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Non-Baryonic Dark Matter in Cosmology. Antonino Del Popolo Department of Physics and Astronomy University of Catania, Italy. IX Mexican School on Gravitation and Mathematical Physics "Cosmology for the XXI Century: Inflation, Dark Matter and Dark Energy".

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Non-Baryonic Dark Matter in Cosmology


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    1. Non-Baryonic Dark Matter in Cosmology Antonino Del Popolo Department of Physics and Astronomy University of Catania, Italy IX Mexican School on Gravitation and Mathematical Physics "Cosmology for the XXI Century: Inflation, Dark Matter and Dark Energy" Puerto Vallarta, Jalisco, Mexico, December 3-7, 2012

    2. LECTURE 3 The nature of dark Matter

    3. So what is DM? Big Bang nucleosynthesis (deuterium abundance) and cosmic microwave background (WMAP) determine baryon contribution ΩB=0.0456±0.0016, ΩM=0.227±0.014 (WMAP+BAO+Ho) Baryons: too few to explain all the dark matter because of nucleosynthesis. Moreover unable to drive galaxy formation (decouple too late from photons, not enough time for gravitational instabilites to grow) Ωlum 3. 10-3(stars, gas, dust) (Persic & Salucci (1992); 0.02 (Fukugita, Hogan & Peebles (1998) (including plasmas in groups and clusters) =>ΩB>Ωlum baryonic dark matter has to exist We already discussed the MACHO, EROS1, etc limits Rees (1977) : DM could be of a “more exotic character”-> e.g., small rest mass neutrinos Aλ=1-10 scale dependent growth factor Tm<0.14 eV T0 =2.35x10-4 (CMB tempertaure now) Fields & Sarkar, 2004

    4. The properties of a good Dark Matter candidate: • Non-baryonic (two reasons: BBN, structure formation) • Stable (protected by a conserved quantum number) • No charge, No colour(weakly interacting) • -if DM non electrically neutral could scatter light -> non DARK • cold, non dissipative (structure formation) • relic abundance compatible to observation

    5. First place to look for candidates: SM • Not short-lived • Not hot • Not baryonic • Desired DM properties • Gravitationally interacting • Unambiguous evidence for new particles

    6. “Ad-Hoc” DM Candidates keV sterile n’s MeV DM Super-heavy DM Neutrino masses and mixing Warm Dark Matter Ultra-GZK Cosmic Rays CR with Energy> Greisen- Zatsepin-Kuzmin cut-off 511 keV line DARK MATTER candidates gauge hierarchy problem especially motivates Terascale masses DM Candidates AXION MSSM LSP UED LKP • Hierarchy problem • (bino, wino, • two neutral • higgsinos)->Neutralinos; • 3 sneutrinos; gravitino Momentum Conserv. (KK-parity): KK photon excitation, Z, Neutrinos, Higgs bosons or graviton Strong CP-problem (PQ Symmetry)

    7. Neutralinos favorite because they have at least three virtues… • 1) Required by supersymmetry, and so motivated by • electroweak symmetry breaking force unification • 2) Stable: the neutralino is typically the LSP, • and so stable (in R-parity conserving supergravity) • 3) Correct relic density, detection promising

    8. DM FORMATION,FREEZE OUT: QUALITATIVE 3)Self-annihilation contained by the competing Hubble expansion:Universe expands: XX qq Assume a new heavy particle X is initially in thermal equilibrium interacting with the SM particles q: (or if X is its own antiparticle ) 1) In the very early universe when TUniv>>mx the processes of creation and annihilation were equally efficient -> X present in large quantities (1) Increasing annihilation strength ↓ 2) Universe cools: T<mx the process of creation exponentially suppressed, annihilation process continues. In thermal equilibrium XX  qq If particles remain in thermal eq. Indefinitely -> number density suppressed (2) gx Degree of freedom of X (3) ← / → Feng, ARAA (2010) → / ← / Expansion-> dilution of WIMPs-> increasingly dominates over the annihilation Rate-> number density of X sufficiently small that they cease to interact with each other, and thus survive to the present day. Zeldovich et al. (1960s)

    9. FREEZE OUT: MORE QUANTITATIVE The Boltzmann equation: ‾ f f→cc ‾ cc→ f f N L [f]=C [f] Dilution from expansion Thermally averaged anihilation cross section • T>>mx (Г>H) n ≈ neq until interaction rate drops below expansion rate T<<mx (Г<H): • T<<mx (Г<H) equilibrium density small: 3Hnx and • deplete number density • For sufficiently small nx annihilation insignificant with • respect dilution due to expansion -> Freez-out • Might expect freeze out at T ~ m, but the universe expands slowly! First guess: m/T ~ ln (MPl/mW) ~ 40

    10. Resulting (relic) density today: ~ xFo / <v> Non-relativistic expansion for heavy states =65, 1 GeV =120, 1 TeV in SM In case of presence of other species i,j=1 -> WIMP Numerical coincidence? Or an indication that dark matter originates from EW physics? • For a particle with a GeV-TeV mass, to obtain a thermal abundance equal to the observed dark matter density, we need an annihilation cross section of <v> ~ pb • Generic weak interaction yields: • <v> ~ 2 (100 GeV)-2 ~ pb WIMP MIRACLE

    11. Neutrinos Light neutrinos: mν≤ 30 eVHDM (relativistic at decoupling, erase density perturbation through free-streaming. MJeans =1012 Mʘ ->Top-Down In SM absence right handed neutrino state-> no neutrino mass (*) BUT adding a right hand state -> Dirac mass for the neutrino (Dirac mass term Adding the term to -> Majorana mass Particles decouple when An example: neutrino decoupling. By dimensional analysis the decoupling T-> Neutrinos more massive than 1 MeV annihilate before decoupling, and while in equilibrium their number is suppressed. Lighter neutrinos <1 MeV do not experience suppression due to annihilation-> calculation of number density of neutrinos different for m<1 MeV, m>1 MeV (*) Unless adding non-renormalizable lepton number violating interactions, HHLL

    12. From the condition t>12Gyr-> (*) and -> Majorana. For Dirac depends from right state interaction HST key project data SIa, BBN ~ Combining with (*) gives: Dirac or Majorana LEP-> excludes In 10 GeV < < 4.7 TeV Dirac excluded by Lab constraints 45 GeV< <100 TeV with and for >45 GeV Majorana has ->cosmologically uninteresting Finally: Neutino mixing, LEP limit on neutrino species -> -> light weakly interacting neutrinos mv≤ 1 MeV mv≥ 1 MeV, Boltzman Equation ->

    13. Excluded by LEP SM Beyond SM Excluded by direct DM experiments

    14. Axions Stellar cooling (globular clusters) Optical & Radio Tlscp. (monoch. emission from A decay in clusters) SN 1987A data (neutron star cooling) Photon Regeneration (Parallel E -laser- and B fields; after optical barrier the E|| component can be regenerated) Microwave cavity Ex. (resonant conversion of A’s in monoch. M.w. radiation) dn-QCD ~10-15 e cm dn-data ~10-26 e cm • Experiments: no CP violation in the QCD sector but natural terms in QCD Lagrangian able to break CP simm. • The theta-term of QCD poses the so-called strong CP-problem • Promoting Q to a dynamical variable, and postulating a spontaneously broken (at a scale fA) global U(1)PQsymmetry, the theta-term is effectively driven to zero • The associated pseudo-NG boson, the axion, features Ωa/ Ωc = (fa/1012GeV)7/6 fA ≤1012 cosmological density limit fA ≥1010 emission from red giants ………. Anomalous Signal reported by the PVLAS collaboration was interpreted as a possible hint(*) (Zavattini et al., Phys.Rev.Lett.96:110406,2006; (**) Rabaden et al., Phys.Rev.Lett.96:110407,2006); Rizzo 2007 problem in the experiment

    15. An Anomalous Signal reported by the PVLAS collaboration was interpreted as a possible hint(*) The claimed signal can be readily tested with a Regeneration setup(**) The proposed experiment will actually be carried out soon at DESY Have Axions been detected?! N • Other Axion detection technique: Polarization Experiments The E||component is depleted by the production of real Axions, resulting in a rotation of the polarization vector and vacuum birifrangence Polarized Light propagating through a transverse magnetic field is affected by Axions Higher order QED effects (“light-by-light”) also contribute and constitute a Background C. Rizzo 2007 showed the experiment result was wrong (*) Zavattini et al., Phys.Rev.Lett.96:110406,2006; (**) Rabaden et al., Phys.Rev.Lett.96:110407,2006

    16. SUSY DM Item 1. (~1979) Item 2. (~1981) Item 3. (~1982) GAUGE-COUPLING UNIFICATION DARK MATTER CANDIDATE FINE-TUNING PROBLEM SM Dm2H~ L2UV SUSY + Lightest Neutralino is a suitable WIMP DM candidate Dm2H~ log(LUV / m) Tracing back the early motivations for low energy Supersymmetry... *See: L.Maiani (1979); S.Dimopoulos,S.Raby,F.Wilczek (1981); H.Pagels, J.R.Primack (1982)

    17. Hierarchy problem, Supersimmetry • SM predict very precisely the results of experiments • This high precision requires calculations of higher orders (HO) • Example MW :first order +HO (%) • Higgs mass, as MW, gets correction from HO • Dependence on cut-off Λ(energy/distance up to which the SM is valid; we know that at distance at which gravity gets important, Planck scale, SM non valid) • All particles get radiative correction to their mass but while for fermions mass increase logarithmically, for scalars quadratically with corrections at 1-loop • The radiative corrections to the Higgs mass (which is expected to be of the order of the electroweak scale MW ∼ 100 GeV) will destroy the stability of the electroweak scale if is higher than ∼ TeV, e.g. if Λ is near the Planck mass -> “HIERARCHY PROBLEM OF THE SM”hierarchy between electroweak scale (~100 GeV) and the Planck scale • SOLUTION: introduce a “supersymmetry” • Since the contribution of fermion loops to δm2s have opposite sign to the corresponding bosonic loops, at the 1-loop level provided quadratic divergenge to Higg mass cancelled δM2Hα ln Λ Supersymmetryis an extension that creates 'superpartners' for all Standard Model particles: squarks,gluinos,charginos, neutralinos, andsleptons . TheMinimal Supersymmetric Standard Model(MSSM): minimal extension to theStandard Model containing the fewest number of new particles and interactions necessary to make a consistent theory

    18. Mass eigenstate of the SUSY partners of the U(1)Y and SU(2) gauge bosons and of the two neutral Higgses • NEUTRALINO MSSM The Neutralino properties depend critically upon its composition • = N11B 0 + N12W 0 + N13Hd0 + N14Hu0 BINO WINO HIGGSINO Ruled out by Direct Detection within the MSSM; viable if mixed with sterile sneutrino • SNEUTRINO ext-MSSM • GRAVITINO Super-WIMPs (not directly detectable) Wide mass range (down to the keV, up to the TeV) Require the extension of the MSSM to include gravitons/axions • AXINO R-PARITY, PROTON DECAY AND STABLE LSPS • Abesence interactions responsible responsible for extremely rapid proton decay->assume the conservation of R-parity: R = (-1) 3B+L+2S (B, L and S= baryon number, lepton number and spin) • R = +1 for all SM particles; R = -1 for all superpartners • R-parity conservation requires superpartners to be created or destroyed in pairs, leading at least one supersymmetric particle (the lightest supersymmetric particle (LSP)) to be stable, even over cosmological timescales. • Minimal model (MSSM) contains the fewest number of new particles and interactions necessary to make a consistent theory (in any case a lot) • Identity of the Lightest Stable Particle (LSP) depends on the hierarchy of the supersymmetric spectrum -> depends from the details of how supersymmetry is broken. • The only electrically neutral and colorless superparnters in (MSSM) are the four neutralinos (superpartners of the neutral gauge and Higgs bosons), three sneutrinos, and the gravitino. The lightest neutralino, in particular, is a very attractive and throughly studied candidate for dark matter (*) Minimal Supersymmetric Standard Model(MSSM) is the minimal extension to theStandard Modelthat realizes N=1supersymmetry.The MSSM was originally proposed in 1981 to stabilize the weak scale, solving thehierarchy problem

    19. PARAMETERS AND SIMPLIFIED MODELS • MSSM, despite its minimality in particles and interactions contains over a hundred (124) new parameters related to supersymmetry breaking. • Often assumed that at some unification scale, all of the gaugino masses receive a common mass, m1/2. Gaugino massses at EW scale obtained running a set of RGEs. Similarly, one often assumes that all scalars receive a common scalar mass, m0, at the GUT scale. • Higgs mixing mass parameter, μ. In MSSM two Higgs doublets -> two vacuum expectation values. One combination of these is related to the Z mass, and therefore is not a free parameter, while the other combination, the ratio of the two vevs, tan β, is free. • If the supersymmetry breaking Higgs soft masses also unified at the GUT scale (and take the common value m0) -> μ and the physical Higgs masses at the weak scale are determined by electroweak vacuum conditions (μ is determined up to a sign). This scenario is often referred to as the constrained MSSM or CMSSM. CSSM parameters: m1/2 gaugino mass •m0 scalar masses •A0: soft breaking trilinear coupling constant (higgs-sfermionsfermion) •tanβ = v1/v2 ratio of the VEVs of the two Higgs •sign(μ) sign of the Higgsino mass parameter (bilinear higgsino coupling constant)

    20. N WHAT’S THE LSP? High-scale  weak scale through RGEs. Gauge couplings increase masses; Yukawa couplings decrease masses “typical” LSPs: c , t̃R Running of the mass parameters in the CMSSM. Here: m1/2 = 250 GeV, m0 = 100 GeV, tan β =3, A0 = 0, and μ < 0. Knowing few input parameters, all of the masses of the supersymmetric particles can be determined. Characteristic features: colored sparticles are typically the heaviest in the spectrum. This is due to the large positive correction to the masses due to α3 in the RGE’s. B (the partner of the U(1)Y) gauge boson), is typically the lightest sparticle. One of the Higgs mass, goes negative triggering electroweak symmetry breaking. (The negative sign in the figure refers to the sign of the mass, even though it is the mass of the sparticles which are depicted.) ~ Olive (2003) RG evolution of the mass parameters Particle physics alone  neutral, stable, cold dark matter

    21. ~ NEUTRALINOS ~ ~ ~ • Four neutralinos, each of which is a linear combination of the R =-1 neutral fermions: the wino W3 (partner of the 3rd component of the SU(2)Lgauge boson); the bino, Bsuperpartner of the U(1)Y gauge field corresponding to weak hypercharge and the two neutral Higgsinos, H1, and H2 Neutralinos: linear combination of bino, wino, and higgsinos • Lightest of the four states referred to as: Neutralino, given by gaugino and higgsino components: • Neutralino mass matrix • M1 and M2 are the bino and wino masses, μ is the higgsino mass parameter, θW is the Weinberg angle and tanβ=v2/v1 the ratio of the vacuum expectation values of Higgs doublets • Mass and composition of the lightest neutralino= f(M1, M2, μ,β) ~ ~ ~ ~ χ0 =N11B+N12W3+N13H1+N14H2 • neutral, colourless, only weak-type interactions • stable if R-parity is conserved, thermal relic • non relativistic at decoupling  Cold Dark Matter • relic density can be compatible with cosmological observations • Relic abundance in excess of the observed dark matter density over much or most of the supersymmetric • parameter space-> consider the regions of parameter space which lead to especially efficient neutralino • annihilation

    22. Relic Abundance • Relic abundance of LSP’s -> solving the Boltzmann equation for the LSP number density in an expanding Universe, after neutralinosgeneral annihilation cross-section is known • Bino, LSP In much of the parameter space of interest (annihilation proceeds mainly through sfermion exchange) • Final neutralino relic • Relic abundance in excess of the observed dark matter density over much or most of the supersymmetric parameter space • To avoid this, we are forced to consider the regions of parameter space which lead to especially efficient neutralino annihilation in the early universe. • Scenarios which can lead to a phenomenologically viable density of neutralino DM --lightest neutralino has a significant higgsino or wino fraction -> can have large couplings-> annihilate efficiently --mass of the lightest neutralino near a resonance, such as the CP-odd Higgs pole -> annihilate efficiently -- lightest neutralino is only slightly lighter than another superpartner (e.g., stau) -> coannihilation-> depletion f=freez-out

    23. Figure. Representative regions of the CMSSM parameter space. . • All scalar masses set to a common • value mo at GUT; the 3 gaugino masses • set to m1/2 a GUT (CMSSM) • A0 = 0 and µ > 0 • Blue region: parameter space in which • neutralino DM abundance consistent • with DM abundance • The shaded regions to the upper left • and lower right are disfavored by the • LEP chargino bound and as a result • of containing a stau LSP, respectively • (focus point region) The LEP bound on the light Higgs mass is shown as a solid line (mh= 114 GeV). RECENT MEASURES ->125 GeV for Higgs Boson mass The region favored by measurements of the muon’s magnetic moment are shown as a light shaded region (at the 3σconfidence level) Region where lightest stau (˜τ ) is the LSP -> not provide a viable dark matter candidate. Just outside of this region, stau slightly heavier than the lightest neutralino,leading to a neutralino LSP which effciently coannihilates with the nearly degenerate stau. In the lower right frame, a viable region also appears along the CP-odd Higgs resonance (m χ0 ~ mA/2). This is often called the A-funnel region.

    24. mSUGRA or CMSSM: simplest (and most constrained) model for supersymmetric dark matter • R-parity conservation, radiative electroweak symmetry breaking • Free parameters (set at GUT scale): m0, m1/2, tan b, A0, sign(m) • 4 main regions where neutralino fulfills WMAP relic density: • bulk region (low m0 and m1/2) • stau coannihilation region m  mstau • hyperbolic branch/focus point (m0 >> m1/2) • funnel region (mA,H 2m) • (5th region? h pole region, large mt ?) H. Baer, A. Belyaev, T. Krupovnickas, J. O’Farrill, JCAP 0408:005,2004

    25. UED AND KK DARK MATTER 4/R 3/R 2/R mass 1/R 0 • Models with extra dimensions:one or more additional dimensions beyond the usual (3+1): (3+1) dimensions (brane) embedded in a (3+δ+1) spacetime (bulk). SM fields confined in the brane; gravity propagates in the extra dimensions. • Hierarchy problem addressed as: extra dimensions compactified on circles (or other topology) of some size, R, (e.g., ADD (Arkani-Hamed, Dimopoulos and Dvali) scenario -> lowers Planck scale energy near the EW. Otherwise: introduce ED with large curvature (e.g., RS (Randall and Sundrum)). ED Motived also by string theory and M-theory (6, 7 ED needed). • General feature of ED theories: upon compactification of ED all of the fields propagating in the bulk have their momentum quantized in units of p2~ 1/R2 -> for each bulk field, a set of Fourier expanded modes, called Kaluza–Klein (KK) states, appears. • Particles moving in extra dimensions appear as heavy particles (a set of copies of normal particles) (KK states). • In the 4-d world, KK states appear as a series (called a tower) of states with masses mn= n/R, (nlabels the mode number). Each of these new states contains the same quantum numbers, such as charge, color, etc • Universal extra dimensions (UED): • All fields of SM propagate universally in the FLAT • extra dimensions << than those in the ADDUniversal • extra dimensions compactified with radii >> Planck length • although smaller than in the ADD model, ~10−18 m • Extra dimensions R~1/TeV … Generation of tower of KK states for each SM field with tree-level masses X (n) n-th KK excitation of the SM field, X X (0) =zero mode (ordinary SM particle

    26. If extra dimensions are compactified (wrapped) around a circle or torus, the extradimensional momentum conservation implies conservation of KK number n-> lightest 1-st level KK state stable. • HOWEVER, Realistic models require an orbifold to be introduced, which leads to the violation of KK number conservation-> introduce KK parity • In order to obtain chiral fermions at zeroth KK level, the extra dimension is compactified on an S1/Z2 orbifold (orbit-fold) • Compactification on an orbifold, S1/Z2, a circle S1 with the extra identification of y with −y.This corresponds to the segment y ∈ [0, πR], a manifold with boundaries at y = 0 and y = πR • A consequence: KK-parity (-1)KK conserved: interactions require an even number of odd KK modes

    27. Mass spectrum for Universal extra dimensions Idea: All SM particles propagate compact spatial extra dimensions • For definiteness, we concentrate on one-extra dimensional case • Dispersion relation: Momentum along the extra dimension  Mass in four-dimensional viewpoint For compactification with radius , is quantized • Momentum conservation in the extra dimension Conservation of KK number in each vertex If extra dimensions are compactified (wrapped) around a circle or torus, the extra dimensional momentum conservation -> conservation of KK number n-> lightest 1-st level KK state stable. Realistic models, however, require an orbifold to be introduced, which leads to the violation of KK number conservation-> introduce KK parity

    28. c.f. minimal SUGRA: and Parameters in UED models Theories with compact extra dimensions can be written as theories in ordinary four dimensions by performing a Kaluza Klein (KK) reduction. Let us now consider that the fifth dimension is compact with the topology of a circle S1 of radius R, which corresponds to the identification of y with y + 2πR. In such a case, the 5D complex scalar field can be expanded in a Fourier series: • Kaluza-Klein expansion (Fourier expansion): Zero modes are identified with SM fields 4D theory Parameters in UED models are completely specified in terms of the SM parameters • Only three free parameters in minimal UED model: : Higgs boson mass : Cutoff scale : Size of extra dimension

    29. Dirac Dirac Chiral Minimal UED In order to obtain chiral fermions at zeroth KK level, the extra dimension is compactified on an S1/Z2 orbifold (orbit-fold) Compactification on an orbifold, S1/Z2, a circle S1 with the extra identification of y with −y.This corresponds to the segment y ∈ [0, πR], a manifold with boundaries at y = 0 and y = πR • In 5D spacetime, spinor representation has 4 complex components Reflection sym. under  Chiral fermions in 4D e.g. • Conservation of KK parity[+ (--) for even (odd) ] { The lightest KK particle (LKP) is stable Dark matter Single KK particle cannot be produced c.f. R-parity and the LSP in SUSY models • Experimental limit on is weaker than other extra-dimensional models: Electroweak precision tests

    30. KK level Fermion (SU(2)L) Gauge boson Scalar (SU(2)L) New particles: Complex scalar Dirac Massive (Mass ) SM particles: Massive Dirac Real scalar Massless Chiral (Mass ) Particle contents in minimal UED Electroweak symmetry breaking effects are suppressed for higher KK modes There appear infinite towers of KK modes with quantum numbers identical to SM particles LPK: KK excitation of photon; Z; neutrinos; Higgs boson; graviton Relatively large zero-mode mass of the Higgs make its first level KK excitation an unlikely candidate.KK sneutrinos excluded by direct detection (as sneutrinos and 4° generation Dirac neutrinos. -> KK photon; KK Z whose mass eigenstates are nearly identical to their gauge eigenstates, B (n) , W 3(n)KK state B(1) annihilates largely to SM (zero-mode) fermions through the t-channel exchange of KK fermions

    31. SM SM UED is similar to SUSY UED SUSY • 1st KK mode mass • Superparticle mass • KK parity stabilizes the LKP  SUSY breaking mass • R parity stabilizes the LSP • Same spin SUSY • Different spin • Kinematics of 1st KK modes resembles that of superparticles with degenerate mass • Attention to spins of new particles and second KK modes Study at linear colliders is mandatory

    32. KK DARK MATTER RELIC DENSITY KK leptons lead to a larger relic abundance, due to the fact that they freeze-out quasi-independently from the LKP and then increase the number of LKPsthrough their decays.

    33. SuperWIMPs gravitino,axino meV meV eV keV MeV GeV TeV Particle Mass Sterile n’s AXIONS MeV DM SuperHeavy Strong CP problem Warm Dark Matter 1013-1016 GeV Ultra-GZK CR’s 511 keV line PASCOS 2006 Beyond WIMPS (a.k.a. Weird Animals) WIMPs First suggested as explanation for the observationof cosmic rays with energy above the so-called GreisenZatsepin-Kuzmin (GZK) cut-off Spin-1/2 SU(2)-singlet particles interacting with the “active”ν via ordinary mass terms

    34. DIRECT DETECTION Experiments which attempt to detect dark matter particles through their elastic scattering with nuclei (normal matter recoiling from DM collisions), including CDMS, XENON , ZEPLIN, EDELWEISS, CRESST, CoGeNT, DAMA/LIBRA, COUPP, WARP, and KIMS . WIMP properties m ~ 100 GeV velocity ~ 10-3 c Recoil energy ~ 1-100 keV Typically focus on ultra-sensitive detectors placed deep underground c c DIRECT DETECTION Direct detection Observe scattering of c’s off nuclei in low bckg. environments

    35. SPIN-INDEPENDENT THEORY N WIMP nucleus recoil energy The spin-independent WIMP-nucleus elastic scattering cross section is where fp and fn are the WIMP’s couplings to protons and neutrons, given by where aq are the WIMP-quark couplings and are quantities measured in nuclear physics Is the fraction of the nucleon’s mass carried by quark q, where and the terms with TG corresponds to Interactions with the gluons in the target through a colored loop diagram. = Using Spin-dependent couplings, 3000 larger than spin-independent couplings

    36. SPIN-INDEPENDENT EXPERIMENT The rate observed in a detector is , where Results are typically reported assuming fp=fn, so sA ~ A2 , and scaled to a single nucleon A detector made up of Germanium targets (CDMS or Edelweiss) would expect a WIMP with a nucleon-level cross section of 10-6 pb (10-42 cm2) to yield approximately 1 elastic scattering event per kilogram-day of exposure. fp and fn are the WIMP’s couplings to protons and neutrons Experiment: number of target nuclei Nuclear physics: form factor Astrophysics: DM velocity distribution Experiment: recoil energy Astrophysics: local DM number density

    37. Neutralino-Nucleon cross sections • Neutralinos can elastically scatter with quarks through either t-channel • CP-even Higgs exchange, or s-channel squark exchange: • Scattering dominated by heavy Higgs (H) exchange through its couplings to strange • and bottom quarks : ∼100 GeV neutralino, 200 GeV heavy Higgs mass-> cross section • with nucleons: 10-5 to 10-7 pb for |μ| ∼ 200 GeV, or 10-7 to 10-9 pb for |μ| ∼ 1 TeV. • 2. Cross section is dominated by light Higgs boson (h) exchange through its couplings • to up-type quarks. μ in the range of 200 GeV to 1 TeV, Higgs (H) is heavier than • about ∼500 GeV, exchange of the light Higgs generally dominates -> 10-8 – 10-10 pb KK-Nucleon cross sections Very small cross section-> ton-scale detectors before this model will be tested by direct detection experiments

    38. DIRECT DETECTION IMPLICATIONS Spin-independent elastic WIMP-nucleon cross-section as function of WIMP mass. Thick blue line XENON100 limit at 90% CL. Expected sensitivity (yellow/green band). The limits from XENON100 (2010), EDELWEISS (2011), CDMS (2009) , CDMS (2011) and XENON10 (2011) are also shown. Expectations from CMSSM are indicated at 68% and 95% CL (shaded gray , gray contour), as well as the 90% CL areas favored by CoGeNT and DAMA WIMPs are assumed to be distributed in an isothermal halo with v0 = 220 km/s, Galactic escape velocity vesc =544 (+64, -46) km/s, and a density of 0.3 GeV/cm3 (0.008 Mʘ/ pc3) σ ~ 1-10 zb Aprile et al. (2011)

    39. DIRECT DETECTION: DAMA Collision rate should change as Earth’s velocity adds constructively/destructively with the Sun’s  annual modulation Drukier, Freese, Spergel (1986) DAMA: 8.9s signal with T ~ 1 year, max ~ June 2 DAMA Collaboration (2008)

    40.  W+ Indirect Detection of Dark Matter Another major class of dark matter searches are those which attempt to detect the products of WIMP annihilations, including gamma rays, neutrinos, positrons, electrons, and antiprotons. Also gamma rays production directly, also production of final stateaγγ, γZ or γh through loop diagrams. -> monoenergetic spectral signatures Eγ = mdm and Eγ = mdm(1-m2Z/4m2dm) WIMP AnnihilationTypical final states include heavy fermions, gauge or Higgs bosons W- • Places where the dark matter is strongly concentrated, • Galactic centreBengtsson et al.‘90, Berezinsky et al. ’94, … • near black holesGondolo&Silk ’99, Bertone et al. ’05, … • Dwarf satellite galaxies, e.g. DRACO Bergstrom ‘06, Profumo ‘06 • Nearby galaxies, e.g. M31 • ExtragalacticUllio et al. ’02, … • MicrohalosNarumoto&Totani ’06; Diemand et al. ‘07

    41. Indirect Detection of Dark Matter  WIMP AnnihilationTypical final states include heavy fermions, gauge or Higgs bosons 2) Fragmentation/Decay Annihilation products decay and/or fragment into some combination of electrons, protons, deuterium, neutrinos and gamma rays  W- q W+ q  e+ 0 p  

    42. Indirect Detection of Dark Matter  WIMP AnnihilationTypical final states include heavy fermions, gauge or Higgs bosons 2) Fragmentation/Decay Annihilation products decay and/or fragment into some combination of electrons, protons, deuterium, neutrinos and gamma rays 3) Synchrotron and Inverse ComptonRelativistic electrons up-scatter starlight to MeV-GeV energies, and emit synchrotron photons via interactions with magnetic fields  W- q W+ q  e+ 0 p    e+

    43. Gamma Rays from WIMPs annihilation Gamma ray flux from annihilation WIMP’s annihilation cross section. ψangle relative to galactic center ρ(r) , DM density spectrum gamma Solid angle observed Depends only on DM distribution and is the average over the observed solid angle of the quantity

    44. Galactic Centre GC flux predictions can vary considerably Inner (<1pc) profile uncertain: • N-body simulations generally predict a cusp • observations show no clear evidence of a cusp/core This causes a large difference. Also, • Difficult to predict the distribution of DM in the inner parsecs (100 pcs N-body sim.) • effects of baryons [Prada ‘04] • background [Zaharijas ‘06] : emission observed from HESS from GC, spectrum • 160 GeV-20 TeV

    45. FERMI The analysis of dwarf spheroidal galaxies yields upper limits on the product of the dark matter pair annihilation cross section and the relative velocity of annihilating particles that are well below those predicted by the canonical thermal relic scenario in a mass range from a few GeV to a few tens of GeV for some annihilation channels. Mazziotta et al. 2012 Feng 2012 Upper limits at 95% CL, same annihilation channels as MW. The continuous lines indicate the upper limits obtained neglecting the systematic uncertainties, while the dotted lines indicate the upper limits obtained including the uncertainties on the J-factors (J(∆Ω)). Dashed Line: as in the MW case. Upper limits at 95% CL on <σv> as a function of the WIMP mass for the annihilation channels µ+µ−, τ+τ−, bb and W+W−. The dashed line is the annihilation cross section of 3 × 10−26 cm3/s in the canonical thermal relic WIMP scenario. - Fermi Launched in 2008 Fermi

    46. Gamma-Ray sourc in GC (FERMI) Analysis of 3.8 years of data from the Fermi-LAT in the inner 7oX 7o toward the MW GC using the current second year Fermi-LAT point source catalog (2FGL), the second- year Fermi-LAT diffuse Galactic map, isotropic Emission model Abazajian & Kaplinghat (20012) TS= point source test statistic signicance= = log-likelihood with and without the source • Detections extended source with gamma-ray spectrum consistent • with DM particle masses ~10 GeV to 1 TeV annihilating to quarks, • and masses approximately 10 GeV to 30 GeV annihilating to • leptons. • A part of the allowed region in this interpretation is in conflict with constraints from Fermi observations of the • Milky Way satellites. • The gamma-ray intensity and spectrum also well fit with emission from a millisecond pulsar (MSP) population • following a density profile like that of lowm ass X-ray binaries observed in M31.

    47. Cosmological signal of DM DM forms structures in gravitational collapse, and in those over-dense regions, DM selfannihilation signal is greatly enhanced. IGRB (Isotropic Gamma Ray Background) • Measurements of the IGRB by Fermi-LAT and EGRET, together with three types of • gamma-ray spectra induced by DM. Cross sections chosen for visulaization • The solid lines are with the Gilmore et al. absorption model applied, and the dotted lines with the Stecker et al. • [69] absorption. Also shown the line spectra convoluted with the energy resolution of the Fermi-LAT • experiment (dashed line). The dotted line passing through the Fermi data points is a • power law with the spectral index of -2.41.