TAUP 2007, Sendai, September Dark Matter Candidates Stefano Scopel Korea Institute for Advanced Study - Seoul TAUP 2007, Sendai, September

TAUP 2007, Sendai, September Outline Evidence for Dark Matter Dark Matter properties neutrinos axions WIMP candidates from UED, Little Higgs, SUSY The neutralino Relic abundance Direct detection Conclusions Topics covered by other talks: Experimental direct searches (Pierluigi Belli, Dan Bauer) Indirect detection – theory (Lars Bergström) Indirect detection – experiment (Piergiorgio Picozza)

TAUP 2007, Sendai, September Evidence for Dark Matter Spiral galaxies rotation curves Clusters & Superclusters Weak gravitational lensing Strong gravitational lensing Galaxy velocities X rays Large scale structure Structure formation CMB anisotropy: WMAP Ω tot =1 Ω dark energy ~0.7 Ω matter ~ 0.27 Ω baryons ~0.05 Ω dark matter ~ 0.22

TAUP 2007, Sendai, September stable (protected by a conserved quantum number) no charge, no colour (weakly interacting) cold, non dissipative relic abundance compatible to observation motivated by theory (vs. “ad hoc”) The properties of a good Dark Matter candidate: subdominant candidates – variety is common in Nature →may be easier to detect *

TAUP 2007, Sendai, September The first place to look for a DM candidate…

TAUP 2007, Sendai, September Neutrino HOT COLD Σm v <0.66 eV (WMAP+LSS+SN) LEP: N ν =2.994±0.012 → m ν ≥45 GeV → Ω ν h 2 ≤ DM searches exclude: 10 GeV ≤ m ν ≤ 5 TeV (similar constraints for sneutrinos and KK-neutrinos) 3 – 7 GeV ~10 eV mix with sterile component (both for neutrinos and sneutrinos) does not work

TAUP 2007, Sendai, September beyond the standard model

TAUP 2007, Sendai, September (Incomplete) List of DM candidates RH neutrinos Axions Lightest Supersymmetric particle (LSP) – neutralino, sneutrino, axino Lighest Kaluza-Klein Particle (LKP) Heavy photon in Little Higgs Models Solitons (Q-balls, B-balls) Black Hole remnants …

TAUP 2007, Sendai, September The axion Pseudo Goldstone boson of Peccei-Quinn symmetry introduced to explain CP conservation in QCD: φ= F e iθ (0.3 < k a <a few) if no inflation after PQ phase trans. : average (flat dist.→ =π 2 /3)→m a ~10 -5 eV 3 productions mechanisms in the early Universe: 1) misalignment (T>Λ QCD ) +coherent oscillations around minimum (T< Λ QCD ) : 2) axion strings (T R >f a ) 3) thermal (m a >10 -3 eV, subdominant) otherwise: smaller m a possible [Tegmark,Aguirre, Rees. Wilczek]

TAUP 2007, Sendai, September Experimental limits: (DAMA, SOLAX, COSME) ADMX, TOKYO g a   from theory & uncertainty in the masses of light quarks, (Buckley,Murayama, arXiv: ) use data from WIMP searches! (but sensitivity improves as (MT) 1/8 ) B g a  a 

TAUP 2007, Sendai, September most popular DM candidates from particle physics (solve hierarchy problem: M W /M Pl ~ ) susy conserved symmetry DM candidate R-parity K-parity T-parity χ ( neutralino) extra dimensions little Higgs B (1) (KK photon) B H (heavy photon) all thermal candidates, massive, with weak-type interactions (WIMPs)

TAUP 2007, Sendai, September the thermal cosmological density of a WIMP X Ω X h 2 ~ 1/ int int = ∫ dx xfxf x0x0 x f =M/T f x 0 =M/T 0 T f =freeze-out temperature T 0 =present (CMB) temperature X f >>1, X non relativistic at decoupling, low temp expansion for : ~a+b/x if σ ann is given by weak-type interactions → Ω X ~0.1-1 …+ cohannihilations with other particle(s) close in mass + resonant annihilations

TAUP 2007, Sendai, September WIMP direct detection  Elastic recoil of non relativistic halo WIMPs off the nuclei of an underground detector  Recoil energy of the nucleus in the keV range  Yearly modulation effect due to the rotation of the Earth around the Sun (the relative velocity between the halo, usually assumed at rest in the Galactic system, and the detector changes during the year)

TAUP 2007, Sendai, September WIMP differential detection rate E R =nuclear energy N T =# of nuclear targets v=WIMP velocity in the Earth’s rest frame Astrophysics ρ χ =WIMP local density f(v)= WIMP velocity distribution function Particle and nuclear physics =WIMP-nucleus elastic cross section usually dominates, α (atomic number) 2

TAUP 2007, Sendai, September Different halo models are possible time-independent part [Belli, Cerulli, Fornengo, Scopel] Interaction on NaI modulation amplitude sizeable variation of the local density: 0.17 < ρ < 1.7

TAUP 2007, Sendai, September

B (1) relic abundance [Servant,Tait, NPB650,391;New J. Phys. 4,99; Kakizai & al., PRD71,123522; Kong, Matchev, JHEP0601,038] coannihilations (many modes with similar masses) resonances (M NLKP ~ 2 x M LKP ) general rule of coannihilation: if cohannihilating particle annihilates than LKP→ relic abundance faster slower smaller larger both cases are possible : KK quarks and gluons vs. KK leptons KK leptons Δ≡fractional mass splitting Ω B (1) h 2 =0.1

TAUP 2007, Sendai, September low direct detection signals: Δ≡(m q1 -m B1 )/m B1

TAUP 2007, Sendai, September Right-handed KK-neutrino Dark Matter: see talk by M.Yamanaka in parallel session

TAUP 2007, Sendai, September GUT unification of gauge couplings

TAUP 2007, Sendai, September The neutralino  The neutralino is defined as the lowest-mass linear superposition of bino B, wino W (3) and the two higgsino states H 1 0, H 2 0 :  neutral, colourless, only weak-type interactions  stable if R-parity is conserved, thermal relic  non relativistic at decoupling  Cold Dark Matter (required by CMB data + structure formation models)  relic density can be compatible with cosmological observations: ≤ Ω χ h 2 ≤  IDEAL CANDIDATE FOR COLD DARK MATTER ~ ~ ~ ~

TAUP 2007, Sendai, September Right-handed sneutrino Dark Matter: see talk by T. Asaka in parallel session

TAUP 2007, Sendai, September

SUGRA (a.k.a. CMSSM) focus point [Feng, Machev, Moroi, Wilczek] stau coannihilationHiggs funnel [Ellis, Olive, Santoso, Spanos] only few regions cosmologically allowed variants (e.g. non-universality of soft masses at the GUT scale or lower unification scale) that increase Higgsino content of the neutralino→ lower relic abundance and higher signals

TAUP 2007, Sendai, September Direct detection in SUGRA [Ellis, Olive, Santoso, Spanos]

TAUP 2007, Sendai, September The Next-to-Minimal MSSM (NMSSM) solves the μ problem, i.e. why μ~M EW in: μH 1 H 2 superpotential: Higgs soft terms in the NMSSM: NMSSM particle content: MSSM+ 2 Higgs (CP-even, CP-odd) 1 neutralino dof The lightest neutralino: CP-even Higgs: μ=λ

TAUP 2007, Sendai, September Relic density and direct detection rate in NMSSM [Cerdeño, Hugonie, López-Fogliani, Muñoz, Teixeira] relic abundance direct detection M 1 =160 GeV, M 2 =320, A λ =400 GeV, A k =-200 GeV, μ=130 GeV, tan β=5 (sizeable direct detection) very light neutral Higgs (mainly singlet) light scalars imply more decay channels and resonant decays neutralino relatively light (< decay thresholds) and mostly singlino high direct detection cross sections (even better for lower M 1 ) tachyons Landau pole unphysical minima W H1H1 H 2 /2 χ,H lighter χ singlino Z

TAUP 2007, Sendai, September Effective MSSM: effective model at the EW scale with a few MSSM parameters which set the most relevant scales M 1 U(1) gaugino soft breaking term M 2 SU(2) gaugino soft breaking term μ Higgs mixing mass parameter tan β ratio of two Higgs v.e.v.’s m A mass of CP odd neutral Higgs boson (the extended Higgs sector of MSSM includes also the neutral scalars h, H, and the charged scalars H ±) m q soft mass common to all squarks m l soft mass common to all sleptons A common dimensionless trilinear parameter for the third family (A b = A t ≡ Am q ; A τ ≡ Am l ) R ≡ M 1 /M 2 ~ ~ ~ ~ ~ ~ ~ SUGRA  R=0.5

TAUP 2007, Sendai, September Can the neutralino be ?

TAUP 2007, Sendai, September Cosmological lower bound on m χ upper bound on Ω CDM h 2 scatter plot: full calculation curve: analytical approximation for minimal Ω CDM h 2 [Bottino, Fornengo, Scopel, PRD68,043506] M 1 <<M 2,μ

TAUP 2007, Sendai, September DAMA modulation region, likelyhood function values distant more than 4 σ from the null result (absence on modulation) hypothesis, Riv. N. Cim. 26 n. 1 (2003) 1-73, astro-ph/ Neutralino – nucleon cross section Color code: ● Ω χ h 2 <  Ω χ h 2 > The elastic cross section is bounded from below  “funnel” at low mass tight correlation between relic abundance and χ -nucleon cross section:

TAUP 2007, Sendai, September How exp. limit change with different halo models (CDMS): A. Bottino, F. Donato, N. Fornengo and S. Scopel Phys.Rev.D72, (2005) largest uncertainty at low masses from high velocity tail of the the distribution

TAUP 2007, Sendai, September Conclusions WIMPs at the TeV scale can be realized in different well-motivated scenarios (KK photon in UED, Heavy photon in Little Higgs, neutralino in SUSY) +”Minimal” extensions of SM (talk by Tytgat in parallel session) they can all provide the Cold Dark Matter with the correct abundance neutralino is still the most popular. Today available in different flavours: SUGRA, nuSUGRA, sub-GUT, Mirage mediation, NMSSM, effMSSM, CPV,… neutralinos can be light astrophysical uncertainties in signal predictions direct searches are already exploring some SUSY scenarios

TAUP 2007, Sendai, September Hopefully, soon we will know better… “One day, all of these will be LHC phenomenology papers”

TAUP 2007, Sendai, September BACK - UP

TAUP 2007, Sendai, September Uncertainties in WIMP-nucleon cross section from nucleonic matrix elements [Bottino,Donato,Fornengo,Scopel, Astrop. Phys. 13,215] pion-nucleon sigma term strange quark content almost 1 order of magnitude increase in the most extreme case (set 3/set 1) set 3/set 1

TAUP 2007, Sendai, September Littlest Higgs Model with T parity (Birkedal et al., PRD74, ) SU(5)/SO(5) global symmetry breaking at f~1 TeV SM Higgs as Goldstone boson associated with this breaking Gauged subgroup [SU(2)xU(1)] 2 of SU(5) broken at f~1 TeV to SM SU(2) L xU(1) Y → extended gauge sector with 4 additional gauge bosons at TeV scale: W H ±,W H 3, B H, with masses: T-parity transformation on gauge fields: [SU(2)xU(1)] 1 →[SU(2)xU(1)] 2 (SM field even, TeV fields odd) “Heavy photon” B H is the lightest T-odd particle (LTP) and can play the role of dark matter candidate B H & SM sector weakly coupled → B H is a WIMP and can provide the correct amount of DM as a thermal relic

TAUP 2007, Sendai, September Upper bound on scale f from naturalness: f ≤ 2 TeV to avoid fine tuning in the Higgs sector Allowed range for Heavy photon mass: Lower bound on scale f from precision electroweak constraints: f≥ 600 GeV

TAUP 2007, Sendai, September Direct detection (a) diagram: (spin independent) (b)+(c) diagrams: (spin dependent) additional spin independent contribution from resonant s-channel scattering B H q→Q→B H q when M~M (same region relevant for coannihilation) ~ ~