1. Candidates for dark matter and the ILC
G. Bélanger (LAPTH- Annecy)

2. Outline Dark matter a new particle?
Dark colliders + astro/cosmo
Supersymmetric dark matter
Non-susy dark matter
vector boson, right-handed neutrino, scalar

3. What is the universe made of?
Dark matter inferred from rotation curve of galaxy
In recent years : new precise determination of cosmological parameters
Data from CMB (WMAP) agree with the one from clusters and supernovae
Dark matter: 23+/- 4%
Baryons: 4+/-.4%
Dark energy 73+/-4%
Neutrinos < 1%
Dark matter dominates over visible matter
Dark matter : guide to New physics models?

4. Open questions -link to new physics
What is symmetry breaking mechanism
Hierarchy problem – new physics
What is DM (new particle WIMP)?
Likely to be related to physics at weak scale
Same new physics at the weak scale can also solve EWSB
Many possible solutions – many possible DM candidates
What is Dark energy ?
rather related to Planck scale
Baryon asymmetry in the universe
Could also be explained with NP at weak scale (eg. electroweak baryogenesis and MSSM with CP violation)
Origin of neutrino mass

5. Dark matter : a new particle?
Weakly interacting particle gives roughly the right annihilation cross section to have Ωh2 ~0.1
Many candidates for weakly interacting neutral stable particles
best known is neutralino in SUSY
Other models with NP at TeV scale have candidates, only need some symmetry to ensure that lightest particle is stable: UED, Warped Xtra-Dim, Little Higgs…
Superweakly interacting particles might also work (gravitino)

6. Colliders : probing new physics
If DM is new particle – can be produced at colliders (LHC, ILC)
What is mass scale – discovery reach
What are properties of DM
Determine the underlying model for NP at the weak scale + consistency checks of underlying model at high scale,
Determination of properties of new particles – how well this can be done is model dependent
From this deduce annihilation cross sections for dark matter
Prediction for relic density – compare with measurement, if “collider prediction” precise enough it mean - Testing underlying cosmological model
Also compute cross section for dark matter scattering on nuclei -> consistent with direct detection results ?
Information on velocity distribution of DM ….

7. Cosmology/Astroparticle
Establish DM and Determination of Ωh2 - with PLANCK 2008 ~5% level
Constrain PP models assuming ΛCDM cosmology
Direct detection
Establish that a new particle is DM + some information on the mass of DM
Compatibility with NP scenario (SUSY or other)
Active area, many experiments underway : Xenon – new results in 2007 –
Caveats:
assumption about local density and velocity distribution
Uncertainties in nuclear matrix elements
Indirect detection
Active area - search for DM in different channels (photons, positrons, neutrinos)
Compatibility with NP scenario

8. DM candidates - examples
Models
Status of neutralino in mSUGRA -CMSSM
Other MSSM
UED
RH neutrino
Scalar
Constraints on models : expectations for mass scale and properties of DM
Prospects for LHC, ILC and astro (DD) - reach
In some cases : probing properties of DM candidates at colliders

9. Neutralino LSP
Nature of neutralino influences annihilation cross-sections
“naturally” correct annnihilation cross-section
Bino with light sleptons – annihilation into fermions
Bino-Higgsino LSP (annihilation in W/t pairs + some coan)
“Fine-tuning” required
Annihilation near resonance (heavy or light Higgs –LEP constraints)
Sfermion coannihilation (stau or stop)
σ of DM too small but density is depleted by coannihilation processes
Only in beyond mSUGRA
Bino-wino LSP (WW + coannihilation)
Bino-wino-Higgsino LSP

10. WMAP – constraining CMSSM
Studies with grid scan and fixed value of parameters (mt) show 4 different regions that are consistent with WMAP – somewhat fine-tuned model LSP is in general bino
Bino – LSP (LEP constraints)
Sfermion Coannihilation
Mixed Bino-Higgsino
Annihilation into W pairs
strong mt dependence
Resonance (Z, light/heavy Higgs)
LEP constraints for light Higgs/Z
Heavy Higgs at large tanβ (enhanced Hbb vertex)

11. Colliders and direct detection
LHC
Good for discovery of coloured particles, squarks, gluinos < TeV
Sparticles in decay chains
Limited reach when all squarks heavy – only chargino/neutralino “light” (in CMSSM when LSP is mixed bino/Higgsino)
ILC – can exceed reach of LHC in large M0-“focus point” –χ+χ-, χ1χj
Direct and indirect detection
Good prospects for mixed bino/Higgsino
Baer et al., hep-ph/

12. Direct detection - limits
Detect dark matter through interaction with nuclei in large detector
Often dominate by Higgs exchange diagram (except when squarks are light)
Higgsino component is necessary to have LSP coupling to Higgs –
Annihilation of LSP in W pairs enhanced for mixed bino/Higgsino – also favoured for indirect detection
Many experiments underway and planned
In 2007 – new results announced from Xenon (Gran-Sasso) best limit ~factor 6 better than CDMS (Ge,Si)
Xenon,E. Aprile, APS 2007

13. MCMC fits to CMSSM
In CMSSM mt is important parameter strongly affects the position of the “focus point” region (DM properties are similar nevertheless – bino-Higgsino) also dependence on other SM parameters
Global fits including SM parameters (mb,mt,α, αS) and MCMC approach + Bayesian statistics
Markov chain Monte Carlo allow many parameters scans
Ωh2, b->sγ, Mw, sin2θWl,BS->μμ, (g-2 )μ + LEP constraints
Allanach et al, hep-ph/ , arXiv:
Roszkowski, Trotta, Ruiz de Austri, arXiv:
Ellis et al. , arXiv: (χ 2 fit)

14. CMSSM – MCMC fit Allanach et al, 07050487
Favoured region is small M0-M1/2 (with stau coan) but focus and Higgs funnel also allowed at 95%CL
Either μ > 0 or μ<0
With flat priors in μ-B : small M0-M1/2 favoured
Good prospects for SUSY at colliders
Dependence on priors – not enough direct signals

15. “Mirage” unification
Mixed modulus-anomaly mediated SUSY breaking MM-AMSB
Apparent (mirage) unification of soft terms at scale Qmir (in minimal model 109 GeV but could even be above GUT scale)
KKLT: type IIB superstring compactification with fluxes
Kachru et al, hep-th/
MSSM soft terms and phenomenology explored
Choi et al, hep-th/ ; Falkowski et al, hep-ph/ ; Kitano et al; Baer et al, hep-ph/
Minimal model specified by 5 ½ parameters : gravitino mass, ratio of MM/AMSB, tan β ,location of fields in extra dimensions: modular weights (n) and gauge kinetic function indices (l)
m3/2, α, tanβ, sign(μ) n, l

16. DM in mirage unification
Gaugino unification at scale Qmir
In minimal model:
M3:M2:M1~ (1-0.3 α)g32 :(1+0.1 α) g22:( α) g12
Shifts in gaugino masses at weak scale compared to CMSSM
E.g. smaller M3/M1 leads to smaller μ at weak scale –Higgsino LSP
Scenarios with
bino-Higgsino LSP – annihilation WW and tt
Bino LSP+ stop coannihilation or Higgs resonance
When M1~-M2 : mixed wino LSP and bino-wino coannihilation
A large fraction of parameter space can give correct relic density assuming conventional thermal production

17. Mirage unification Main mechanisms for relic density within WMAP range
Higgs funnel (6)
Higgsino LSP (5)
Bino-wino LSP (8)
LHC reach over full parameter space (only for this choice of parameters)
ILC covers bino-wino region misses part of A-funnel and Higgsino regions
nm=1/2, nH=1
Baer, Park, Tata, Wang, hep-ph/

18. Probing cosmology using collider information
Within the context of a given model can one make precise predictions for the relic density at the level of WMAP(10%) and even PLANCK (3%) therefore test the underlying cosmological model.
Assume discovery SUSY/Higgs, precision from LHC? Precision for ILC?
Answer depends strongly on underlying NP scenario, many parameters enter computation of relic density, only a handful of relevant ones for each scenario – work is going on both for LHC and ILC
A few benchmark scenarios studied in detail
1st step : CMSSM scenario that predict relic density in agreement with WMAP.
2nd step : MSSM scenarios
Other scenarios

19. One sample benchmark: SPS1a’
M0=70, M1/2=250, A0=-300,tanβ=10
bino+ stau coannihilation
Annihilation into fermions
Coannihilation with staus
Relevant parameters : LSP mass, couplings, slepton masses
stau-neutralino mass difference (for coannihilation processes – factor e -ΔM)

20. LHC+ILC and SPS1A’
Start with CMSSM then estimate error from LHC measurements+ vary all MSSM parameters within these errors
LHC: measure neutralino-stau mass difference + 3 neutralino masses
Nojiri et al hep-ph/
Also important to measure sfermion/ neutralino parameters and setting limits on Higgs, other coan. particles …
With better determination of stau and neutralino masses – ILC much better “prediction” of relic density.
Other CMSSM scenarios can be hard for LHC – ILC provide more precise measurements (when within reach)
Baltz et al, hep-ph/

21. Colliders + direct detection
With measurements from LHC+ILC can we refine predictions for direct/indirect detection? YES
LCC1 (not exactly same as SPS1a’) relic density too high
Prediction for spin-independent cross-section
Observable by 2010
Factor of 3 uncertainty, improves significantly at ILC1000 (heavy Higgs mass)

22. Another example : Higgsino- LCC2
If squarks are heavy difficult scenario for LHC
only gluino accessible, chargino/neutralino in decays
mass differences could be measured from neutralino leptonic decays,
Relic density of DM depend on parameters of neutralino, need to be determine at % level
Recent study shows that necessary precision cannot be reached
Light Higgsinos possibly many accessible states at ILC
chargino pair production sensitive to bino/Higgsino mixing parameter
Baltz, et al , hep-ph/

23. LHC+ILC+direct detection – LCC2
Mixed bino-Higgsino LSP
Large spin-independent cross-section
Xenon best limit pb
Ambiguities at LHC –ILC improves
Study of bino-Higgsino scenario at LHC within context of NUHM –Polesello et al (Les Houches07) –results to come soon
ILC – additional information in cases where hA is accessible?

24. DM in UED
String theory and M theory : best candidate for consistent theory of quantum gravity and unification of all interactions
Xtra dim models solve the hierachy problem either with compactified dim on circles of radius R effectively lowering the Planck scale near EW scale or introducing large curvature (warped)
UED: flat Xdim , all fields propagate in the “bulk”
Each bulk field has tower of KK states , mn~n/R
Explain:
3 families from anomaly cancellation
Dynamical EWSB
No rapid proton decay

25. Vector boson DM – UED
UED : All SM field propagate through all dim. of space R~TeV-1
KK parity for proton stability
Minimal UED: LKP is B (1), partner of hypercharge gauge boson (spin 1)
s-channel annihilation of LKP (gauge boson) typically more efficient than that of neutralino LSP
Compatibility with WMAP means rather heavy LKP, GeV
Tait, Servant ( 2002 )
Mostly relevant for multi-TeV colliders
Kong, Matchev, hep-ph/

26. Right-handed Dirac neutrino
Typical framework: sterile Dirac neutrino under SM but charged under extra symmetry SU(2)R
Phenomenologically viable model with warped extra-dimensions and right-handed neutrino (GeV-TeV) as Dark Matter was proposed (LZP)
Agashe, Servant, PRL93, (2004)
Stability requires additional symmetry , but symmetry might be necessary for EW precision or for stability of proton
νR can couple to Z through ν’L- νR or Z-Z’ mixing –naturally small
Main annihilation channel – Z/Z’ exchange

27. Direct detection : Dirac neutrino
Dirac neutrino: spin independent interaction dominated by Z exchange (vector-like coupling)  very large cross-section for direct detection
coupling ZνRνR cannot be too large
Current DM experiments already restricts νR to
~MZ/2, ~MH/2 or M(νR) > 700GeV
Vectorial coupling : elastic scattering on proton << neutron
Direct detection is best way to probe this type of model
At colliders: signal for KK quarks (Dennis et al. hep-ph/071158) and/or Z’ and/or invisible Higgs – to be explore Z
GB, Pukhov, Servant

28. Scalar dark matter (singlet)
Extensions of SM Higgs sector that can affect Higgs phenomenology
Simplest extension : add scalar singlet to SM + discrete symmetry-> stable scalar
Singlet couples to Higgses –responsible for annihilation
Higgs exchange also gives spin-independent direct detection

29. Scalar DM -
No resonance annihilation needed DD directly related to annihilation cross-section
Good prospects for direct detection
Colliders : singlet modify properties of Higgs decays, (invisible decay)
LHC can look for those, need high luminosity – ILC good probe of invisible Higgs
No early signs of NP at LHC, yet possible signal in Direct detection – ILC with invisible H could provide important info.
Barger et al

30. WIMPS
GUT-scale models include string inspired models (e.g.moduli-dominated), AMSB, Split SUSY, Compressed SUSY, NUHM, mirage mediation

31. Conclusions
Many models of SUSY or other NP with DM candidate in general motivated by EWSB problem
Mass of DM varies over a wide range
If LHC discover new particles, will give precious information on NP model and on potential DM candidate – some complementarity with direct/indirect detection
Precise measurements of properties of DM at LHC (in favourable cases) and especially at ILC can reduce (PP) uncertainty in prediction of relic density and/or cross-sections in direct/indirect detection –might even test cosmological model

32. Determination of parameters LHC : SPA1A
Decay chain
Signal: jet +dilepton pair
Can reconstruct four masses from endpoint of ll and qll
In particular stau-neutralino mass difference
Here Δm (NLSP-LSP) = 10.5GeV
Mixing in the stau sector obtained from
For LSP couplings need 3 masses (χ1 χ2 χ4) and assume tanβ
Assume tanβ known + limit on heavy stau and on heavy Higgs
.087 < ΩCDMh2<.138

33. LHC and DM How will LHC see dark matter? What can LHC measure?
Missing energy
Sample decay chain
What can LHC measure?
Mass differences (using endpoints) – percent level
Masses (endpoints +cross-sections + theory) more difficult – Lester,Parker, White ’05
Some properties of particles: spin.. (Barr –hep-ph/ )
Reconstruct underlying model parameters especially if theoretical assumption
White, hep-ph/

34. Non-universal gaugino masses
String inspired moduli-dominated : LSP has important wino component
Binetruy et al, hep-ph/
Non universal SUGRA,
Depending on the GUT scale relation between gaugino masses can find WMAP compatible region in all the M0-M1/2 plane
GB, Boudjema, Cottrant, Pukhov, Bertin,Nezri, Orloff, Baer, Belyaev, Birkedal-Hansen, Nelson, Mambrini, Munoz…
M1~M2  LSP is mixed bino-wino annihilation more efficient, scale of LSP ~ 500GeV
M1=1.8M2|GUT
mixed bino/wino
Higgs exchange
GB, et al, NPB706(2005)

35. Non-universality
Many high scale models with non-universal gaugino masses and/or non-universal Higgs masses
Heterotic supersting with orbifold compactification, SUSY breaking dominated by moduli field
XtraDim SUSY GUT models, SUSY breaking via gaugino mediation
Pheno -motivated
Compressed SUSY : if M3<M2 at GUT scale, less fine-tuning to have small values of m2Hu – squarks not so heavy relative to LSP
Martin, PhysReVD74 (2007)
From DM point of view: in these models, easier to get LSP not pure bino ---
Can find WMAP compatible regions in all M0-M1/2 plane
Mixed bino-Higgsino LSP or mixed bino-wino LSP or even bino-wino-Higgsino LSP : annihilation efficent, scale of LSP can be several hundred GeV
Higgsino-LSP not necessarily associated with very heavy scalar spectrum and very heavy Higgs like in mSUGRA

36. Non-universal Higgs masses
Motivated by SO(10) or SU(5) GUTs – Higgs fields in different representation than fermion field
μ smaller than in CMSSM –LSP bino/Higgsino (even at low M0)
Annihilation via Higgs resonance even when tanβ not large
Even when squarks are not as heavy as in CMSSM, ILC reach (chargino pair) can exceed that of LHC
ILC: when heavy Higgs not so heavy – ee->hA, H+H-
When μ small : also all neutralinos and charginos
ILC
ILC
Baer et al hep-ph/