis, NOT exclusion! Spin Dependent cross-section Realistic simulated data -10 Kg CF 4 - DAQ : 5 months -Bckg rate = 0.07 /kg/day - Angular resolution: 15° (FWHM) J. Billard - IDM 2010 From: Exclusion strategy To: Discovery strategy

12 II.e Systematical studies Satisfactory results on a large range of exposure (N WIMP ) and background fraction (λ) Low exposure results: 1.25 kg.year CF4 detector = 25 WIMPs and 50 background WIMP from Cygnus within 25° but… poor significance (HINT of DM detection) High exposure results: 5 kg.year CF4 detector = 100 WIMPs and 200 background WIMP from Cygnus within 10° High significance (5σ) ! (DISCOVERY of DM) Angular signature Significance Angular signature: Significance: J. Billard - IDM 2010

13 Case of a null detection J. Billard, F. Mayet, D. Santos, arXiv: background events. No WIMP J. Billard - IDM 2010

14 III.a Directional exclusion limit methods Considering only the angular part of the event distribution No assumptions on the energy spectrum of background Three methods can be used for directional detection:  Poisson method No assumptions on the origin of events  1D Maximum Gap method ( S. Yellin, Phys.Rev. D66 (2002) ) Uses only the theoretical WIMP event distribution to set limits See also: The Maximum Patch Method (S. Henderson et.al, Phys.Rev.D78:015020,2008)  Directional Likelihood method ( J. Billard et.al, arXiv: ) Considers the theoretical distributions of both WIMP and background events to set the most restrictive limits J. Billard - IDM 2010

15 III.b Directional likelihood Method Goal = Estimate the expected number of : WIMP events : μ s Background events : μ b Consider flat priors and an extended likelihood function Poisson distributionLikelihood λ (1 – λ) Marginalize over μ b to get: P(μ s | D) 30 Background events 0 WIMP J. Billard - IDM 2010

Pure background 16 III.c Comparison of the three methods For each input and each method : 10,000 toy Monte Carlo experiments. From each experiment, we can estimate the median value of the upper limit σ med. Directional Likelihood Method overcomes the others … especially at high background contamination Detector characteristics -10 Kg CF 4 - DAQ : 3 years - Recoil energy range [5, 50] keV Poisson Max Gap Likelihood m Χ = 100 GeV/c 2 J. Billard - IDM 2010

17 III.d Experimental effects: Sense Recognition (SR) With Sense Recognition Without Sense Recognition Pure background Sense of the recoiling nuclei? ? ? Recoil track m Χ = 100 GeV/c 2 Likelihood with SR Likelihood without SR No sense recognition mildly affect exclusion limit … Caution : the conclusion does not hold for discovery J. Billard - IDM 2010

18 III.e Experimental effects: angular resolution Perfect angular resolution σ Θ = 45 ° 10 background events + 1 WIMP Key issue for directional detection m Χ = 100 GeV/c 2 Angular resolution has negligible effect on directional exclusion limits For robustness: Need for detector commissionning, e.g. using a neutron field J. Billard - IDM 2010 Poisson Max Gap Likelihood

19 III.f Effect of the energy threshold E R1 A lower energy threshold leads to: More restrictive limits A higher sensitivity to light WIMPs Most important experimental effect E R2 = 200 keV One order of magnitude between 5 and 50 keV threshold J. Billard - IDM background events + 1 WIMP

20 III.g Prospects for a MIMAC type detector 2 cases: No events (In black) 300 background events - With SR (red) - Without SR (pink) - No directional information (blue) Detector characteristics -10 Kg CF 4 - DAQ : 3 years - Recoil energy range [5, 50] keV - 10° Angular resolution Exclusion limits from such a detector would be very competitive (1 to 4 orders of magnitude below the actual limits) Interest of directional detection to set upper limits J. Billard - IDM 2010

21 Discovery of Dark Matter Exclusion of Dark Matter J. Billard - IDM 2010 High SD WIMP-proton cross-section (down to ~10-4) High significance discovery of DM Low SD WIMP-proton cross-section (down to ~ ) Competitive exclusion limits Using a dedicated statistical methods applied to directional data Conclusion 2 possible scenarios

22 Backup slides J. Billard - IDM 2010

23 Likelihood analysis result P is calculated using Poissonian statistics J. Billard - IDM 2010

24 Illustration of the directional likelihood method Illustration of the method 30 simulated background events and 0 WIMP event: μ exc is obtained from the pdf of μ s σ exc is directly derived from μ exc

25 Evolution of the 1D angular spectrum in function of the energy range (left) and the WIMP mass (right) Sun Recoil  Fraction of events per solid angle as a function of the opening angle γ J. Billard - IDM 2010

26 Sphère isothermeHalo triaxial (ellipsoidal) Evolution of the 2D angular distribution in function of the halo model Extreme cases Still pointing toward the Cygnus Constellation J. Billard - IDM 2010

27 SD interactionSI interaction Axial and scalar cross-sections are not correlated! E. Moulin et al, PLB 614 (2005)143

28 m WIMP 100 GeV.c -2 Fluorine target Increasing E Recoil 10 – 20 keV 30 – 40 keV 50 – 60 keV WIMP-induced recoil distribution Directional detection phenomenology J. Billard - IDM 2010 The signal is still directional for any recoil energy! Increasing directionality

29 The signal is still directional for any WIMP mass value! Increasing M WIMP 10 GeV.c GeV.c -2 1 TeV.c -2 WIMP-induced recoil distribution 5 < Er < 50 keV Fluorine target Directional detection phenomenology J. Billard - IDM 2010 Increasing directionality