WIMPs: An Introduction

Transcription

1 WIMPs: An Introduction Manuel Drees Bonn University & Bethe Center for Theoretical Physics Introduction to WIMPs p. 1/59

2 Contents 1 The WIMP Miracle Introduction to WIMPs p. 2/59

3 Contents 1 The WIMP Miracle 2 Have WIMPS been Detected (Directly)? Introduction to WIMPs p. 2/59

4 Contents 1 The WIMP Miracle 2 Have WIMPS been Detected (Directly)? 3 Asymmetric Dark Matter? Introduction to WIMPs p. 2/59

5 Contents 1 The WIMP Miracle 2 Have WIMPS been Detected (Directly)? 3 Asymmetric Dark Matter? 4 WIMPs and Colliders Introduction to WIMPs p. 2/59

6 Contents 1 The WIMP Miracle 2 Have WIMPS been Detected (Directly)? 3 Asymmetric Dark Matter? 4 WIMPs and Colliders 5 Summary Introduction to WIMPs p. 2/59

7 Conditions for Dark Matter Candidates Requirements for a good DM candidate χ: Must have lifetime τ χ τ U Introduction to WIMPs p. 3/59

8 Conditions for Dark Matter Candidates Requirements for a good DM candidate χ: Must have lifetime τ χ τ U Must be electrically neutral (otherwise not dark) Introduction to WIMPs p. 3/59

9 Conditions for Dark Matter Candidates Requirements for a good DM candidate χ: Must have lifetime τ χ τ U Must be electrically neutral (otherwise not dark) Must have correct relic density: Ω χ 0.22 Introduction to WIMPs p. 3/59

10 Conditions for Dark Matter Candidates Requirements for a good DM candidate χ: Must have lifetime τ χ τ U Must be electrically neutral (otherwise not dark) Must have correct relic density: Ω χ 0.22 If DM consists of thermally produced elementary particles: Leads to events with missing E T at colliders! Introduction to WIMPs p. 3/59

11 Conditions for Dark Matter Candidates Requirements for a good DM candidate χ: Must have lifetime τ χ τ U Must be electrically neutral (otherwise not dark) Must have correct relic density: Ω χ 0.22 If DM consists of thermally produced elementary particles: Leads to events with missing E T at colliders! Counter examples: axions; dark atoms; primordial black holes; kev neutrinos: not covered in this talk. Note: Proves that LHC does not recreate conditions of the early universe! Introduction to WIMPs p. 3/59

12 The WIMP Miracle Assume χ was in full thermal equilibrium with SM particles at sufficiently high temperature T : χ production rate n χ σ(χχ SM)v χ > expansion rate H Introduction to WIMPs p. 4/59

13 The WIMP Miracle Assume χ was in full thermal equilibrium with SM particles at sufficiently high temperature T : χ production rate n χ σ(χχ SM)v χ > expansion rate H n χ e m χ/t, σ(χχ SM)v T 0 or2, H T 2 /M Planck Introduction to WIMPs p. 4/59

14 The WIMP Miracle Assume χ was in full thermal equilibrium with SM particles at sufficiently high temperature T : χ production rate n χ σ(χχ SM)v χ > expansion rate H n χ e m χ/t, σ(χχ SM)v T 0 or2, H T 2 /M Planck = equality ( freeze-out ) reached at T F m χ /20 Introduction to WIMPs p. 4/59

15 The WIMP Miracle Assume χ was in full thermal equilibrium with SM particles at sufficiently high temperature T : χ production rate n χ σ(χχ SM)v χ > expansion rate H n χ e m χ/t, σ(χχ SM)v T 0 or2, H T 2 /M Planck = equality ( freeze-out ) reached at T F m χ /20 = Ω χ h pb c σ(χχ SM)v Introduction to WIMPs p. 4/59

16 The WIMP Miracle Assume χ was in full thermal equilibrium with SM particles at sufficiently high temperature T : χ production rate n χ σ(χχ SM)v χ > expansion rate H n χ e m χ/t, σ(χχ SM)v T 0 or2, H T 2 /M Planck = equality ( freeze-out ) reached at T F m χ /20 = Ω χ h pb c σ(χχ SM)v Indicates weak scale χχ annihilation cross section: σ(χχ any)v cm 3 s 1 Introduction to WIMPs p. 4/59

17 WIMPs and Early Universe Ω χ h 2 can be changed a lot in non standard cosmologies (involving T T BBN ): Increased: Higher expansion rate H(T T F ); additional non thermal χ production at T < T F ;... Introduction to WIMPs p. 5/59

18 WIMPs and Early Universe Ω χ h 2 can be changed a lot in non standard cosmologies (involving T T BBN ): Increased: Higher expansion rate H(T T F ); additional non thermal χ production at T < T F ;... Decreased: Reduced expansion rate H(T T F ); entropy production at T < T F ;... Introduction to WIMPs p. 5/59

19 WIMPs and Early Universe Ω χ h 2 can be changed a lot in non standard cosmologies (involving T T BBN ): Increased: Higher expansion rate H(T T F ); additional non thermal χ production at T < T F ;... Decreased: Reduced expansion rate H(T T F ); entropy production at T < T F ;... Determining σ(χχ SM) allows probe of very early Universe, once χ has been established to be the DM particle! e.g. MD, Iminniyaz, Kakizaki, arxiv: Introduction to WIMPs p. 5/59

20 High T Production of DM Particles Sometimes χ production from thermalized SM particles is called thermal production even if χ never was in thermal equilibrium: Introduction to WIMPs p. 6/59

21 High T Production of DM Particles Sometimes χ production from thermalized SM particles is called thermal production even if χ never was in thermal equilibrium: If σ(χχ SM) 1/s: Production maximal at T m χ ( freeze in, Hall et al., arxiv: ) Introduction to WIMPs p. 6/59

22 High T Production of DM Particles Sometimes χ production from thermalized SM particles is called thermal production even if χ never was in thermal equilibrium: If σ(χχ SM) 1/s: Production maximal at T m χ ( freeze in, Hall et al., arxiv: ) If σ(χχ SM) s/λ 4 : Produced dominantly at highest possible temperature, T R. Introduction to WIMPs p. 6/59

23 High T Production of DM Particles Sometimes χ production from thermalized SM particles is called thermal production even if χ never was in thermal equilibrium: If σ(χχ SM) 1/s: Production maximal at T m χ ( freeze in, Hall et al., arxiv: ) If σ(χχ SM) s/λ 4 : Produced dominantly at highest possible temperature, T R. Either way, χ interactions with SM particles are too weak to give missing E T signal, unless χ has partners that can be produced via gauge interactions (ex.: gravitino G, axino ã) Introduction to WIMPs p. 6/59

24 High T Production of DM Particles Sometimes χ production from thermalized SM particles is called thermal production even if χ never was in thermal equilibrium: If σ(χχ SM) 1/s: Production maximal at T m χ ( freeze in, Hall et al., arxiv: ) If σ(χχ SM) s/λ 4 : Produced dominantly at highest possible temperature, T R. Either way, χ interactions with SM particles are too weak to give missing E T signal, unless χ has partners that can be produced via gauge interactions (ex.: gravitino G, axino ã) Interactions are too weak for direct detection; indirect detection is possible only for unstable DM candidates. Introduction to WIMPs p. 6/59

25 Have WIMPs Been Detected Directly? Direct detection search for elastic WIMP nucleon scattering Introduction to WIMPs p. 7/59

26 Have WIMPs Been Detected Directly? Direct detection search for elastic WIMP nucleon scattering Kinematics: v χ v Sun 10 3 c Introduction to WIMPs p. 7/59

27 Have WIMPs Been Detected Directly? Direct detection search for elastic WIMP nucleon scattering Kinematics: v χ v Sun 10 3 c = energy transfer to nculeus A: ( ) Q < min 10 6 m 2 χ m A, 10 6 m A < 100 kev Introduction to WIMPs p. 7/59

28 Have WIMPs Been Detected Directly? Direct detection search for elastic WIMP nucleon scattering Kinematics: v χ v Sun 10 3 c = energy transfer to nculeus A: ( ) Q < min 10 6 m 2 χ m A, 10 6 m A < 100 kev = Cannot excite (most) nuclei! Introduction to WIMPs p. 7/59

29 Have WIMPs Been Detected Directly? Direct detection search for elastic WIMP nucleon scattering Kinematics: v χ v Sun 10 3 c = energy transfer to nculeus A: ( ) Q < min 10 6 m 2 χ m A, 10 6 m A < 100 kev = Cannot excite (most) nuclei! Momentum transfer < 100 MeV = may need to worry about elastic form factors; quite well understood (for spin indep. scattering) Introduction to WIMPs p. 7/59

30 Recoil Spectrum dr dq F(Q) 2 v max v min dv v f 1 (v) Introduction to WIMPs p. 8/59

31 Recoil Spectrum dr dq F(Q) 2 v max v min dv v f 1 (v) f 1 (v) : WIMP velocity distribution. Usually assumed Maxwellian in rest frame of the galaxy, cut off at v esc = v max. Gives roughly exponentially falling spectrum. Introduction to WIMPs p. 8/59

32 Normalized Recoil Spectra 1/R dr/dq [1/keV] m χ =100 GeV, A=73 m χ =100 GeV, A=136 m χ =10 GeV, A=73 m χ =10 GeV, A= Q [kev] Introduction to WIMPs p. 9/59

33 Experimental Challenges Spectrum backed up against instrumental threshold Q min Introduction to WIMPs p. 10/59

34 Experimental Challenges Spectrum backed up against instrumental threshold Q min Rates of current interest background rate, e.g. from radioactive decay (for most materials) = try to discriminate between nuclear recoil (signal) and e/γ induced events (background)! Introduction to WIMPs p. 10/59

35 Experimental Challenges Spectrum backed up against instrumental threshold Q min Rates of current interest background rate, e.g. from radioactive decay (for most materials) = try to discriminate between nuclear recoil (signal) and e/γ induced events (background)! Will go through three claimed signals: DAMA(/LIBRA), CoGeNT, CRESST. Introduction to WIMPs p. 10/59

36 DAMA Pure scintillation detectors (doped NaI) in Gran Sasso: 6 years with 100 kg (DAMA) 6 years with 250 kg (DAMA/LIBRA) Introduction to WIMPs p. 11/59

37 DAMA Pure scintillation detectors (doped NaI) in Gran Sasso: 6 years with 100 kg (DAMA) 6 years with 250 kg (DAMA/LIBRA) All events are counted. Introduction to WIMPs p. 11/59

38 DAMA Pure scintillation detectors (doped NaI) in Gran Sasso: 6 years with 100 kg (DAMA) 6 years with 250 kg (DAMA/LIBRA) All events are counted. Observe few percent modulation of total rate Introduction to WIMPs p. 11/59

39 DAMA Pure scintillation detectors (doped NaI) in Gran Sasso: 6 years with 100 kg (DAMA) 6 years with 250 kg (DAMA/LIBRA) All events are counted. Observe few percent modulation of total rate Compatible with 50 GeV WIMP scattering off I, or 10 GeV WIMP scattering off Na. Introduction to WIMPs p. 11/59

40 DAMA Results 2-6 kev Residuals (cpd/kg/kev) DAMA/NaI (0.29 ton yr) (target mass = 87.3 kg) DAMA/LIBRA (0.53 ton yr) (target mass = kg) 2-6 kev Time (day) Residuals (cpd/kg/kev) DAMA/LIBRA 250 kg (0.87 ton yr) Time (day) Introduction to WIMPs p. 12/59

41 DAMA: Problems No e/γ discrimination is attempted, although some (statistical) discrimination should be possible using light curve Introduction to WIMPs p. 13/59

42 DAMA: Problems No e/γ discrimination is attempted, although some (statistical) discrimination should be possible using light curve Deduced shape of spectrum weird: Falls towards small Q! (Depends on 3 dimensional WIMP velocity distribution.) Introduction to WIMPs p. 13/59

43 DAMA: Problems No e/γ discrimination is attempted, although some (statistical) discrimination should be possible using light curve Deduced shape of spectrum weird: Falls towards small Q! (Depends on 3 dimensional WIMP velocity distribution.) Amplitude of modulation is getting smaller! E.g. in 2 6 kev ee bin (in units of 10 3 /kg day kev ee ): DAMA : 20.0 ± 3.2 LIBRA : 10.7 ± 1.9 LIBRA : 8.5 ± 2.2 Ratio LIBRAII DAMA = 0.43 ± 0.13 More than 4σ away from 1! Results for 2 4, 2 5 kev ee bins similar. Introduction to WIMPs p. 13/59

44 DAMA: Problems No e/γ discrimination is attempted, although some (statistical) discrimination should be possible using light curve Deduced shape of spectrum weird: Falls towards small Q! (Depends on 3 dimensional WIMP velocity distribution.) Amplitude of modulation is getting smaller! E.g. in 2 6 kev ee bin (in units of 10 3 /kg day kev ee ): DAMA : 20.0 ± 3.2 LIBRA : 10.7 ± 1.9 LIBRA : 8.5 ± 2.2 Ratio LIBRAII DAMA = 0.43 ± 0.13 More than 4σ away from 1! Results for 2 4, 2 5 kev ee bins similar. No convincing non WIMP interpretation of modulation known. Introduction to WIMPs p. 13/59

45 CoGeNT: Time Averaged Analysis Operate cryogenic Ge detectors with very low threshold Q min. Introduction to WIMPs p. 14/59

46 CoGeNT: Time Averaged Analysis Operate cryogenic Ge detectors with very low threshold Q min. Originally: Found excess relative to simple bckgd model at very low Q = small m χ ; Introduction to WIMPs p. 14/59

47 CoGeNT: Time Averaged Analysis Operate cryogenic Ge detectors with very low threshold Q min. Originally: Found excess relative to simple bckgd model at very low Q = small m χ ; χ 2 fit with signal not significantly better than with pure background: no claim of signal in published paper! Introduction to WIMPs p. 14/59

48 CoGeNT: Time Averaged Analysis Operate cryogenic Ge detectors with very low threshold Q min. Originally: Found excess relative to simple bckgd model at very low Q = small m χ ; χ 2 fit with signal not significantly better than with pure background: no claim of signal in published paper! This September: More data, re evaluateed background = size of possible signal reduced by factor 5! Introduction to WIMPs p. 14/59

49 CoGeNT: Results Introduction to WIMPs p. 15/59

50 CoGeNT: Results Introduction to WIMPs p. 15/59

51 CoGeNT: Modulation After 15 months of data taken: Find 2.8σ evidence for annual modulation Introduction to WIMPs p. 16/59

52 CoGeNT: Modulation After 15 months of data taken: Find 2.8σ evidence for annual modulation Much too large to be compatible with time averaged signal, for standard halo Introduction to WIMPs p. 16/59

53 CoGeNT: Modulation After 15 months of data taken: Find 2.8σ evidence for annual modulation Much too large to be compatible with time averaged signal, for standard halo No event by event e/γ rejection at these low energies Introduction to WIMPs p. 16/59

54 CoGeNT: Summary No signal claimed in time averaged analysis! Introduction to WIMPs p. 17/59

55 CoGeNT: Summary No signal claimed in time averaged analysis! There is a large, poorly understood background Introduction to WIMPs p. 17/59

56 CoGeNT: Summary No signal claimed in time averaged analysis! There is a large, poorly understood background Modulation signal statistically very weak, and way too large Introduction to WIMPs p. 17/59

57 CRESST Uses cryogenic CaWO 4 crystals; detect scintillation light and heat: Allows event by event discrimination! See 67 events after cuts. Introduction to WIMPs p. 18/59

58 CRESST Uses cryogenic CaWO 4 crystals; detect scintillation light and heat: Allows event by event discrimination! See 67 events after cuts. Unfortunately, quite large backgrounds (rough estimates, not final fit): e/γ events: 8 α background: 9.2 n background: 1.5 to 11.4 Pb recoil (from 210 Po decay): 17 Introduction to WIMPs p. 18/59

59 CRESST Uses cryogenic CaWO 4 crystals; detect scintillation light and heat: Allows event by event discrimination! See 67 events after cuts. Unfortunately, quite large backgrounds (rough estimates, not final fit): e/γ events: 8 α background: 9.2 n background: 1.5 to 11.4 Pb recoil (from 210 Po decay): 17 Much of fitted excess has essentially no light: only half a signal Introduction to WIMPs p. 18/59

60 CRESST Uses cryogenic CaWO 4 crystals; detect scintillation light and heat: Allows event by event discrimination! See 67 events after cuts. Unfortunately, quite large backgrounds (rough estimates, not final fit): e/γ events: 8 α background: 9.2 n background: 1.5 to 11.4 Pb recoil (from 210 Po decay): 17 Much of fitted excess has essentially no light: only half a signal No. of α events is correlated with no. of signal events after α subtraction. Introduction to WIMPs p. 18/59

61 CRESST: Results Introduction to WIMPs p. 19/59

62 CRESST: Results Introduction to WIMPs p. 19/59

63 CRESST: Results What is negative light yield? Introduction to WIMPs p. 19/59

64 CRESST: Correlation events in signal region (α subtracted) y = 0.44x (χ 2 = 7.3 / 6 d.o.f.) Data y = 7.2 (χ 2 = 11.4 / 7 d.o.f.) events in α reference region Introduction to WIMPs p. 20/59

65 Exclusion Limits from Other Expts Best limit for larger masses from Xenon100. Uses ionization and scintillation. Very few events after cuts. Alas, not safe for m χ 12 GeV: bound strongly depends on high v tail of f 1 (v), and on experimental energy resolution. Introduction to WIMPs p. 21/59

66 Exclusion Limits from Other Expts Best limit for larger masses from Xenon100. Uses ionization and scintillation. Very few events after cuts. Alas, not safe for m χ 12 GeV: bound strongly depends on high v tail of f 1 (v), and on experimental energy resolution. Xenon10 more robust at small Q; excludes DAMA, CRESST, original CoGeNT signal for usual WIMP Introduction to WIMPs p. 21/59

67 Exclusion Limits from Other Expts Best limit for larger masses from Xenon100. Uses ionization and scintillation. Very few events after cuts. Alas, not safe for m χ 12 GeV: bound strongly depends on high v tail of f 1 (v), and on experimental energy resolution. Xenon10 more robust at small Q; excludes DAMA, CRESST, original CoGeNT signal for usual WIMP CDMS (+ EDELWEISS) second best for not too small m χ. Uses phonons and ionization. Very few events after cuts. Not safe below 12 GeV. Introduction to WIMPs p. 21/59

68 Exclusion Limits from Other Expts Best limit for larger masses from Xenon100. Uses ionization and scintillation. Very few events after cuts. Alas, not safe for m χ 12 GeV: bound strongly depends on high v tail of f 1 (v), and on experimental energy resolution. Xenon10 more robust at small Q; excludes DAMA, CRESST, original CoGeNT signal for usual WIMP CDMS (+ EDELWEISS) second best for not too small m χ. Uses phonons and ionization. Very few events after cuts. Not safe below 12 GeV. CDMS low Q analysis uses phonons only; sizable number of events. Excludes DAMA, original CoGeNT for usual WIMP. Introduction to WIMPs p. 21/59

69 Exclusion Limits from Other Expts Best limit for larger masses from Xenon100. Uses ionization and scintillation. Very few events after cuts. Alas, not safe for m χ 12 GeV: bound strongly depends on high v tail of f 1 (v), and on experimental energy resolution. Xenon10 more robust at small Q; excludes DAMA, CRESST, original CoGeNT signal for usual WIMP CDMS (+ EDELWEISS) second best for not too small m χ. Uses phonons and ionization. Very few events after cuts. Not safe below 12 GeV. CDMS low Q analysis uses phonons only; sizable number of events. Excludes DAMA, original CoGeNT for usual WIMP. SIMPLE heated droplet detector: Challenges DAMA. Introduction to WIMPs p. 21/59

70 Theory of WIMP Nucleus Scattering L eff = c N NN χχ + an Nγµ N χγ µ χ + b N Nγµ γ 5 N χγ µ γ 5 χ For scalar χ: γ µ i µ in 2 nd term; 3 rd term absent For Majorana χ: 2 nd term absent 1 st, 2 nd term give spin independent (s.i.) interaction, 3 rd term gives spin dependent (s.d.) interaction. Usual WIMP : same s.i. scattering on p and n! Introduction to WIMPs p. 22/59

71 Isospin violation in s.i. interaction? σ s.i. χp σ s.i. χn true for Higgs exchange (in particular, in (N)MSSM): massive quarks are same for p, n! Introduction to WIMPs p. 23/59

72 Isospin violation in s.i. interaction? σ s.i. χp σ s.i. χn true for Higgs exchange (in particular, in (N)MSSM): massive quarks are same for p, n! Not true for q, q (1) exchange: quark charges matter! But: M(χq χq) has same sign for all quarks: no cancellations = isospin violation in praxis not important, since all nuclei have similar n/p ratio. Introduction to WIMPs p. 23/59

73 Isospin violation in s.i. interaction? σ s.i. χp σ s.i. χn true for Higgs exchange (in particular, in (N)MSSM): massive quarks are same for p, n! Not true for q, q (1) exchange: quark charges matter! But: M(χq χq) has same sign for all quarks: no cancellations = isospin violation in praxis not important, since all nuclei have similar n/p ratio. Gauge boson exchange can break isospin: coefficients a p,a n may differ in sign! M(χq χq) is now linear in (new) quark charges. Introduction to WIMPs p. 23/59

74 Large isospin violation in s.i. interaction? M(χA χa) 2 Za p + (A Z)a n 2 = need a p a n < 0 for significant isospin violation: arrange for cancellation in unwanted nuclei (e.g. Xe). Introduction to WIMPs p. 24/59

75 Large isospin violation in s.i. interaction? M(χA χa) 2 Za p + (A Z)a n 2 = need a p a n < 0 for significant isospin violation: arrange for cancellation in unwanted nuclei (e.g. Xe). Does not work for CDMS vs. CoGeNT: same target! Introduction to WIMPs p. 24/59

76 Large isospin violation in s.i. interaction? M(χA χa) 2 Za p + (A Z)a n 2 = need a p a n < 0 for significant isospin violation: arrange for cancellation in unwanted nuclei (e.g. Xe). Does not work for CDMS vs. CoGeNT: same target! Increases required a p even more, to describe claimed signals = Need new light gauge bosons! Introduction to WIMPs p. 24/59

77 Large isospin violation in s.i. interaction? M(χA χa) 2 Za p + (A Z)a n 2 = need a p a n < 0 for significant isospin violation: arrange for cancellation in unwanted nuclei (e.g. Xe). Does not work for CDMS vs. CoGeNT: same target! Increases required a p even more, to describe claimed signals = Need new light gauge bosons! Combined analyses: (e.g. Kopp, Schwetz, Zupan, arxiv: [hep-ph]) Still cannot explain all data consistently! Introduction to WIMPs p. 24/59

78 Weisskopf s (?) Theorem A theory that explains all data must be wrong, since at any given point some data are wrong. Introduction to WIMPs p. 25/59

79 Weisskopf s (?) Theorem A theory that explains all data must be wrong, since at any given point some data are wrong. Competition between null experiments with few (background) events after cuts, and claimed signals with large, not always well understood backgrounds! Introduction to WIMPs p. 25/59

80 Asymmetric Dark Matter? Cosmology: Ω DM 5Ω baryon : strange coincidence? Introduction to WIMPs p. 26/59

81 Asymmetric Dark Matter? Cosmology: Ω DM 5Ω baryon : strange coincidence? Ω baryon determined by baryon antibaryon asymmetry, not by thermal decoupling of baryons: try same thing for WIMPs? Introduction to WIMPs p. 26/59

82 Asymmetric Dark Matter? Cosmology: Ω DM 5Ω baryon : strange coincidence? Ω baryon determined by baryon antibaryon asymmetry, not by thermal decoupling of baryons: try same thing for WIMPs? Most attractive: χ χ asymmetry related to baryon asymmetry [O(50) papers] = number density n χ n p after annihilating away symmetric component Introduction to WIMPs p. 26/59

83 Asymmetric Dark Matter? Cosmology: Ω DM 5Ω baryon : strange coincidence? Ω baryon determined by baryon antibaryon asymmetry, not by thermal decoupling of baryons: try same thing for WIMPs? Most attractive: χ χ asymmetry related to baryon asymmetry [O(50) papers] = number density n χ n p after annihilating away symmetric component Needs 2 to 3 times larger χ χ annihilation cross section than for thermal WIMPs! Introduction to WIMPs p. 26/59

84 Explaining Ω DM /Ω baryon Follows if m χ 5m p! Introduction to WIMPs p. 27/59

85 Explaining Ω DM /Ω baryon Follows if m χ 5m p! Alas: m χ has no known relation to m p. m χ 5m p just as mysterious as Ω DM 5Ω baryon = Haven t explained anything! Introduction to WIMPs p. 27/59

86 Explaining Ω DM /Ω baryon Follows if m χ 5m p! Alas: m χ has no known relation to m p. m χ 5m p just as mysterious as Ω DM 5Ω baryon = Haven t explained anything! Circular logic: ADM with m χ 5 GeV interesting because there are signals for low mass WIMPs; low mass WIMPs interesting because ADM explains Ω DM /Ω baryon?? Introduction to WIMPs p. 27/59

87 WIMPs and Colliders 1 Generalities: WIMP DM Production and Missing E T Introduction to WIMPs p. 28/59

88 WIMPs and Colliders 1 Generalities: WIMP DM Production and Missing E T 2 Light Gauge Bosons Introduction to WIMPs p. 28/59

89 WIMPs and Colliders 1 Generalities: WIMP DM Production and Missing E T 2 Light Gauge Bosons 3 SUSY DM and the LHC Inverse Problem Introduction to WIMPs p. 28/59

90 WIMPs and Colliders 1 Generalities: WIMP DM Production and Missing E T 2 Light Gauge Bosons 3 SUSY DM and the LHC Inverse Problem 4 Higgs Searches and Direct DM Detection Introduction to WIMPs p. 28/59

91 Cannot predict missing E T from χχ production Thermal WIMP: Only know total χχ SM cross section; contribution of specific final states (e + e, uū + d d) not known Introduction to WIMPs p. 29/59

92 Cannot predict missing E T from χχ production Thermal WIMP: Only know total χχ SM cross section; contribution of specific final states (e + e, uū + d d) not known Ω χ h 2 determined from σ(χχ SM) near threshold (T F m χ /20 = s 4m 2 χ). At colliders need 3 body final state to get signature (e.g. e + e χχγ, q q χχg) = typically need σ(χχ SM) at s 6 to 10m 2 χ! Introduction to WIMPs p. 29/59

93 Model-independent approach Goodman et al., arxiv: and ; Bai, Fox, Harnik, arxiv: ; Wang, Li, Shao, Zhang, arxiv: ; Fox, Harnek, Kopp, Tsai, arxiv: Parameterize χ interaction with relevant SM fermion through dim 6 operator; e.g. for hadron colliders: L eff = G χ χγ χ χ qγ q q Introduction to WIMPs p. 30/59

94 Model-independent approach Goodman et al., arxiv: and ; Bai, Fox, Harnik, arxiv: ; Wang, Li, Shao, Zhang, arxiv: ; Fox, Harnek, Kopp, Tsai, arxiv: Parameterize χ interaction with relevant SM fermion through dim 6 operator; e.g. for hadron colliders: L eff = G χ χγ χ χ qγ q q χ Majorana = Γ χ {1,γ 5,γ µ γ 5 } Γ q {1,γ 5,γ µ,γ µ γ 5 } If Γ χ, Γ q {1,γ 5 } : G χ = m q /(2M 3 ) (chirality violating!), else Γ χ = 1/(2M 2 ) Rajamaran, Shepherd, Tait, Wijango, arxiv: Introduction to WIMPs p. 30/59

95 Model-independent approach Goodman et al., arxiv: and ; Bai, Fox, Harnik, arxiv: ; Wang, Li, Shao, Zhang, arxiv: ; Fox, Harnek, Kopp, Tsai, arxiv: Parameterize χ interaction with relevant SM fermion through dim 6 operator; e.g. for hadron colliders: L eff = G χ χγ χ χ qγ q q χ Majorana = Γ χ {1,γ 5,γ µ γ 5 } Γ q {1,γ 5,γ µ,γ µ γ 5 } If Γ χ, Γ q {1,γ 5 } : G χ = m q /(2M 3 ) (chirality violating!), else Γ χ = 1/(2M 2 ) Rajamaran, Shepherd, Tait, Wijango, arxiv: Compute monojet signal from q q χχg, compare with monojet limits (current bound) and background (ultimate reach)! Introduction to WIMPs p. 30/59

96 Γ χ = γ µ γ 5 (corr. to spin-dep. interact.) Introduction to WIMPs p. 31/59

97 Γ χ = 1 (corr. to spin-indep. interact.) Introduction to WIMPs p. 32/59

98 Remarks For Γ χ = 1 (spin-indep. interact.): Current bound poor; ultimate LHC reach interesting only for m χ 5 GeV. Introduction to WIMPs p. 33/59

99 Remarks For Γ χ = 1 (spin-indep. interact.): Current bound poor; ultimate LHC reach interesting only for m χ 5 GeV. For Γ χ = γ µ γ 5 (spin-dep. interact.): LHC bound better than (comparable to) direct search limit for m χ ( ) 20 GeV; future reach factor 10 3 better, if no other BSM source of missing E T exists. Introduction to WIMPs p. 33/59

100 Remarks For Γ χ = 1 (spin-indep. interact.): Current bound poor; ultimate LHC reach interesting only for m χ 5 GeV. For Γ χ = γ µ γ 5 (spin-dep. interact.): LHC bound better than (comparable to) direct search limit for m χ ( ) 20 GeV; future reach factor 10 3 better, if no other BSM source of missing E T exists. Γ χ = γ 5 similar to first case; cannot be probed in direct WIMP detection (rate v 2 χ) Introduction to WIMPs p. 33/59

101 Remarks For Γ χ = 1 (spin-indep. interact.): Current bound poor; ultimate LHC reach interesting only for m χ 5 GeV. For Γ χ = γ µ γ 5 (spin-dep. interact.): LHC bound better than (comparable to) direct search limit for m χ ( ) 20 GeV; future reach factor 10 3 better, if no other BSM source of missing E T exists. Γ χ = γ 5 similar to first case; cannot be probed in direct WIMP detection (rate v 2 χ) Bound does not hold if mass of mediator particle max(m χ, E/ T )! Introduction to WIMPs p. 33/59

102 Remarks For Γ χ = 1 (spin-indep. interact.): Current bound poor; ultimate LHC reach interesting only for m χ 5 GeV. For Γ χ = γ µ γ 5 (spin-dep. interact.): LHC bound better than (comparable to) direct search limit for m χ ( ) 20 GeV; future reach factor 10 3 better, if no other BSM source of missing E T exists. Γ χ = γ 5 similar to first case; cannot be probed in direct WIMP detection (rate v 2 χ) Bound does not hold if mass of mediator particle max(m χ, E/ T )! Altogether: very limited usefulness for most actual WIMP models. Introduction to WIMPs p. 33/59

103 2 DM and Light (Gauge) Bosons (At least) 3 kinds of WIMP models require light (m few GeV) (gauge) bosons U: MeV DM: Suggested as explanation of 511 kev line (= slow e + ) excess from central region of our galaxy (Boehm et al., astro-ph/ ). Should have m χ 10 MeV (γ constraints) = m χ m U 200 MeV to mediate χχ e + e ; fixes g Uχχ g Ue+ e /m2 U! (Unless 2m χ m U.) Introduction to WIMPs p. 34/59

104 2 DM and Light (Gauge) Bosons (At least) 3 kinds of WIMP models require light (m few GeV) (gauge) bosons U: MeV DM: Suggested as explanation of 511 kev line (= slow e + ) excess from central region of our galaxy (Boehm et al., astro-ph/ ). Should have m χ 10 MeV (γ constraints) = m χ m U 200 MeV to mediate χχ e + e ; fixes g Uχχ g Ue+ e /m2 U! (Unless 2m χ m U.) PAMELA/FermiLAT inspired TeV DM: Needs light boson for Sommerfeld enhancement (e.g. Arkani-Hamed et al., arxiv: (4)) (χχ U U 4l is also somewhat less constrained by γ spectrum than χχ 2l.) Introduction to WIMPs p. 34/59

105 DAMA/CoGeNT inspired few GeV DM: Needs light mediator to achieve sufficiently large σ χp. (2 different mediators for isospin violation to evade bounds: Cline, Frey, arxiv: ) Introduction to WIMPs p. 35/59

106 Light Gauge Bosons (cont d) In all cases: U couplings to (most) SM particles must be 1 to evade bounds! (g µ 2, meson decays, ν cross sections, APV,... ). Introduction to WIMPs p. 36/59

107 Light Gauge Bosons (cont d) In all cases: U couplings to (most) SM particles must be 1 to evade bounds! (g µ 2, meson decays, ν cross sections, APV,... ). Possible explanation: kinetic mixing with γ/b boson! Is 1-loop effect = squared Uf f coupling is O(α 3 ). Introduction to WIMPs p. 36/59

108 Light Gauge Bosons (cont d) In all cases: U couplings to (most) SM particles must be 1 to evade bounds! (g µ 2, meson decays, ν cross sections, APV,... ). Possible explanation: kinetic mixing with γ/b boson! Is 1-loop effect = squared Uf f coupling is O(α 3 ). Uχχ coupling may well be large. Introduction to WIMPs p. 36/59

109 Signatures of light gauge bosons If m U > 2m χ : U χχ dominant! Is invisible = need extra tag, e.g. e + e γu γ+ nothing. Introduction to WIMPs p. 37/59

110 Signatures of light gauge bosons If m U > 2m χ : U χχ dominant! Is invisible = need extra tag, e.g. e + e γu γ+ nothing. Physics background s = lower energy is better! Borodatchenkova, Choudhury, MD, hep-ph/ Introduction to WIMPs p. 37/59

111 Signatures of light gauge bosons If m U > 2m χ : U χχ dominant! Is invisible = need extra tag, e.g. e + e γu γ+ nothing. Physics background s = lower energy is better! Borodatchenkova, Choudhury, MD, hep-ph/ Instrumental backgrounds (not from e + e annihilation) seem large Introduction to WIMPs p. 37/59

112 Sensitivity at B factories (100 fb 1) m χ > M U /2 max. sensitivity (e + e - channel) g χ g er upper bound from g e -2 max. sensitivity (invisible channel) 1e-06 1e-08 m χ < M U / M U [GeV] Red, black: Regions allowed by Ω χ, σ(χχ e + e ). Introduction to WIMPs p. 38/59

113 Signatures of light gauge bosons (cont.d) If m U < 2m χ : U l + l Introduction to WIMPs p. 39/59

114 Signatures of light gauge bosons (cont.d) If m U < 2m χ : U l + l Sufficiently light U can even be produced in fixed target experiments: e N e e + e N (tridents), with peak in M e+ e Introduction to WIMPs p. 39/59

115 Signatures of light gauge bosons (cont.d) If m U < 2m χ : U l + l Sufficiently light U can even be produced in fixed target experiments: e N e e + e N (tridents), with peak in M e+ e First exptl. results from MAMI A1 arxiv: and JLAB APEX arxiv: Excludes new mass ranges around 200 to 300 MeV for A U kinetically mixed with photon. Introduction to WIMPs p. 39/59

116 Signatures of light gauge bosons (cont.d) If m U < 2m χ : U l + l Sufficiently light U can even be produced in fixed target experiments: e N e e + e N (tridents), with peak in M e+ e First exptl. results from MAMI A1 arxiv: and JLAB APEX arxiv: Excludes new mass ranges around 200 to 300 MeV for A U kinetically mixed with photon. Also, KLOE-2 performed search, mostly for φ Uη: no signal. arxiv: Introduction to WIMPs p. 39/59

117 A1 and APEX results Introduction to WIMPs p. 40/59

118 SUSY DM and LHC Inverse Problem Saw above: WIMP searches at colliders not promising, if WIMP is only accessible new particle. Fortunately, in many cases the WIMP is the lightest of many new particles! True in SUSY. (Also in Little Higgs.) Introduction to WIMPs p. 41/59

119 SUSY DM and LHC Inverse Problem Saw above: WIMP searches at colliders not promising, if WIMP is only accessible new particle. Fortunately, in many cases the WIMP is the lightest of many new particles! True in SUSY. (Also in Little Higgs.) Recall: Primary motivation for SUSY not related to DM! Introduction to WIMPs p. 41/59

120 SUSY DM and LHC Inverse Problem Saw above: WIMP searches at colliders not promising, if WIMP is only accessible new particle. Fortunately, in many cases the WIMP is the lightest of many new particles! True in SUSY. (Also in Little Higgs.) Recall: Primary motivation for SUSY not related to DM! Stabilizes hierarchy m 2 Higgs M2 Planck Introduction to WIMPs p. 41/59

121 SUSY DM and LHC Inverse Problem Saw above: WIMP searches at colliders not promising, if WIMP is only accessible new particle. Fortunately, in many cases the WIMP is the lightest of many new particles! True in SUSY. (Also in Little Higgs.) Recall: Primary motivation for SUSY not related to DM! Stabilizes hierarchy m 2 Higgs M2 Planck Allows unification of gauge couplings Introduction to WIMPs p. 41/59

122 SUSY DM and LHC Inverse Problem Saw above: WIMP searches at colliders not promising, if WIMP is only accessible new particle. Fortunately, in many cases the WIMP is the lightest of many new particles! True in SUSY. (Also in Little Higgs.) Recall: Primary motivation for SUSY not related to DM! Stabilizes hierarchy m 2 Higgs M2 Planck Allows unification of gauge couplings In scenarios with unified Higgs masses: EWSB requires sizable hierarchy! (Not in NUHM2.) Introduction to WIMPs p. 41/59

123 SUSY DM and LHC Inverse Problem Saw above: WIMP searches at colliders not promising, if WIMP is only accessible new particle. Fortunately, in many cases the WIMP is the lightest of many new particles! True in SUSY. (Also in Little Higgs.) Recall: Primary motivation for SUSY not related to DM! Stabilizes hierarchy m 2 Higgs M2 Planck Allows unification of gauge couplings In scenarios with unified Higgs masses: EWSB requires sizable hierarchy! (Not in NUHM2.) HLS theorem, relation to superstrings: don t single out weak scale. Introduction to WIMPs p. 41/59

124 Features of SUSY Need superpartner for each SM particle: Same rep. of gauge group, spin differs by 1/2 Introduction to WIMPs p. 42/59

125 Features of SUSY Need superpartner for each SM particle: Same rep. of gauge group, spin differs by 1/2 Need at least 2 Higgs doublets (anomalies, m t m b 0) Introduction to WIMPs p. 42/59

126 Features of SUSY Need superpartner for each SM particle: Same rep. of gauge group, spin differs by 1/2 Need at least 2 Higgs doublets (anomalies, m t m b 0) SUSY implies equal masses for partners = SUSY must be broken Introduction to WIMPs p. 42/59

127 Features of SUSY Need superpartner for each SM particle: Same rep. of gauge group, spin differs by 1/2 Need at least 2 Higgs doublets (anomalies, m t m b 0) SUSY implies equal masses for partners = SUSY must be broken Naturalness: sparticle masses should be at weak scale (strictly true only for 3rd generation, elw gauginos) Introduction to WIMPs p. 42/59

128 Features of SUSY Need superpartner for each SM particle: Same rep. of gauge group, spin differs by 1/2 Need at least 2 Higgs doublets (anomalies, m t m b 0) SUSY implies equal masses for partners = SUSY must be broken Naturalness: sparticle masses should be at weak scale (strictly true only for 3rd generation, elw gauginos) In simplest, R parity invariant scenario: lightest superparticle LSP is stable: satisfies one condition for DM candidate! Introduction to WIMPs p. 42/59

129 SUSY DM candidate: sneutrino ν Disfavored theoretically: not LSP in constrained models Introduction to WIMPs p. 43/59

130 SUSY DM candidate: sneutrino ν Disfavored theoretically: not LSP in constrained models Excluded experimentally by direct searches Introduction to WIMPs p. 43/59

131 SUSY DM candidate: sneutrino ν Disfavored theoretically: not LSP in constrained models Excluded experimentally by direct searches ν R can be candidate in extended theories, e.g. with gauged U(1) B L at TeV scale Introduction to WIMPs p. 43/59

132 SUSY DM candidate: neutralino χ 0 1 Mixture of B, W 3, h 0 u, h 0 d Introduction to WIMPs p. 44/59

133 SUSY DM candidate: neutralino χ 0 1 Mixture of B, W 3, h 0 u, h 0 d In constrained models: often is lightest sparticle in visible sector! (Other possibility: lightest stau τ 1 ) Introduction to WIMPs p. 44/59

134 SUSY DM candidate: neutralino χ 0 1 Mixture of B, W 3, h 0 u, h 0 d In constrained models: often is lightest sparticle in visible sector! (Other possibility: lightest stau τ 1 ) In most of parameter space: χ 0 1 B, and predicted Ω χ 0 1 h 2 too large! O(1 to 10) rather than O(0.1) in standard cosmology, Introduction to WIMPs p. 44/59

135 SUSY DM candidate: neutralino χ 0 1 Mixture of B, W 3, h 0 u, h 0 d In constrained models: often is lightest sparticle in visible sector! (Other possibility: lightest stau τ 1 ) In most of parameter space: χ 0 1 B, and predicted Ω χ 0 1 h 2 too large! O(1 to 10) rather than O(0.1) in standard cosmology, but DM allowed regions of parameter space do exist even in constrained models! Introduction to WIMPs p. 44/59

136 Regions with correct Ω χ 0 1 h 2 Co annihilation region: m χ 0 1 m τ1 Introduction to WIMPs p. 45/59

137 Regions with correct Ω χ 0 1 h 2 Co annihilation region: m χ 0 1 m τ1 Higgs funnel(s): m χ 0 1 m h /2, m A /2 Introduction to WIMPs p. 45/59

138 Regions with correct Ω χ 0 1 h 2 Co annihilation region: m χ 0 1 m τ1 Higgs funnel(s): m χ 0 1 m h /2, m A /2 Well tempered neutralino: µ M 1 M Z = χ 0 1 is B h 0 mixture. (Requires m q m g in cmssm; can be arranged anywhere in NUHM.) Introduction to WIMPs p. 45/59

139 Regions with correct Ω χ 0 1 h 2 Co annihilation region: m χ 0 1 m τ1 Higgs funnel(s): m χ 0 1 m h /2, m A /2 Well tempered neutralino: µ M 1 M Z = χ 0 1 is B h 0 mixture. (Requires m q m g in cmssm; can be arranged anywhere in NUHM.) Note: DM allowed region of (m 0,m 1/2 ) plane of cmssm depends on A 0, tan β! Introduction to WIMPs p. 45/59

140 Impact of LHC searches Is model dependent: Only probe g, q sector so far! Here: Assume cmssm for defineteness. Introduction to WIMPs p. 46/59

141 Impact of LHC searches Is model dependent: Only probe g, q sector so far! Here: Assume cmssm for defineteness. Well tempered neutralino, A pole need large m q : limits still fairly weak: m g,min increased from 400 GeV to 550 GeV Introduction to WIMPs p. 46/59

142 Impact of LHC searches Is model dependent: Only probe g, q sector so far! Here: Assume cmssm for defineteness. Well tempered neutralino, A pole need large m q : limits still fairly weak: m g,min increased from 400 GeV to 550 GeV τ 1 co annihilation requires m q m g : good for LHC searches; still plenty of allowed region left. Introduction to WIMPs p. 46/59

143 Impact of Indirect DM Searches No halo signal in co annihilation region; ν from Sun small Introduction to WIMPs p. 47/59

144 Impact of Indirect DM Searches No halo signal in co annihilation region; ν from Sun small Signals very small in A funnel Introduction to WIMPs p. 47/59

145 Impact of Indirect DM Searches No halo signal in co annihilation region; ν from Sun small Signals very small in A funnel Well-tempered neutralino most promising, especially ν from Sun, but present limits not constraining Introduction to WIMPs p. 47/59

146 Impact of direct WIMP Searches XENON, CDMS EDELWEISS begin to probe well tempered neutralino Introduction to WIMPs p. 48/59

147 Impact of direct WIMP Searches XENON, CDMS EDELWEISS begin to probe well tempered neutralino Signals in other regions very small Introduction to WIMPs p. 48/59

148 Impact of Future WIMP Discovery at Collider Generically: could determine: WIMP mass: Very useful for indirect searches (greatly reduced look elsewhere problem); less so for direct searches, once m χ m N Introduction to WIMPs p. 49/59

149 Impact of Future WIMP Discovery at Collider Generically: could determine: WIMP mass: Very useful for indirect searches (greatly reduced look elsewhere problem); less so for direct searches, once m χ m N WIMP couplings: Determine cross sections and final states in indirect searches; determine cross sections in direct searches Introduction to WIMPs p. 49/59

150 Impact of Future WIMP Discovery at Collider Generically: could determine: WIMP mass: Very useful for indirect searches (greatly reduced look elsewhere problem); less so for direct searches, once m χ m N WIMP couplings: Determine cross sections and final states in indirect searches; determine cross sections in direct searches Most interesting to me: Predict Ω χ h 2, compare with observation: Constrain very early universe! Introduction to WIMPs p. 49/59

151 Fitting SUSY parameters at LHC ( inverse problem ) Feasibility (resulting errors) very strongly depend on where we are in parameter space! Introduction to WIMPs p. 50/59

152 Fitting SUSY parameters at LHC ( inverse problem ) Feasibility (resulting errors) very strongly depend on where we are in parameter space! Good: Low sparticle masses, many leptons e,µ in final states. Introduction to WIMPs p. 50/59

153 Fitting SUSY parameters at LHC ( inverse problem ) Feasibility (resulting errors) very strongly depend on where we are in parameter space! Good: Low sparticle masses, many leptons e,µ in final states. Not so good: Large masses, mostly hadronic final states. Introduction to WIMPs p. 50/59

154 Fitting SUSY parameters at LHC ( inverse problem ) Feasibility (resulting errors) very strongly depend on where we are in parameter space! Good: Low sparticle masses, many leptons e,µ in final states. Not so good: Large masses, mostly hadronic final states. Two approaches: Case studies, broad scans of parameter space Introduction to WIMPs p. 50/59

155 Case study: τ 1 co annihilation region in cmssm Needs m τ1 m χ GeV Arnowitt et al., arxiv: = χ 0 2 τ 1τ, χ ± 1 τ ± 1 ν τ have nearly unit branching ratio = no di lepton edges! Introduction to WIMPs p. 51/59

156 Case study: τ 1 co annihilation region in cmssm Needs m τ1 m χ GeV Arnowitt et al., arxiv: = χ 0 2 τ 1τ, χ ± 1 τ ± 1 ν τ have nearly unit branching ratio = no di lepton edges! τ 1 χ 0 1τ gives rather soft τ: Difficult to detect! Introduction to WIMPs p. 51/59

157 Case study: τ 1 co annihilation region in cmssm Needs m τ1 m χ GeV Arnowitt et al., arxiv: = χ 0 2 τ 1τ, χ ± 1 τ ± 1 ν τ have nearly unit branching ratio = no di lepton edges! τ 1 χ 0 1τ gives rather soft τ: Difficult to detect! Study three classes of final states: (i) 2τ + 2j + E/ T (ii)4 non b j + E/ T (iii) leading b + 3j + E/ T Introduction to WIMPs p. 51/59

158 Case study: τ 1 co annihilation region in cmssm Needs m τ1 m χ GeV Arnowitt et al., arxiv: = χ 0 2 τ 1τ, χ ± 1 τ ± 1 ν τ have nearly unit branching ratio = no di lepton edges! τ 1 χ 0 1τ gives rather soft τ: Difficult to detect! Study three classes of final states: (i) 2τ + 2j + E/ T (ii)4 non b j + E/ T (iii) leading b + 3j + E/ T Fit many kinematical distributions simultaneously, including slope of softer p τ T spectrum in sample (i) = predict 0 Ω χ 1 h 2 to 10%! Introduction to WIMPs p. 51/59

159 Result of fit 0.12 Ω ~ h 2 χ M (GeV) Introduction to WIMPs p. 52/59

160 Result of fit 0.12 Ω ~ h 2 χ M (GeV) Unfortunately, chosen benchmark point (m g = 830 GeV, m q 750 GeV) is most likely excluded! Introduction to WIMPs p. 52/59

161 Scan of Parameter Space Arkani-Hamed et al., hep-ph/ parameter description of weak scale MSSM Introduction to WIMPs p. 53/59

162 Scan of Parameter Space Arkani-Hamed et al., hep-ph/ parameter description of weak scale MSSM Fix m A = 850 GeV, A 3 = 800 GeV Introduction to WIMPs p. 53/59

163 Scan of Parameter Space Arkani-Hamed et al., hep-ph/ parameter description of weak scale MSSM Fix m A = 850 GeV, A 3 = 800 GeV Randomly choose m q, g [600, 1000] GeV, other masses [100, 1000] GeV, tan β [2, 50] Introduction to WIMPs p. 53/59

164 Scan of Parameter Space Arkani-Hamed et al., hep-ph/ parameter description of weak scale MSSM Fix m A = 850 GeV, A 3 = 800 GeV Randomly choose m q, g [600, 1000] GeV, other masses [100, 1000] GeV, tan β [2, 50] Consider 1808 observables, both counting rates and binned distributions Introduction to WIMPs p. 53/59

165 Scan of Parameter Space Arkani-Hamed et al., hep-ph/ parameter description of weak scale MSSM Fix m A = 850 GeV, A 3 = 800 GeV Randomly choose m q, g [600, 1000] GeV, other masses [100, 1000] GeV, tan β [2, 50] Consider 1808 observables, both counting rates and binned distributions Introduce χ 2 like variable ( S AB ) 2 = 1 n sig n sig i=1 ( s A i s B i σ AB i ) 2 Only significant signatures included Introduction to WIMPs p. 53/59

166 Scan of Parameter Space Arkani-Hamed et al., hep-ph/ parameter description of weak scale MSSM Fix m A = 850 GeV, A 3 = 800 GeV Randomly choose m q, g [600, 1000] GeV, other masses [100, 1000] GeV, tan β [2, 50] Consider 1808 observables, both counting rates and binned distributions Introduce χ 2 like variable ( S AB ) 2 = 1 n sig n sig i=1 ( s A i s B i σ AB i ) 2 Only significant signatures included Allow 1% syst. error (15% on total signal rate), 10 fb 1 of 14 TeV data, no background Introduction to WIMPs p. 53/59

167 Scan of Parameter Space Arkani-Hamed et al., hep-ph/ parameter description of weak scale MSSM Fix m A = 850 GeV, A 3 = 800 GeV Randomly choose m q, g [600, 1000] GeV, other masses [100, 1000] GeV, tan β [2, 50] Consider 1808 observables, both counting rates and binned distributions Introduce χ 2 like variable ( S AB ) 2 = 1 n sig n sig i=1 ( s A i s B i σ AB i ) 2 Only significant signatures included Allow 1% syst. error (15% on total signal rate), 10 fb 1 of 14 TeV data, no background MC: ( S AB ) 2 > = models differ at > 95% c.l. Introduction to WIMPs p. 53/59

168 Results and Remarks Found 283 degenerate pairs, with (δs AB ) 2 < 0.285, for 43,026 models (i.e., sets of parameters) Introduction to WIMPs p. 54/59

169 Results and Remarks Found 283 degenerate pairs, with (δs AB ) 2 < 0.285, for 43,026 models (i.e., sets of parameters) Note Their observables are correlated = (δs AB ) 2 is no true χ 2 = need MC to intepret it, from comparing runs with different random no. seed: is this reliable estimator for comparing different parameter sets? Introduction to WIMPs p. 54/59

170 Results and Remarks Found 283 degenerate pairs, with (δs AB ) 2 < 0.285, for 43,026 models (i.e., sets of parameters) Note Their observables are correlated = (δs AB ) 2 is no true χ 2 = need MC to intepret it, from comparing runs with different random no. seed: is this reliable estimator for comparing different parameter sets? Statistics looks weird! Comparing two simulations of same model, get 611 (out of 2600) cases where some 2l observable has > 5σ discrepancy: way too many! Introduction to WIMPs p. 54/59

171 Simpler approach Bornhauser and MD, in progress Define 12 disjunct event classes, depending on no., charge, flavor of leptons Introduction to WIMPs p. 55/59

172 Simpler approach Bornhauser and MD, in progress Define 12 disjunct event classes, depending on no., charge, flavor of leptons Consider 7 mostly uncorrelated observables for each class: No. of events; n τ ± ; n b ; n j ; n 2 j ; H T Introduction to WIMPs p. 55/59

173 Simpler approach Bornhauser and MD, in progress Define 12 disjunct event classes, depending on no., charge, flavor of leptons Consider 7 mostly uncorrelated observables for each class: No. of events; n τ ± ; n b ; n j ; n 2 j ; H T Define proper χ 2, incl. corr. between n j, n 2 j, only including significant observables: test with MC. Introduction to WIMPs p. 55/59

174 Results of simpler approach W/o syst. error: only one of 283 degenerate pairs has p > 0.05, and two parameter sets really are very similar! (Except for heavy sleptons.) Introduction to WIMPs p. 56/59

175 Results of simpler approach W/o syst. error: only one of 283 degenerate pairs has p > 0.05, and two parameter sets really are very similar! (Except for heavy sleptons.) Introducing syst. errors as Arkani-Hamed et al.: 41 out of 283 pairs have p > 0.05; still are pretty similar physically Introduction to WIMPs p. 56/59

176 Results of simpler approach W/o syst. error: only one of 283 degenerate pairs has p > 0.05, and two parameter sets really are very similar! (Except for heavy sleptons.) Introducing syst. errors as Arkani-Hamed et al.: 41 out of 283 pairs have p > 0.05; still are pretty similar physically Introducing SM background, but no syst. error: 12 pairs have p > 0.05 Introduction to WIMPs p. 56/59

177 Results of simpler approach W/o syst. error: only one of 283 degenerate pairs has p > 0.05, and two parameter sets really are very similar! (Except for heavy sleptons.) Introducing syst. errors as Arkani-Hamed et al.: 41 out of 283 pairs have p > 0.05; still are pretty similar physically Introducing SM background, but no syst. error: 12 pairs have p > 0.05 With systematic errors and background: 71 pairs have p > Introduction to WIMPs p. 56/59

178 4 Impact of Higgs Searches In many WIMP models, Higgs exch. dominates χp scattering, in which case σ χp 1/m 4 H : crucial to know Higgs mass! Introduction to WIMPs p. 57/59

179 4 Impact of Higgs Searches In many WIMP models, Higgs exch. dominates χp scattering, in which case σ χp 1/m 4 H : crucial to know Higgs mass! In SUSY at large tan β: 0 σ χ 1 p tan 2 β/m 4 A : need info on heavy Higgses! Introduction to WIMPs p. 57/59

180 4 Impact of Higgs Searches In many WIMP models, Higgs exch. dominates χp scattering, in which case σ χp 1/m 4 H : crucial to know Higgs mass! In SUSY at large tan β: 0 σ χ 1 p tan 2 β/m 4 A : need info on heavy Higgses! TeVatron and CMS searches for H,A τ + τ significantly increase lower bound on DM allowed m χ 0 1 in general MSSM (Aborno Vasquez, Belanger, Boehm, arxiv: ); exclude scenarios with very large σ χ 0 1 p. Introduction to WIMPs p. 57/59