COLUMNAR RECOMBINATION JIN LI INSTITUTE FOR BASIC SCIENCE CYGNUS2015 CONFERENCE JUN.3, 2015

Transcription

1 COLUMNAR RECOMBINATION JIN LI INSTITUTE FOR BASIC SCIENCE CYGNUS2015 CONFERENCE JUN.3,

2 The dark matter in the Universe Dark Matter is stable, non-baryonic, nonrelavistic, and interactes gravitationally We don t know what s it: mass / spin / coupling / composition Cosmology suggests to probe EW scale DM ~ <σ A v> 1 σ A = α 2 / M 2 EW 2

3 Dark Matter around the Sun in the Milky way 3

4 WIMP (Weakly interacting Massive Particles) scattering 4

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7 Columnar Recombination (CR) CR increases as angle α decreases. Drift field exists ( ions and electrons pass each other) High ionization density (stronger collective charge effects) 7

8 Directional Distribution per unit target mass Radon transformation: v ME 2 min 2 8

9 Maxwellian Distribution of f(v) Define: R 2 n v / ; E 2 v / M Reaction rate if earth is static in galaxy. Maximum recoil energy for a WIMP with velocity v 0. 9

10 WIMP Flux and Recoil Direction CS 2 gas 10

11 Daily modulation of rate on fixed lab-angles Magnitude for 7 lab-fixed directions 11

12 Directional observables z So far, all study used the directional variable or (θ,φ) only, possibly integrated over a fixed range of energy. We should use both Energy and direction. Here, we measure Nuclear recoil polar angle θ L, not φ! φ θ L Nuclear recoil y x 12

13 Signal and Null hypothesis Define: x E v v Signal: Standard Isothermal halo model, x E =1. E 0 Earth s speed Spread in Maxwellian distribution z WIMP θ Background: No relative speed between earth and WIMP, x E =0. With: x v v min E E 0 0 Compact Expression: 2 d R R0 ded cos 2E 0 ( Ee ) ( x cos x) E 2 13

14 Distribution of Energy and direction WIMP z Arbitrary orientation: θ 0 θ L 2 d R R0 ded cos d 4E L L 0 ( Ee ) ( x cos cos x sin sin cos x) E 0 L E 0 L L 2 Space-fixed Detector 14

15 In polar angle detection and no sense detection case Polar angle detection: ded 2 d R 2 cos 0 L 4 R 0 E 0 ( Ee ) ( x cos cos x sin sin cos x) E 0 L E 0 L L 2 d L Axial detector (no sense detection): d R d R d R ded cos ded cos ded( cos ) L L L 15

16 Distributions of Energy and polar angle ded 2 d R cos L No Head-Tail isotropic perpendicular parallel 16

17 Space- and Earth-fixed Detectors WIMP z θ 0 θ L Space-fixed Detector Earth-fixed Detector

18 Distribution for Earth-fixed detector The angle between detector and WIIMP wind θ 0 is a function of time t in units of sidereal days: cos cos cos sin sin cos(2 ) 0 D D t Replace θ 0, then a distribution in three variables is formed: 2 2 d R d R 2 R ded dt ded E cos cos 0 L L 4 t 2 0 ( Ecos 0cos L Esin 0sin Lcos L ) () ( ) x pt Ee x x d 0 L pt ( ) 1 ( tis uniformly distributed) 18

19 Angular-only detector Suppose the energy information is not detected or recorded. d dr cos L 0 de 2 d R ded cos L R e x x 2 0 ( xe cos ) E E 2 cos erf ( cos ) 1 It can be expressed with an analytic expression! 19

20 Comparisons for Space-fixed detectors Median of q value as a function of cosθ 0. Sensitivity Plot Low sensitivity due to folding of positive and negative cosθ L values at cosθ 0 around

21 Comparisons for Earth-fixed detectors Optimal orientation at =45 degree, for Earth-fixed axial detectors. Trivial dependence on a head-tail detector but nontrivial on an axial detector. The optimal polar angle for Earth-fixed detector is 45 degree, slightly larger than the 42 degree of WIMP s angle, so that the WIMP direction leans slightly inside the cone of detector s trajectory. This can be understood as a balance between the strong advantage of being at the cone to allow parallel orientation (cosθ L =0) at the closest point the and the tendency to minimize the angle at other times of Earth s rotation. 21

22 Standard Xenon Detector With Xenon Helm form factor (E). Detector threshold 3keV. Space-fixed The number of point interactions as N pint, without threshold and form factor effect, directly relates to the detector performance. 2 d R pint ded ( E) 1 N de d R M T 2 d R obs ; det.range T obs obs / pint N M f N N ded T Earth-fixed For 200 events 22

23 Detector performance table arxiv: Required number of events for 3σ discovery: 636 kg year measurement for a cm 2 spin-independent WIMP-nucleon cross-section. 35

24 J.Billard s 1,2,3D plot J.Billard, PRD, 2015 Note special conditions: Considering Earth-fixed, Modane location only. WIMP mass is known and fixed to 50 GeV. Head-tail only. Energy threshold 5 kev. Signal purity = 0.4. Isotropic background of 10keV exponential shape. Also in the paper: A factor of 8 worse for 1D, without sense??? 1

25 Experimental study of Columnar Recombination Coincident decay of 241 Am source. 35mm diameter 23

26 Measurement of track angle relative to electric field Rise-time Taking account of electron diffusion. Validation can be done by drift velocity: Track length at 1 bar of pulse height: Pressure in bar L v 0.8 t t P 2 2 d r,max r,min 24

27 Charge collection dependence on the angle 25

28 Current knowledge of CR (in xenon with TMA) Nuclear recoil energy deposit. High ion density negligible diffusion. TMA will speed up thermalization process. Penning transfer. The ionization potential of TMA is less than the first excitation energy of xenon (8.315 ev). Xe* + TMA Xe + TMA + + e. Charge exchange. Xenon ions will undergo charge exchange reactions with the TMA molecule, directly or through an intermediate excited state. Xe + + TMA Xe + TMA +. Recombination of ionized TMA. UV scintillation with wavelength around 300 nm will occur for recombined TMA ions with electrons. (Columnar Recombination works) 26

29 Penning efficiency of electron and gamma deposit First-order modelling arxiv: Penning Excimer formation Quenching 27

30 Experimental measurement of Penning effect Nakajima, et al, arxiv: kev gamma-ray from 241 Am source 28

31 How is Penning effect in nuclear recoil? Nakajima, et al, arxiv: Pure Xeon Most of Xe scintillaiton light seems to be absorbed by TMA at >0.1% level. So it is essential for high Penning transfer and charge exchange efficiency. We still lack the knowledge of penning effect in nuclear recoil. With TMA 29

32 Other penning efficiency study O. Sahin-JINST 5(2010)P05002 The maximum transfer rate observed in a more realistic analysis done by including a 3D field calculation exceeds by 30-50% (relative) the values. arxiv: Ar-Xe Mixture 55 Fe source 5.9 kev and 22.2 kev deposit Ar-C 2 H 2 Mixture 30

33 Other possibilities See Baracchini s talk about Negative Ion Time Expansion Chamber on Tuesday. 2

34 Columnar Recombination For 30 kev nuclear recoil in xenon Work function for scintillation and ionization for NR : W S nr =150 ev and W I nr =125 ev. Ionization Excitation Perfect columnar alignment: 80% Recombination 20% Ionization R/I = 4 Perfect columnar perpendicularity: 40% Recombination 60% Ionization R/I=0.67 R/I=0.15 for electron recoils. 31

35 Real Columnar Recombination case We observe the Recombination (C) and Ionization (I) signals. Calculation : Xenon as target Xenon Helm Form Factor. A 30 kev nuclear recoil 395 electrons Fraction go to Recombination Fraction go to Ionization sin L sin L With TMA mixture (penning transfer) Need to be justifiled Threshold: Corresponding to two scintillation photons (R) and two collected electrons. Resolution: Fano factor works because it is the Gas Xenon (Use 2D convolution). 32

36 Realistic Columnar Recombination Detector Distributions Effective working function for ionization for NR in TMA mixture-filled xenon detector is W I eff =30keV/395=75.9 ev. Efficiency for scintillation photon detection C =10%. Efficiency for ionization charge I =50%. C E I E 2 2 ( sin L) ; ( sin L) FW C / ; FW I / ; ( F 0.14) eff eff C I C I I I Correlation should be considered. d R dcdi d R ded cos 2 2 L J( E, cos ; C, I) G( C; ) G( I; ) L C I 33

37 Distributions for Ionization v.s. Recombination for real CR detector isotropic parallel perpendicular 34 The integrals (total rate) of all distributions are same.

38 Detector performance table arxiv: Required number of events for 3σ discovery: 636 kg year measurement for a cm 2 spin-independent WIMP-nucleon cross-section. 35

39 Conclusion Experimental proof for Columnar Recombination effect. Combining energy information simultaneously will reduce the statistics needed for 3.7(4.0) times for a space (Earth)-fixed axial detector. A general axial polar detector with 6.3 times the statistics has the same performance as a general full 3D tracking detector. A space-fixed detector is generally found to be 3 and 2 times more sensitive than an Earth-fixed detector. For a realistic xenon columnar recombination detector, a 636 kg year measurement can reach a 3 sigma directional signal in space-fixed case. 36

40 BACKUP 37

41 Working electrical field and Ionization density The ionization density of a 30 kev xeonon ion is about 5 times the 5.4 MeV alpha. The figure shows that the optimum working electric field does not depend on the pressure, hence, does not depend on the ionization density. Ratio of collected charge between para. and perp. 38

42 Validation plots Drift coefficient 39

43 In detector frame fixed to earth (full direction) 40

44 Plot in profile histogram for CR detector xe Parallel 1, cos 1 0 xe 0 Isotropic Error bars for 500 events of data size. 41

45 Full information 3-d detector: 3D distribution. 2 2 d R d R ded de d cos R L 2D plane detector: 2 d R ded L Polar detector: 2 d R ded cos L All distributions need numerical integration, with Jacobian terms. When resolution is included, another round of 2D integration is needed. Distributions depends on (WIMP mass, cross section, Earth speed, Earth Direction, cutoff speed, energy threshold, ). Study of the sensitivity of all parameters and their correlations are needed. 42

46 Test statistics: Likelihood ratio test statistic Likelihood of a fixed alternative hypothesis Likelihood of null hypothesis Example: Null hypothesis Alternative hypothesis 43

47 Profile Likelihood Ratio method Profile likelihood ratio: ( ) 0 L( 0, ) L( ˆ, ) Test statistic: q 2ln ( ) 0 Parameter for alternate hypothesis, floated p value: p f ( q H ) dq obs q 0 0 χ 2 distribution q asymptotically follows a χ 2 distribution from Wilk s theorem: p P( x) dx obs q The significance value Z can then be obtained from p value: Z 1 (1 p) For one parameter of interest, Z in units of σ is : Z q 44

48 Hypothesis testing Null hypothesis Rejection factor, or confidence level. 0 q obs R f ( q H ) dq 1 p 0 Acceptance factor, or probability to reject the null hypothesis at confidence level R. A When is q obs equal to the median of the distribution f(q H 1 ), A=50%. q f ( q H ) dq obs 1 Alternative hypothesis Procedure: We generate 1000 samples of dataset under alternate hypothesis (signal, x E =1), obtain the median of q as q med. 45

49 Existing experiments Large Mass Difficult! 46

50 Sensitivity from directional observables No forward-backward 3-d detector; Standard Halo Model; CS 2 target; Helm form factor; m χ = 100 GeV; 20 kev threshold; experimental angular resolution; Statistical test method No energy threshold Perfect resolution PHYSICAL REVIEW D 71, (2005) 47

51 Sensitivity from directional observables (2D detector) Model A: standard B: triaxial C: standard plus stream 2D detector in a plane; CS 2 target; 20 kev threshold; Perfect resolution; Statistical test method With sense NO sense 48 PHYSICAL REVIEW D 72, (2005)

52 Sensitivity from directional observables (comparison) Xenon target; Helm form factor; m χ = 100 GeV; 10 kev threshold; Perfect resolution; Likelihood Method Another independent calculation Number of events required: Rotate the detector, so the earth s moving direction always lies in the 2D detection plane. PHYSICAL REVIEW D 75, (2007) 49

53 Challenges in analysis 3D case with Resolution effect: Does not depend on φ depend on φ 2D plane detector: Polar detector (new): dr dcos 2 d R d dr dcos L d dr cos L Transform to detector frame, then project in to plane with direction in φ L, integration in θ L needed. Detector polar angle θ L in detector frame, integration in φ L needed. 50

54 Test statistics Coordinate system dependent: W is large for large anisotropy; W~χ 32 for isotropy. 51

55 Test statistics for 2D plane Rayleigh 52

56 Recombination proof in Xenon gas Volume (geminate) Recombination at low(high) electric field. Bolotnikov & Ramsey NIM A 428 (1999)

57 54

58 Scintillation in Crystal can depend on angle Stilbene crystal scintillator 55