SUSY Candidates. Talk outline. Ben Allanach (University of Cambridge) SUSY dark matter: generalities Neutralino Gravitino Sneutrino Axino

Transcription

1 SUSY Candidates by Ben Allanach (University of Cambridge) Talk outline SUSY dark matter: generalities Neutralino Gravitino Sneutrino Axino SUSY Candidates Please ask questions while I m talking B.C. Allanach p.

2 Muggles View of a Neutralino SUSY Candidates B.C. Allanach p. 2

3 SUSY Dark Matter DM SM σ DM SM For t, this describes annihilation - tells us how much is thermally produced. It also allows dark matter indirect detection. For t, it s production at (e.g.) the LHC For t, it s direct detection SUSY Candidates B.C. Allanach p. 3

4 Prediction of SUSY Ω DM h 2 Common assumption: SUSY relic in thermal equilibrium with n eq (MT) 3/2 exp( M/T). Else: non-thermal production from decay of other particles (e.g. moduli) Freeze-out with T f M f /25 once interaction rate < expansion rate (t eq critical) Many different particle species, all of whom end up as DM: solve coupled Boltzmann equations for each Resulting DM relic density strongly dependent on details of SUSY spectrum/couplings SUSY Candidates B.C. Allanach p. 4

5 Caveats SUSY dark matter usually stabilised by an assumed R parity symmetry Usually, implicitly assumed that LSP constitutes all of dark matter Examples of non-standard cosmology that would change the prediction: Extra degrees of freedom Low reheating temperature Extra dimensional models Anisotropic cosmologies SUSY Candidates B.C. Allanach p. 5

6 Supersymmetric Copies H SUSY Candidates B.C. Allanach p. 6

7 Supersymmetric Copies H 2 H 2 SUSY Candidates B.C. Allanach p. 6

8 Candidate I: The neutralino eg Ellis, Olive et al PLB565 (23) 76 m (GeV) χ W m h = 4 GeV χ ± χ χ W + m χ ± = 4 GeV χ h χ b τ tan β =, µ > A b b τ A mixture of γ, Z, H,2. Can also co-annihilate with t to form tγ. 2 χ b χ γ m /2 (GeV) SUSY Candidates B.C. Allanach p. 7

9 Collider SUSY Dark Matter Production Strong sparticle production and decay to dark matter particles. 7 TeV p q q q q p 7 TeV q,g q,g q Interaction ~ q q ~ q χ χ Any (light enough) dark matter candidate that couples to hadrons can be produced at the LHC SUSY Candidates B.C. Allanach p. 8

10 Collider Check Need corroboration with direct detection. If we can pin particle physics down, a comparison between the predicted relic density and that observed is a test of the cosmological assumptions used in the prediction. a Thus, if it doesn t fit, you change the cosmology until it does. a BCA, G. Belanger, F. Boudjema, A. Pukhov, JHEP 42 (24) 2.; M. Nojiri, D. Tovey, JHEP 63 (26) 63 SUSY Candidates B.C. Allanach p. 9

11 LHC SUSY Measurements b b l + l g b2 χ 2 l χ Events/.5 GeV/ fb / 97 P 229. P2 8.7 P3.29 m 2 ll = (m2 χ m 2 l )(m 2 l m 2 2 χ ) m 2 l 5 5 M ll (GeV) Q: Can we measure enough of these to pin SUSY a down? a BCA, Lester, Parker, Webber, JHEP 9 (2) 4 SUSY Candidates B.C. Allanach p.

12 Predicting Ωh 2 From LHC Not much left that s allowed but edge measurements allow reasonable Ωh 2 error a for 3 fb / 54 Constant Mean.46 Sigma.966E- Experiments/bin Ωh 2 Q: What about other bits of parameter space? a M Nojiri, G Polesello, D Tovey, JHEP 63 (26) 63, hep-ph/5224. SUSY Candidates B.C. Allanach p.

13 Neutralino Dark Matter Detection BCA, Hooper, arxiv: χ = N B B + N W W + Nd Hd + N u Hu atmos ν µ 5 km 2 yr h χ q IceCube -5 P/P(max) SUSY Candidates m χ (TeV) B.C. Allanach p. 2 log [σ χn, SI (pb)]

14 Candidate II: The gravitino Ω Gh 2 = m G m NSP Ω NSP h 2 No direct/indirect detection possibilities Possibilities for long lived NSPs eg τ τ G: heavily ionising track at LHC, wait for it to decay t 4 8 s a. Decay can affect BBN abundances b : Energetic γs destroy D, 4 He, 6 Li or overproduce 7 Li. a Ellis, Raklev, Oye hep-ph/6726 b Feng, Su, Takayama hep-ph/4223 SUSY Candidates B.C. Allanach p. 3

15 Candidate II: The gravitino 5 m 3/2 = GeV, tan β =, µ > m (GeV) r < τ NSP < 4 s τ RPV G νγ/l lν 26 s m /2 (GeV) ( λ 7 ) 2 ( m G GeV ) 3 Lola, Osland, Raklev arxiv:77.25; Buchmuller, Covi, Hamaguchi, Ibarra, Yanagida hep-ph/7284 SUSY Candidates B.C. Allanach p. 4

16 Candidate III: Sneutrino Normally, MSSM sneutrinos annihilate too efficiently to give sufficient relic density. But: RH sneutrinos could work with Dirac m ν Doesn t thermalise in early universe Produced by scattering/decay of MSSM particles Constraints again coming from BBN, since NSP can decay into a highly energetic neutrino which scatters off a background one, generating energetic γs through e + e a Some models have very good prospects for IceCube signals a Ishiwata, Kawasaki, Kohri, Moroi arxiv:92.78 SUSY Candidates B.C. Allanach p. 5

17 Candidate IV: The Axino PQ symmetry to solve strong CP problem gives axion a with decay constant f 5 9 GeV. We have SUSY copy ã of m =kev TeV. Produced: From decays of NSP Ωã = mãω NSP /m NSP. Thermally when temperature was just below reheating temperature e.g. g g gã, q g qã a Must include g gã processes at finite temperature. a Strumia, arxiv: SUSY Candidates B.C. Allanach p. 6

18 Summary Many candidates in SUSY for dark matter Even for one candidate, the dark matter detection/lhc signals vary widely Sometimes, dark matter detection signals are predicted to be absent We hope that DM is not too heavy and couples somehow to protons. Then, the LHC will provide guidance SUSY Candidates B.C. Allanach p. 7

19 Supplementary Material SUSY Candidates B.C. Allanach p. 8

20 WMAP5+BAO+Ia Fits SUSY Candidates B.C. Allanach p. 9

21 WMAP5+BAO+Ia Fits Ω DM h 2 =.43 ±.34 Power law ΛCDM fit SUSY Candidates B.C. Allanach p. 9

22 Global SUSY Fits Q: Why perform global fits to SUSY using DM+indirect data? SUSY Candidates B.C. Allanach p. 2

23 Global SUSY Fits Q: Why perform global fits to SUSY using DM+indirect data? SUSY Candidates B.C. Allanach p. 2

24 Solar Neutralinos ( ) ( ) 2 C 3 9 s σχp GeV 7 pb m χ χ χ b b,ww,zz,h,... ν µ ν µ ICE CUBE SUSY Candidates B.C. Allanach p. 2

25 Other literature 4 Roszkowski, Ruiz & Trotta (27) 4 Roszkowski, Ruiz & Trotta (27) CMSSM, µ > ZEPLIN I m (TeV) (pb)] Log[σ p SI EDELWEISS I CDMS II 9.5 CMSSM µ> m /2 (TeV) m χ (TeV) eg R. R. de Austri, R. Trotta and L. Roszkowski, arxiv:75.22: agreement! SUSY Candidates B.C. Allanach p. 22

26 Universality Reduces number of SUSY breaking parameters from to 3: tan β v 2 /v m, the common scalar mass (flavour). M /2, the common gaugino mass (GUT/string). A, the common trilinear coupling (flavour). These conditions should be imposed at M X O( 6 8 ) GeV and receive radiative corrections /(6π 2 ) ln(m X /M Z ). Also, Higgs potential parameter sgn(µ)=±. SUSY Candidates B.C. Allanach p. 23

27 Implementation We use 95% C.L. direct search constraints Ω DM h 2 =.43 ±.2 Boudjema et al δ(g 2) µ /2 = (29.5 ± 8.8) Stöckinger et al B physics observables including BR[b sγ] Eγ >.6 GeV = (3.52 ±.38) 4 Electroweak data W Hollik, A Weber et al 2 ln L = i χ 2 i + c = i (p i e i ) 2 σ 2 i + c SUSY Candidates B.C. Allanach p. 24

28 Additional observables δ (g 2) µ 2 3 ( GeV M SUSY ) 2 tan β χ ± i γ µ γ µ ν µ χ µ µ BR[b sγ] tan β(m W /M SUSY ) 2 χ ± i γ H ± γ b t i s b t s SUSY Candidates B.C. Allanach p. 25

29 msugra Global Fits There are 3 methodologies of doing these type of global fits: Markov Chain Monte Carlo: BCA et al; Ruiz de Austri et al: primary interpretation is Bayesian but usual χ 2 minimum interpretation is possible (see later). MultiNest: Ruiz de Austri et al: Bayesian interpretation only. Minimising χ 2 /Profile likelihood: Buchmueller et al. Impressive array of electroweak observables. Moving to a hybrid approach. Frequentist interpretation only. SUSY Candidates B.C. Allanach p. 26

30 Application of Bayes L p(d m,h) is pdf of reproducing data d assuming pmssm hypothesis H and model parameters m p(m d,h) = p(d m,h) p(m,h) p(d, H) p(m d,h) is called the posterior pdf. We will compare p(m,h) = c with a different prior. p(m,m /2 d,h) = do p(m,m /2,o d,h) SUSY Candidates B.C. Allanach p. 27

31 Global Fits II m (TeV) µ > M /2 (TeV) strong weak gaugino slepton log σ/fb P/P(max) m (TeV) µ > P(µ>) P(µ<) =.4.7 µ < M /2 (TeV) P/P(max) SUSY Candidates B.C. Allanach p

32 m ( GeV) BCA, Cranmer, Weber, Lester, arxiv: allanach/benchmarks/kismet.html m (TeV) M /2 (TeV) tan β = 35 Killer Inference for Susy METeorology flat tan β P/P(max) L = fb - fb - fb - 3 fb - g ~ () g ~ (2) CMS g ~ (3) m (TeV) flat µ,b M /2 (TeV) P/P(max) b s γ limit g ~ (5) g ~ (25) q ~ (25) 6 q ~ (2) q ~ (5) 4 M h 2 limit Charged LSP SUSY Candidates m (GeV) B.C. Allanach p. 29 q ~ ()

33 Killer Inference for Susy METeorology BCA, Cranmer, Weber, Lester, arxiv: Bayesian Bayesian 2 m ( GeV) tan β = 35 L = fb - fb - fb - 3 fb - CMS g ~ g ~ (3) (2) g ~ () 2 8 b s γ limit g ~ (5) g ~ (25) q ~ (25) 6 q ~ (2) q ~ (5) 4 M h 2 limit Charged LSP SUSY Candidates m (GeV) B.C. Allanach p. 3 q ~ ()

34 Natural Prior II Calling M S typical size of soft terms: m,m /2,µ M S, M s M S /GeV M X. p(m,m /2,A,B,µ) MX max M 5 S dm S max 4 arxiv: SUSY Candidates B.C. Allanach p. 3

35 pmssm Fits 25 pmssm input parameters are: M,2,3, A t,b,τ,µ, m H,2, tan β, m dr,l = m sr,l, mũr,l = m cr,l, mẽr,l = m µr,l, m t, b, τ R,L m t, m b (m b ) α s (M Z ) MS, α (M Z ) MS, M Z. Combined Bayesian fit a : Observable Measurement Fit(Log) m W [GeV] ± Γ Z [GeV] ± eff lep sin θ.2324 ± δ (g-2) 3.2 ± µ l R ± R.2629 ± b R.72 ± c A.53 ± e A.923 ± b A.67 ± c b FB A.992 ±.6.4 c FB A.7 ± BR(B X s γ) 3.55 ± O meas - O fit / σ meas 2 3 R. ±.32. BR(B τ ν) u R.5 ±.4. M Bs.375 ± CDM h Ω. ± a S.S. AbdusSalam, BCA, F. Quevedo, F. Feroz, M. Hobson, arxiv: SUSY Candidates B.C. Allanach p. 32

36 Large Volume String Models BCA, Dolan, arxiv:86.84 m (TeV) Flat µ,b tan β P/P(max) m (TeV) P/P(max).9 Flat tan β tan β M /2 = A = m / 3 M X = GeV Two constraints enough! SUSY Candidates B.C. Allanach p. 33

37 Model Comparison Calculate the Bayesian evidence of each model Z i = p(d m,h i ) p(m H i ) dm p(h d) p(h d) = p(d H )p(h ) p(d H )p(h ) = Z p(h ) Z p(h ), p i /p lin msugra asymmetric a L DM Model/Prior linear log flat µ,b msugra 3 4 mamsb LVS a SUSY Candidates AbdusSalam, BCA, Dolan, Feroz, Hobson, arxiv: B.C. Allanach p. 34

38 Ice Cube Neutralinos can become trapped in the sun h Z coupling σ χ p,sd [ N d 2 N u 2 ] 2 dominates. A σv/v : Ṅ = C A N 2, Γ = 2 A N 2 = 2 C tanh 2 ( C A t ) dn νµ de νµ = C F Eq 4πD 2 ES ( dnν de ν ) Inj N ev dnνµ de νµ dσ ν dy R µ(( y)e ν )A eff de νµ dy SUSY Candidates B.C. Allanach p. 35

39 CMSSM Regions After WMAP+LEP2, bulk region diminished. Need specific mechanism to reduce overabundance: τ coannihilation: small m, m τ m χ. Boltzmann factor exp( M/T f ) controls ratio of species. τ χ τγ, τ τ τ τ. Higgs Funnel: χ χ A b b/τ τ at large tan β. Also via a h at large m small M /2. Focus region: Higgsino LSP at large m : χ χ WW/ZZ/Zh/t t. t coannihilation: high A, m t m χ. t χ gt, t t tt a SUSY Candidates Datta, Djouadi, Drees, hep-ph/549 B.C. Allanach p. 36

40 Annihilation Mechanism Define stau co-annihilation when m τ is within % of m χ and Higgs pole when m h,a is within % of 2m χ. χ mechanism flat prior natural prior h pole.25.7 A pole.4.4 τ co-annihilation.26.8 rest.3.6 b, τ τ τ h,a τ χ b,τ SUSY Candidates B.C. Allanach p. 37 χ γ

41 No Dark Matter Fits P per bin µ> µ< Ω DM h 2 m (TeV) M /2 (TeV) P/P(max) Huge χ 2 from the dark matter relic density SUSY Candidates B.C. Allanach p. 38

42 LHC vs LC in SUSY Measurement LHC (start date 27) produces strongly interacting particles up to a few TeV. Precision measurements of mass differences possible if the decay chains exist: possibly per mille for leptons, several percent for jets. ILC has several energy options: 5- GeV, CLIC up to 3 TeV. Linear colliders produce less strong particles but much easier to make precision measurements of masses/couplings. Q: What energy for LC? Q: What do we get from LHC a? a LHC/ILC Working Group Report: hep-ph/4364 SUSY Candidates B.C. Allanach p. 39

43 Bulk Region M Nojiri, G Polesello, D Tovey, JHEP 63 (26) 63, hep-ph/5224. for 3 fb. SPA point m = 7 GeV, m /2 = 25 GeV, A = 3 GeV, tan β =, µ > : Ωh 2 =.8. Put in m max ll m low lq, mhigh, m min llq, m l L m χ, m max ll lq χ χ l + l 4% χ χ τ + τ 28% χ χ ν ν 3% χ τ Zτ 4% χ τ Aτ 8% τ τ ττ 2%, m max llq, (χ 4 ), mmax ττ, m h. SUSY Candidates B.C. Allanach p. 4

44 Neutralino mass matrix Neutralino masses measured: χ,2,4 but need mixing matrix to determine couplings. Left with tan β. M m Z c β s W m Z s β s W M 2 m Z c β c W m Z s β c W m Z c β s W m Z c β c W µ () m Z s β s W m Z s β c W µ SUSY Candidates B.C. Allanach p. 4

45 Neutralino mass matrix Neutralino masses measured: χ,2,4 but need mixing matrix to determine couplings. Left with tan β abs(z ) abs(z 2 ) abs(z 3 ).8 abs(z 4 ) tanβ SUSY Candidates B.C. Allanach p. 4