Constraints on Effective Dark Matter Interactions. Tzu-Chiang Yuan ( ) Institute of Physics, Academia Sinica Taipei, Taiwan

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1 Constraints on Effective Dark Matter Interactions Tzu-Chiang Yuan ( ) Institute of Physics, Academia Sinica Taipei, Taiwan 1

2 Outline Introduction Relic Density Direct Detections Indirect Detections Colliders Constraints on Dark Matter Effective Interactions Summary Ref: Kingman Cheung, Yue-Lin Tsai, Po-Yan Tseng and TCY, JCAP 2012, arxiv:

3 Introduction 3

Rotation Curves of Galaxies At large r, one expects: Observed rotation curves exhibit flat behavior at large distances v 1/ r v Const First observed for Coma cluster (more or

4 Rotation Curves of Galaxies At large r, one expects: Observed rotation curves exhibit flat behavior at large distances v 1/ r v Const First observed for Coma cluster (more or less spherical) in 1933 by Zwicky using Virial Theorem. Suggested dark matter with universal halo density profile. (Kepler) (Observed) Fritz Zwicky ( ) Dark Matter? 4

5 Dark Matter Hypothesis ~200 kpc for bright galaxy 5

0 SNe Ω Λ Ω m h 2 =0.1334 +0.0056 0.0055 Ω b h 2 =0.02260 ± 0.00053 Ω CDM h 2 =0.

6 Standard ΛCDM Model of Cosmology Energy Budget ρ cr 3H2 0 8πG, Ω i ρ i ρ cr ρ cr = h 2 g cm 3 H 0 = 0 h km sec 1 Mpc 1 h =0.704 ± SNe Ω Λ Ω m h 2 = Ω b h 2 = ± Ω CDM h 2 = ± Ω Λ = t 0 = ± 0.11 Gyr 0.5 BAO Flat CMB Ω m 6

7 Four Different Approaches Cosmology: CMB (Relic Density, Baryon Acoustic Oscillations (BAO)), Large Scale Structure, Big Bang Nucleosynthesis (BBN), Strong and Weak Gravitational Lensing, Bullet Cluster, distant Type Ia supernovae,... Direct Detection (Terrestrial): DM scatter off nuclei in terrestrial detectors - recoil energy spectrum Indirect Detection (Astrophysical): DM annihilation into SM particles (gamma rays, electron/positron, antimatter, neutrinos etc) at massive astrophysical objects, in Sun or Earth Production and detected indirectly as missing energy at LHC 7

8 Relic Density 8

9 Relic Density of a Particle Species A particle species in the early Universe has to have a sufficiently fast interaction rate to maintain its thermal equilibrium. A particle will decouple when its annihilation rate falls below the Hubble expansion rate of the Universe. The abundance of a heavy particle is governed by the Boltzmann eq a 3 d(na3 ) dt = dn dt +3Hn = σv n 2 eq n 2 Non-relativistic limit: SM + SM χ + χ χ + χ SM + SM n eq = g mt 2π 3/2 e m/t, m T σv = a + bv 2 = a +6 b x, x m T v 1 a and b are S and P wave contributions 9

10 Freeze-out condition : x F m T F = ln c(c + 2) 45 8 nσ A v ȧ/a H g mm pl (a +6b/x F ) 2π 3 g x F c is a order 1 constant fixed by matching later and early time evolution Ω X h GeV 1 x F 1 M Pl g a +3b/x F Typically x F 20 30, and g Thus Ω X h xf 20 g 80 1/2 Ω X h cm 3 s 1 σ A v WIMP miracle 1 a +3b/xF 3 26 cm 3 /s 0.1 pb σ A v Ω CDM h 2 (WMAP) = ± Put lower limits on σ A v

11 Direct Detection 11

12 Direct Detection CRESST-II,... EDELWEISS-II,CDMS-II,... XENON0,ZEPLIN-III,... DAMA,CoGeNT,TEXONO/CDEX,... v 3 χ + N χ ( ) + N 12

13 Kinematics of Direct Detection A WIMP striking a nucleus will induce a recoil energy E lab R = q 2 2M nucleus = µ2 χn v2 M nucleus (1 cos θ ) [Exercise] q : WIMP s momentum µ χn = reduced mass = m χm nucleus m χ +M nucleus For m χ M nucleus and v 300 km/s, we have E R M nucleus v kev Tiny! 13

Recoil Energy Spectrum (per unit time per unit recoil energy) dr de R = ρ 0 m N m χ vmax v min vf(v) dσ χn de R (v, E R ) d 3 v Astrophysics Particle Physics v max = galactic escape velocity 650km/s

14 Recoil Energy Spectrum (per unit time per unit recoil energy) dr de R = ρ 0 m N m χ vmax v min vf(v) dσ χn de R (v, E R ) d 3 v Astrophysics Particle Physics v max = galactic escape velocity 650km/s v min = E R M N /2µ 2 1/2 χn DM local density ρ 0 =(0.30 ± 0.05) GeV cm 3.(Rotation curves) Truncated Boltzmann- Maxwell s distribution in the galactic rest frame f (v gal )= 1 2πσ exp v gal 2 2σ 2 Θ(v max v gal ) 14

15 Model Example: MSSM By integrating out heavy Higgses, Z-boson and squarks in MSSM, effective interactions between DM and SM fields are obtained L eff = f SI ( χχ)( qq)+f SD ( χγ µ γ 5 χ)( qγ µ γ 5 q) O 7 O 4!!!! H, h!! ~ q Z!! q ~ q q q q q q q q 15

16 Cheng and Chiang, arxiv: Comparison with other works DarkSUSY! Ellis et al! Cheng Our! and Chiang f (p)! Tu 0.023! 0.020! 0.018! f (n)! Tu 0.019! 0.014! 0.011! f (p)! Td 0.034! 0.026! 0.021! f (n)! Td 0.041! 0.036! 0.035! f (p)! Ts 0.14! 0.118! 0.053! f (n)! Ts 0.14! 0.118! 0.053!!u! 0.77! 0.78! 0.85 (0.84)!!d! -0.40! -0.48! (-0.44)!!s! -0.12! -0.15! (-0.03)! 13 16

17 Drees and Gerbier Cross-section [cm 2 ] (normalised to nucleon)!40!42!44 DAMA (no channeling) CoGeNT CDMS XENONLE CDMS XENON0 CDMS+EDELWEISS EDELWEISS SUSY 68%, 95%, + LEP-CMSSM constraints DAMA (no channeling) SUSY 68%, 95% 0 00 WIMP Mass [GeV/c 2 ] 17

18 SD pure neutron cross section [cm 2 ] WIMP Mass [GeV/c 2 ] XENON 1 pb = 36 cm 2 SIMPLE Collaboration Spin -Dependent Results CMSSM arxiv:

19 Fermionic DM Effective Operators O 7 = f C f 7 m f Λ 3 7 ( χχ) ff, O 1 = f C f 1 Λ 2 1 ( χγ µ χ) fγµ f, O 8 = f ic f 8 m f Λ 3 8 χγ 5 χ ff, O 2 = f C f 2 Λ 2 2 χγ µ γ 5 χ fγµ f, O 9 = f ic f 9 m f Λ 3 9 ( χχ) fγ 5 f, O 3 = f O 4 = f O 5 = f O 6 = f C f 3 Λ 2 3 C f 4 Λ 2 4 C f 5 Λ 2 5 C f 6 Λ 2 6 ( χγ µ χ) fγµ γ 5 f, χγ µ γ 5 χ fγµ γ 5 f, ( χσ µν χ) fσµν f, χσ µν γ 5 χ fσµν f, Cheung, Tseng, Tsai, Yuan, arxiv: O = f C f m f Λ 3 χγ 5 χ fγ 5 f. O 11 = C 11 Λ 3 11 O 12 = ic 12 Λ 3 12 O 13 = C 13 Λ 3 13 O 14 = ic 14 Λ 3 14 ( χχ) α s 12π Gµν G µν χγ 5 χ α s 12π Gµν G µν αs ( χχ) 8π Gµν Gµν, χγ 5 χ α s 8π Gµν Gµν.,, 19

20 Scalar DM Effective Operators O 15 = f O 16 = f ic f 15 Λ 2 15 ic f 16 Λ 2 16 χ µ χ fγ µ f, χ µ χ fγ µ γ 5 f, O 17 = f C f 17m f Λ 2 17 χ χ ff, O 18 = f O 19 = C 19 Λ 2 19 O 20 = C 20 Λ 2 20 Cheung, Tseng, Tsai, Yuan, arxiv: ic18m f f χ χ fγ 5 f, Λ 2 18 χ χ α s 12π Gµν G µν χ χ α s 8π Gµν Gµν., 20

21 NR reduction for Direct Detection At present epoch, v/c ~ -3, NR limit is applicable Only O 1,O 4,O 5,O 7,O 11,O 16,O 17 and O 19 exist in NR reduction Furthermore, only O 1, O 4 and O 7 are independence because SI: O 1 and O 7 ; SD : O 4 O 5 O 4 O 11 O 7 O 15 O 1 O 17 O 7 O 19 O 7 21

22 O 1 (Majorana) and O 7 (Majorana or Dirac) Coherent spin-independent cross section O 1 O 7 σ SI χn (0) = µ2 χn π b N 2 b N = Zb p +(A Z) b n b p =2 σ SI χn (0) = µ2 χn π f N 2 f N = Zf p +(A Z) f n f p,n = m p,n Λ 3 7 b n = Cu 1 Λ 2 1 q=u,d,s C u 1 Λ 2 1 C q 7 f (p,n) Tq f (p,n) TG 1 + Cd 1 Λ Cd 1 Λ 2 1 q=u,d,s, f (p,n) TG f (p,n) Tq. Q=c,b,t C Q 7 22

23 O 4 (Majorana or Dirac) Spin-dependent cross section (for Dirac DM) σχn SD 8µ2 χn (0) N= π G2 F Λ 2 J(J + 1) N Λ = 1 J (a p S p + a n S n ) a p,n = q=u,d,s 1 C q 4 2GF Λ 2 4 q (p,n) a 0 = a p + a n, a 1 = a p a n. 23

24 Constraints on Effective Interactions Our approach (adopted by other several groups as well): (1) assumption: the connector sector must be heavy and integrated out (2) DM can be (real/complex) scalar or (Majorana/ Dirac) fermionic; vector DM not considered (3) effective interaction of WIMP DM with SM particles (4) model independent study for a large class of models Direct detection experiments can place upper limits on cross sections hence lower limits on effective scales Λ 24

25 2σ Lower Limits for Λ From Direct Detection SI (XENON0) SD (XENON, ZEPLIN, SIMPLE) 5 O1 Dirac O7 Dirac O7 Majorana O11 Dirac O11 Majorana O15 Dirac O17 Complex O19 Complex O4 Dirac O4 Majorana O5 Dirac 4! (GeV)! (GeV) M " (GeV) 0 00 M " (GeV) NR reduction: only O 1 & O 7 are independent. Cheung, Tseng, Tsai, Yuan, arxiv: NR reduction: O 5 reduces to O 4 25

26 σ Upper Limits for Λ From Relic Density! (GeV)! (GeV) (axial) vector/tensor exchange " 2 (#h 2, WMAP, upper) = 4 60 O 1 O 2 O 3 O 40 4 O 5 O 6 20 m " (GeV) Gluonic interaction " 2 (#h 2, WMAP, upper) = 4 O 11 O 12 O 13 O 14 m " (GeV)! (GeV)! (GeV) O 7 O 8 O 9 O (pseudo) scalar exchange " 2 (#h 2, WMAP, upper) = 4 m " (GeV) Complex scalar dark matter " 2 (#h 2, WMAP, upper) = 4 Cheung, Tseng, Tsai, Yuan, arxiv: O 15 O 16 O 17 O 18 O 19 O 20 m " (GeV) 26

27 Indirect Detection 27

28 Indirect Detection Indirect signals from DM annihilation into gamma rays (line or continuum), neutrinos, antimatter like positrons and antiproton,... Ambiguous due to possible astrophysical sources like pulsars, cosmic rays,... If the final states are charged (positron, antiproton, etc), predictions depend on parameters in propagation model, since they can lose energy while traversing in the cosmic medium Gamma rays and neutrinos have lesser propagation effects Pamela, Fermi-LAT, AMS-02, HESS, Veritas,... Neutrino telescopes: IceCube, ANTARES,... 28

29 PAMELA p Data (20) p/p p/p -5 BESS 2000 (Y. Asaoka et al.) BESS 1999 (Y. Asaoka et al.) -5 BESS-polar 2004 (K. Abe et al.) CAPRICE 1994 (M. Boezio et al.) PAMELA CAPRICE 1998 (M. Boezio et al.) HEAT-pbar 2000 (A. S. Beach et al.) PAMELA kinetic energy [GeV] kinetic energy [GeV] 2 * Data very close to background. * It can provide stringent constraints on contributions from DM. 29

Diffuse Gamma Rays Spectrum (Fermi-LAT) PRL 4, 11 (20) s 1 sr 1 MeV] 2 dn/de [cm 2 E 2 3 4 power law fit galactic diffuse extragalactic diffuse CR background sources data model s 1 sr 1 ] 2 dn/de

30 Diffuse Gamma Rays Spectrum (Fermi-LAT) PRL 4, 11 (20) s 1 sr 1 MeV] 2 dn/de [cm 2 E power law fit galactic diffuse extragalactic diffuse CR background sources data model s 1 sr 1 ] 2 dn/de [MeV cm 2 E 3 4 EGRET Sreekumar et al EGRET Strong et al Fermi LAT EGB Softer than EGRET! Energy [MeV] 5 * DM can make contribution to diffuse γ rays; hence constrained by Fermi-LAT measurement Energy [MeV] 5 30

31 DM γ, ν 31

32 The photon spectrum E 2 (dφ/de γ ) versus the photon energy -5 (E 2 d!/de) " (GeV cm -2 s -1 sr -1 ) -6 π 0 decays inverse Compton scattering IC EGB bremsstrahlung Fermi LAT( 0 < b <20 0,0 0 <l<360 0 ) # 0 decay IC bremsstrahlung EGB bkgd=# 0 +IC+bremss+EGB DM bkgd+dm E " (GeV) χχ q q π 0 + X 2γ + X, m χ = 50 GeV; O 1 with Λ =0.87 TeV (3σ) 32

33 2σ Lower Limits for Λ From Diffuse Gamma Ray Flux! (GeV)! (GeV) (axial) vector/tensor exchange #" 2 ($, Fermi LAT, upper) = 4 NFW O 1 O 2 O 3 O 4 O 5 O 6 m " (GeV) Gluonic interaction #" 2 ($, Fermi LAT, upper) = 4 NFW O 11 O 12 O 13 O 14 m " (GeV)! (GeV)! (GeV) (pseudo) scalar exchange #" 2 ($,Fermi LAT,upper) = 4 NFW O 7 O 8 O 9 O m " (GeV) Complex scalar dark matter #" 2 ($, Fermi LAT, upper) = 4 NFW O 15 O 16 O 17 O 18 O 19 O 20 m " (GeV) 33

34 DM e +, p, d 34

35 2σ Lower Limits for Λ From PAMELA Antiproton Flux! (GeV)! (GeV) (axial) vector/tensor exchange #" 2 (anti-p,pamela,upper) = 4 NFW, $=500 MV O 1 O 2 O 3 O 4 O 5 O 6 m " (GeV) Gluonic interaction #" 2 (anti-p,pamela,upper) = 4 NFW, $=500 MV O 11 O 12 O 13 O 14 m " (GeV)! (GeV)! (GeV) O 7 O 8 O 9 O (pseudo) scalar exchange #" 2 (anti-p,pamela,upper) = 4 NFW, $=500 MV m " (GeV) Complex scalar dark matter #" 2 (anti-p,pamela,upper) = 4 NFW, $=500 MV O 15 O 16 O 17 O 18 O 19 O 20 m " (GeV) 35

36 Colliders Runs at Now 36

37 Mono-jets/Mono-photons The effective DM interactions can contribute by attaching either a gluon or a photon to one of the quark legs of the relevant operators DM Signals : Missing Energy Data sets: Mono-jet and mono-photon from CDF and D0 Mono-jet from ATLAS No excess is found. Put lower limits on effective scales. 37

38 Monojet + Missing ET (χχ) O eff O eff (χχ) O eff (χχ) 38

39 2σ Lower Limits for Λ From Mono-jet/photon O1 O2 O3 O4 O5 O O7 O8 O9 O 00 35! (GeV) 800! (GeV) M " (GeV) 0 00 M " (GeV) O11 O12 O13 O O15 O16 O17 O18 O19 O ! (GeV) ! (GeV) M " (GeV) M " (GeV) 39

Global Fittings WMAP relic density can provide upper limits on Λ Direct detection, indirect detection and collider mono-photon/jet can provide lower

40 Global Fittings WMAP relic density can provide upper limits on Λ Direct detection, indirect detection and collider mono-photon/jet can provide lower limits on Λ Global fittings by combing all experiments can provide both upper and lower limits on Λ Idea works for any explicit model of dark matter too 40

41 Combining χ 2 χ 2 (total) = χ 2 (direct) + χ 2 (collider) + χ 2 (gamma) + χ 2 (antiproton) For mixed m χ, varying Λ 2 for each operator until χ 2 χ 2 (total) χ 2 (total) min =4 WMAP constrains Λ from above. 41

5 O 1 WMAP7 DD+ID+COLL. 4 Allowed region WMAP DD+ID+coll. Fermionic DM Λ (GeV) 4 Λ (GeV) Arrow direction is allowed region 5 m χ (GeV) O 3 WMAP7 DD+ID+COLL. 4 O 2 m χ (GeV) O 4 WMAP7 DD+ID+COLL.

42 5 O 1 WMAP7 DD+ID+COLL. 4 Allowed region WMAP DD+ID+coll. Fermionic DM Λ (GeV) 4 Λ (GeV) Arrow direction is allowed region 5 m χ (GeV) O 3 WMAP7 DD+ID+COLL. 4 O 2 m χ (GeV) O 4 WMAP7 DD+ID+COLL. Only O 2 has allowed region from global fittings Other operators have lower limits higher than upper limits Λ (GeV) Λ (GeV) m χ (GeV) O 5 WMAP7 DD+ID+COLL. Λ (GeV) Λ (GeV) 5 4 m χ (GeV) O 6 WMAP7 DD+ID+COLL. m χ (GeV) m χ (GeV) 42

43 Fermionic DM (cont.) Λ (GeV) O 7 WMAP7 DD+ID+COLL. Λ (GeV) O 8 WMAP7 DD+ID+COLL. Only O 9 has allowed regions from 1 m χ (GeV) 1 m χ (GeV) O WMAP7 DD+ID+COLL. global fittings Λ (GeV) Λ (GeV) 1 O 9 Allowed region WMAP DD+ID+coll. m χ (GeV) 1 m χ (GeV) 43

44 Fermionic DM (Gluonic Operators) Λ (GeV) O 11 WMAP7 DD+ID+COLL. Λ (GeV) O 12 WMAP7 DD+ID+COLL. 1 0 m χ (GeV) 1 m χ (GeV) No allowed regions O 13 WMAP7 DD+ID+COLL. O 14 WMAP7 DD+ID+COLL. are found Λ (GeV) Λ (GeV) 1 0 m χ (GeV) 1 m χ (GeV) 44

45 5 O 15 WMAP7 DD+ID+COLL. 4 Allowed region WMAP DD+ID+coll. 4 Scalar DM Λ (GeV) Λ (GeV) O 16 m χ (GeV) m χ (GeV) Only O 16 has allowed region from global fittings Λ (GeV) 4 1 O 17 WMAP7 DD+ID+COLL. m χ (GeV) O 19 WMAP7 DD+ID+COLL. Λ (GeV) 4 1 O 18 WMAP7 DD+ID+COLL. m χ (GeV) O 20 WMAP7 DD+ID+COLL. Λ (GeV) Λ (GeV) 1 m χ (GeV) 1 m χ (GeV) 45

46 No evidence of DM from particle physics yet! All evidences are from heaven so far! (I know. We can t ignore DAMA/LIBRA and CoGeNT yet.) Summary Particle DM is definitely needed at various scales (1) largest cosmological scales (WMAP), (2) galaxy cluster scales (Coma Cluster), (3) dwarf galaxies, (4) Bullet Clusters,... Three important complementary particle DM probes: direct detection, indirect detection, and collider. No lack of theoretical ideas for particle DM candidates. Popular model like MSSM is highly constrained now. Effective DM interaction -- model independent approach but has limitations. Combing results from different experiments provide important constraints on DM models or effective interactions. We live in exciting time!! Stay tuned for new results from LHC8 and AMS

47 References 1. China group: Q.H. Cao, C.R. Chen, C.S. Li, H. Zhang (JHEP, ) Zheng, Yu, Shao, Bi, Li, Zhang (NPB, ) Wang, C.S. Li, Shao, Zhang ( ) 2. Fermilab group: Y. Bai, P.J. Fox, R. Harnik (JHEP, ) Fox, Harnik, Kopp, Tsai (PRD, ) Fox, Harnik, Kopp, Tsai ( ) 3. UC-Urvine group: Goodman, Ibe, Rajaraman, Shepherd, Tait, YU (PLB, ) Goodman, Ibe, Rajaraman, Shepherd, Tait, YU (PRD, ) Goodman, Ibe, Rajaraman, Shepherd, Tait, YU (NPB, ) Rajaraman, Shepherd, Tait, Wijangro ( ) 4. Taiwan group: KC, Song, P.Y. Tseng (JCAP, ) KC, Mawatari, Senaha, Tseng, TC Yuan (JHEP, ) KC, P.Y. Tseng, TC Yuan (JCAP, 11.23) KC, P.Y. Tseng, TC Yuan (JCAP, ) KC, P.Y. Tseng, Tsai, TC Yuan (in progress) (JCAP, 2012) 47

48 48

Cosmic Antiproton and Gamma-Ray Constraints on Effective Interaction of the Dark matter

Cosmic Antiproton and Gamma-Ray Constraints on Effective Interaction of the Dark matter Authors: Kingman Cheung, Po-Yan Tseng, Tzu-Chiang Yuan Physics Department, NTHU Physics Division, NCTS Institute