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Non-Baryonic Dark Matter in Cosmology

Non-Baryonic Dark Matter in Cosmology

Antonino Del PopoloAntonino Del Popolo

Department of Physics and AstronomyDepartment of Physics and Astronomy

University of Catania, Italy 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

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LECTURE 3 The nature of dark Matter

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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 matterbecause 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 existWe already discussed the MACHO, EROS1, etc limits Rees (1977) : DM could be of a “more exotic character”-> e.g., small rest mass neutrinos

Fields & Sarkar, 2004

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0

2 10mTA A

T

Aλ =1-10 scale dependent growth factor Tm<0.14 eV

T0 =2.35x10-4 (CMB tempertaure now)

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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

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Desired DM properties

First place to look for candidates: SM

• Not baryonic

Unambiguous evidence for new particles

• Not hot

• Not short-lived

• Gravitationally interacting

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DARK MATTER candidatesDARK MATTER candidates

DM CandidatesDM Candidates

AXIONAXION MSSM LSPMSSM LSP UED LKPUED LKP

Strong CP-problemStrong CP-problem(PQ Symmetry)(PQ Symmetry)

““Ad-Hoc” DM CandidatesAd-Hoc” DM Candidates

Super-heavy DMSuper-heavy DMMeV DMMeV DMkeV sterile keV sterile ’s’s

Neutrino massesand mixing

Warm Dark Matter511 keV line

Ultra-GZK Cosmic RaysCR with Energy> Greisen-Zatsepin-Kuzmin cut-off

•Hierarchy problem

(bino, wino, two neutral higgsinos)->Neutralinos;3 sneutrinos; gravitino

Momentum Conserv.Momentum Conserv.(KK-parity):(KK-parity):KK photon excitation, Z, KK photon excitation, Z, Neutrinos, Higgs bosons Neutrinos, Higgs bosons or gravitonor graviton

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Neutralinos favorite because they have at least three virtues…

1) Required by supersymmetry, and so motivated byelectroweak 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

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DM FORMATION,FREEZE OUT: QUALITATIVE

3) Self-annihilation contained by the competing Hubble expansion:Universe

expands: XX qq

→←/

→←//

Zeldovich et al. (1960s)

(1)

(2)

(3)

Increasingannihilation

strength

↓

Feng, ARAA (2010)

Assume a new heavy particle X is initially in thermal equilibrium interacting with the SM particles q: (or if X is its own antiparticle )

XX qq XX qq

1) In the very early universe when TUniv>>mx

the processes of creation and annihilation were equally efficient -> X present in large quantities

XX

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

XX

gx Degree of freedom of X

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.

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FREEZE OUT: MORE QUANTITATIVE

• The Boltzmann equation:

Dilution fromexpansion

→ f f‾ f f→‾

• T>>mx (Г>H) n ≈ neq until interaction rate drops below expansion rate T<<mx (Г<H) :

• Might expect freeze out at T ~ m, but the universe expands slowly! First guess: m/T ~ ln (MPl/mW) ~ 40

Thermally averaged anihilation cross section

•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

N

L [f]=C [f]

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•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

=65, 1 GeV=120, 1 TeVin SM

Resulting (relic) density today: ~ xFo / <v>

Numerical coincidence? Or an indication that dark matter originates from EW physics?

WIMP MIRACLE

Non-relativistic expansion for heavy states

In case of presence of other species

i,j=1 -> WIMP

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NeutrinosLight neutrinos: mν≤ 30 eV HDM (relativistic at decoupling, erase densityperturbation 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

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mv≤ 1 MeV

mv≥ 1 MeV, Boltzman Equation ->

HST key project dataSIa, BBN

From the condition t>12Gyr-> (*) and ->

Majorana. For Diracdepends from right state interaction

~

Combining with (*) gives: Dirac or Majorana

LEP-> excludes

45 GeV< <100 TeV with In 10 GeV < < 4.7 TeV Diracexcluded by Lab constraints

and for >45 GeV Majorana has ->cosmologically uninteresting

Finally: Neutino mixing, LEP limit on neutrino species -> -> light weakly interacting neutrinos

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SM

Beyond SM

Excluded by LEP

Excluded by direct DM experiments

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AxionsAxions

Experiments: no CP violation in the QCD sector but natural terms in QCD Lagrangian able to break CP simm.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 The theta-term of QCD poses the so-called strong CP-problemstrong CP-problem

aa GG

g ~

32 2

2

PERTQCD LL 102516 10cm e 10cm e 105 nd

Promoting Promoting to a to a dynamical variabledynamical variable, and postulating a spontaneously broken (at a scale , and postulating a spontaneously broken (at a scale ffAA) global ) global

U(1)U(1)PQPQ symmetry, the theta-term is effectively symmetry, the theta-term is effectively driven to zerodriven to zero

Ωa/ Ωc = (fa/1012GeV)7/6 The associated pseudo-NG The associated pseudo-NG boson, the boson, the axionaxion, features, features

AA fm GeV 10 eV 62.0

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fA ≤1012 cosmological density limit

fA ≥1010 emission from red giants……….

dn-QCD ~10-15 e cm dn-data ~10-26 e cm

Stellar cooling(globular clusters)

SN 1987A data(neutron star cooling)

Microwave cavity Ex.(resonant conversion of A’s in monoch. M.w. radiation)

Optical & Radio Tlscp.(monoch. emission from

A decay in clusters)

Photon Regeneration(Parallel E -laser- and B fields;

after optical barrier the E|| component can be regenerated)

Anomalous SignalAnomalous Signal reported by the reported by the PVLASPVLAS collaboration was interpreted as a possible hint 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

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Have Axions been detected?!Have Axions been detected?!

Other Axion detection technique: Other Axion detection technique: Polarization ExperimentsPolarization Experiments

Polarized LightPolarized Light propagating propagating through a transverse magnetic through a transverse magnetic

field is affected by field is affected by AxionsAxions

(*) Zavattini et al., Phys.Rev.Lett.96:110406,2006; (**) Rabaden et al., Phys.Rev.Lett.96:110407,2006

The The EE|||| component is component is depleteddepleted by the by the

production of real Axions, resulting production of real Axions, resulting in a in a rotationrotation of the polarization vector of the polarization vector

and vacuum and vacuum birifrangencebirifrangence

Higher order QED effects (“Higher order QED effects (“light-by-lightlight-by-light”) ”) also contribute and constitute a Backgroundalso contribute and constitute a Background

An An Anomalous SignalAnomalous Signal reported by the reported by the PVLASPVLAS collaboration was interpreted as a possible hintcollaboration was interpreted as a possible hint(*)(*)

The claimed signal can be readily testedtested with a RegenerationRegeneration setup(**)

The proposed experiment will actually be carried out soon at DESYDESY

C. Rizzo 2007 showed the experiment result was wrong

N

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SUSY DMSUSY DM

Tracing back the early motivations for low energy Supersymmetrylow energy Supersymmetry...

Item 1. Item 1. (~1979)

FINE-TUNING PROBLEMFINE-TUNING PROBLEM GAUGE-COUPLING GAUGE-COUPLING UNIFICATIONUNIFICATION

Item 2. Item 2. (~1981)

DARK MATTER DARK MATTER CANDIDATECANDIDATE

Item 3. Item 3. (~1982)

*See: L.Maiani (1979); S.Dimopoulos,S.Raby,F.Wilczek (1981); H.Pagels, J.R.Primack (1982)

m2H~ 2

UV

m2H~ log(UV / m)

+

SM

SUSY

Lightest Neutralino is a suitable WIMP

DM candidate

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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

• δM2

Hα ln ΛSupersymmetry is an extension that creates 'superpartners' for all Standard Model particles: squarks, gluinos, charginos, neutralinos, and sleptons . The Minimal Supersymmetric Standard Model (MSSM): minimal extension to the Standard Model containing the fewest number of new particles and interactions necessary to make a consistent theory

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• 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

R-PARITY, PROTON DECAY AND STABLE LSPS

(*) Minimal Supersymmetric Standard Model (MSSM) is the minimal extension to the Standard Model that realizes N=1 supersymmetry.The MSSM was originally proposed in 1981 to stabilize the weak scale, solving the hierarchy problem

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• 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.

PARAMETERS AND SIMPLIFIED MODELS

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)

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WHAT’S THE LSP?

• High-scale weak scale through RGEs.

• Gauge couplings increase masses;Yukawa couplings decrease masses

• “typical” LSPs: , R

Particle physics alone neutral, stable, cold dark matter

Olive (200

3)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 canbe 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.)

RG evolution of the mass parameters

~

N

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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)L gauge boson); the bino, B superpartner 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)

•neutral, colourless, only weak-type interactionsstable if R-parity is conserved, thermal relic•non relativistic at decoupling Cold Dark Matter•relic density can be compatible with cosmological observations

χ0 =N11B+N12W3+N13H1+N14H2

~ ~ ~ ~

~~

~ ~

•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

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• Relic abundance of LSP’s -> solving the Boltzmann equation for the LSP number density in an expanding Universe, after neutralinos general 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

Relic Abundance

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•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)

Figure. Representative regions of the CMSSM parameter space.

.

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 3 σ confidence 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.

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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 A0, sign()

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

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UED AND KK DARK MATTER

mas

s

1/R

2/R

3/R

4/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 ADD Universal 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, XX (0) =zero mode (ordinary SM particle

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• 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 KK conserved: interactions require an even number of odd KK modes

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Universal extra dimensionsUniversal extra dimensions

For definiteness, we concentrate on one-extra dimensional case

Idea: All SM particles propagate compact spatial extra dimensionsIdea: All SM particles propagate compact spatial extra dimensions

Dispersion relation:

Momentum along the extra dimension Mass in four-dimensional viewpoint

For compactification with radius ,

Mass spectrum for

is quantized

Momentum conservation in the extra dimensionConservation of KK number in each vertex

If extra dimensions are compactified (wrapped) around a circle or torus, the extradimensional 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

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Parameters in UED modelsParameters in UED models

: Cutoff scale: Size of extra dimension : Higgs boson mass

Kaluza-Klein expansion (Fourier expansion):

Parameters in UED models are completely specified in terms of the SM parametersParameters in UED models are completely specified in terms of the SM parameters

c.f. minimal SUGRA: and

Only three free parameters in minimal UED model:

Zero modes are identified with SM fields

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:

4D theory

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Minimal UEDMinimal UED

Conservation of KK parity [+ (--) for even (odd) ]The lightest KK particle (LKP) is stable

c.f. R-parity and the LSP in SUSY models

Reflection sym. under

Experimental limit on is weaker than other extra-dimensional models:

Electroweak precision tests

Single KK particle cannot be produced Dark matter

In 5D spacetime, spinor representation has 4 complex components

Chiral fermions in 4D e.g.

DiracDiracChiral

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∈

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Particle contents in minimal Particle contents in minimal UEDUED

Electroweak symmetry breaking effects are suppressed for higher KK modes

There appear infinite towers of KK modes with quantumnumbers identical to SM particles

There appear infinite towers of KK modes with quantumnumbers identical to SM particles

KK level

New particles:

MasslessMassive

Massive(Mass )

Dirac

Gauge boson Fermion (SU(2)L)

Real scalar

Scalar (SU(2)L)

SM particles:(Mass )

DiracChiral

Complex scalar

LPK: KK excitation of photon; Z; neutrinos; Higgs boson; gravitonRelatively 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

32Study at linear colliders is mandatoryStudy at linear colliders is mandatory

UEDSUSY

R parity stabilizes the LSP

Kinematics of 1st KK modes resembles that of superparticles with degenerate mass

KK parity stabilizes the LKP

Attention to spins of new particles and second KK modes

Superparticle mass 1st KK mode mass

UED is similar to SUSYUED is similar to SUSY

SUSY breaking mass

SMSM

SUSY Same spin

Different spin

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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.

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Beyond WIMPS (a.k.a. Weird Animals)Beyond WIMPS (a.k.a. Weird Animals)PASCOS 2006

eV meV eV MeV GeVkeV TeV

WIMPsParticle MassParticle Mass

AXIONS

Strong CPproblem

Sterile ’s

Warm Dark Matter

MeV DM

511 keV line

SuperHeavy

1013-1016 GeVUltra-GZK CR’s

SuperWIMPs

gravitino,axino

Spin-1/2 SU(2)-singlet particles Spin-1/2 SU(2)-singlet particles interacting with the “active” interacting with the “active” νν via ordinary mass termsvia ordinary mass terms

First suggested as explanation for the observationof cosmic rays with energy above the so-called GreisenZatsepin-Kuzmin (GZK) cut-off

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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

DIRECT DETECTION

Observe scatteringof ’s off nucleiin low bckg.environments

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2)()(

1AqFfZAZf

vdq

dAnp

si

Direct detection

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SPIN-INDEPENDENT THEORY

WIMP nucleus recoil energy

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.

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

Using Spin-dependent couplings, 3000 larger than spin-independent couplings

N

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SPIN-INDEPENDENT EXPERIMENT• The rate observed in a detector is , where

• Results are typically reported assuming fp=fn, so A ~ 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.

Experiment:numberof targetnuclei

Astrophysics:local DMnumber density

Experiment:recoil

energy

Astrophysics:DM velocitydistribution

Nuclearphysics:

form factor

fp and fn are the WIMP’s couplings to protons and neutrons

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Neutralino-Nucleon cross sections

Neutralinos can elastically scatter with quarks through either t-channelCP-even Higgs exchange, or s-channel squark exchange:

1. 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

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DIRECT DETECTION IMPLICATIONS

σ ~ 1-10 zb

Spin-independent elastic WIMP-nucleon cross-sectionas function of WIMP mass. Thick blue line XENON100 limitat 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 of0.3 GeV/cm3 (0.008 Mʘ/ pc3

)

Aprile et al. (2011)

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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: 8.9 signal with – T ~ 1 year, max ~ June 2

DA

MA

Co

llab

ora

tion

(20

08

)

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Indirect Detection of Dark Matter

1) WIMP Annihilation Typical final states include heavy fermions,

gauge or Higgs bosons

W+

W-

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-m2

Z/4m2dm)

Places where the dark matter is strongly concentrated,

Galactic centre Bengtsson et al.‘90, Berezinsky et al. ’94, … near black holes 　 Gondolo&Silk ’99, Bertone et al. ’05, … Dwarf satellite galaxies, e.g. DRACO Bergstrom ‘06, Profumo ‘06Nearby galaxies, e.g. M31Extragalactic Ullio et al. ’02, …

Microhalos Narumoto&Totani ’06; Diemand et al. ‘07

43

Indirect Detection of Dark MatterIndirect Detection of Dark Matter

1) WIMP Annihilation Typical 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+

W-

e+ q

q

p

0

44

Indirect Detection of Dark MatterIndirect Detection of Dark Matter

1) WIMP Annihilation Typical 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 Compton Relativistic electrons up-scatter starlight to MeV-GeV energies, and emit synchrotron photons via interactions with magnetic fields

W+

W-

e+ q

q

p

0

e+

45

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 solidangle of the quantity

Gamma Rays from WIMPs annihilation

46

Galactic Centre

/

1

sssDM r

rr

rr

GC flux predictions can vary considerably

Profile γ Ave JMoore 1.5 3×104

NFW 1.0 103

Kra 0.7 30

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

47

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.Fermi

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.

Mazziotta et al. 2012

FERMI

FermiLaunched in 2008

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.

-

Feng 2012

48

49

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 secondyear Fermi-LAT point source catalog (2FGL), the second-year Fermi-LAT diffuse Galactic map, isotropic Emission model

• 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.

Abazajian & Kaplinghat (20012)TS= point source test statistic signicance= =

log-likelihood with and without the source

50

Cosmological signal of DMDM 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-LATexperiment (dashed line). The dotted line passing through the Fermi data points is apower law with the spectral index of -2.41.

51

Cosmological signal of DMDM 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-LATexperiment (dashed line). The dotted line passing through the Fermi data points is apower law with the spectral index of -2.41.

52

Extended gamma-ray emission from galaxy clusters

Upper limit for the DM annihilation cross-section in the bb channel.

µ+µ. channel.-

PT (point source) model

Extended profiles

Canonical thermal cross-section of ion of 3 x10 -26 cm3/s

Joint analysis of the Milky Way dwarf galaxies

Han et al. (2012)

From 3-year Fermi-LAT data

53

Charged Cosmic Rays from WIMPs annihilation

WIMP annihilations throughout the galactic halo-> charged cosmic rays, including electrons, positrons, protons and antiprotons. From spectrum of the particles-> signatures of DM annihilations.

PAMELA experiment (began June of 2006): anomalous rise in the cosmic ray positron fraction (the positron to positron-plus-electron ratio) above 10 GeV, confirming earlier indications from HEAT and AMS-01.

ATIC balloon experiment: data revealing a feature in the cosmic ray electron (plus positron) spectrum between approximately 300 and 800 GeV, peaking at around 600 GeV

WMAP experiment: excess of microwave emission from the central region of the MW: interpreted as synchrotron emission from a population of electrons/positrons with a hard spectral index

FERMI…. PAMELA

ATIC

54

Electron-Positron DiffusionElectron-Positron Diffusion•When electrons/positrons are produced in dark matter annihilations, they travel through the galaxy’s tangled magnetic fields, losing energy via synchtrotron and inverse Compton

•Resulting spectrum can be calculated by solving the diffusion-loss equation:

•For 10-50 GeV e+/- in the inner galaxy, leads to

~0.1-1 kpc diffusion (~1-10)

Diffusion Constant

Energy Loss Rate

Source Term

55

PAMELA results of antiparticles in cosmic rays

Nature 458, 607 (2009)

Positron fraction

ATIC bump Fermi excess

The total electron+positron spectrum

Spectrum from GALPROP (Moskalenko & Strong) pure secondary production of positrons during the propagation of cosmic-rays in the galaxy

Chang et al. Nature456, 362 2008 PRL102:18110 1,2009

Excess of galactic cosmic-ray electrons

at energies of ~300-800GeV

Fermi LAT CR electron spectrum (redfilled circles; gray band systematic errors).

56

Compilation of recent and less recent data in charged cosmic rays, superimposed on plausible but uncertain astrophysical backgrounds from secondary production. Left: positron fraction. Center: antiproton flux. Right: sum of electrons and positrons.

Charged cosmic ray data interpreted in terms of Dark Matter annihilations: the flux from the best fit DM candidate (a 3 TeV DM particle annihilating into τ+ τ- with a cross section of 2 10 -22 cm3/sec) is the lower dashed line and is summed to the supposed background, giving the pink flux which fits the data. Left, center and right like in previous figure

57

ARE THESE DARK MATTER?Energy spectrum shape consistent with WIMP dark matter candidates BUT to

produce the PAMELA and ATIC signals WIMPs must

1. annihilate dominantly to charged leptons (to produce sufficiently hard spectrum, and to avoid the overproduction of cosmic ray antiprotons)

2. Furthermore very large annihilation rate required: 100-1000 times higher than is naively expected for a thermal relic -> this require a large annihilation cross

3. Solution:

-- Local inhomogeneities in the dark matter distribution boost the annihilation rate

– Alternative production mechanism (non thermal mech.)– WIMPS interacting through exchange of very light particles can annihilate

through non-perturbative processes ->

Cirelli, Kadastik, Raidal, Strumia (2008)

Arkani-Hamed, Finkbeiner, Slatyer, Weiner (2008)

Feldman, Liu, Nath (2008); Ibe, Murayama, Yanagida (2008)

Guo, Wu (2009); Arvanitaki et al. (2008)

• Pulsars can explain PAMELA• Zhang, Cheng (2001); Hooper, Blasi, Serpico (2008)

• Yuksel, Kistler, Stanev (2008); Profumo (2008)

• Fermi-LAT Collaboration (2009)

• Dark matter particles which annihilate directly to e+e-

generate an edge in cosmic ray e- spectrum that drops suddenly at Ee = mX. Pulsars produce spectra which fall off more gradually.

Fermi-LAT Collaboration (2009)

KK dark matter with m ~ 600 GeV

ATIC (2008)

now

Freez-out

Blue line: pulsars model

58

WMAP As A Synchrotron TelescopeWMAP As A Synchrotron Telescope•In addition to CMB photons, WMAP was used to provide the best measurements to date of the standard interstellar medium emission mechanisms: thermal dust, spinning dust, ionized gas, and synchrotron.

•Data is “contaminated” by a number of galactic foregrounds that must be accurately subtracted

Thermal Dust

Soft Synchrotron

Free-Free

WMAP

Soft Synchrotron - From SN shocks; morphology traced by the 408 MHz Haslam mapFree-Free - Hot gas electron/ion thermal Bremsstrahlung; morphology traced by the H recombination line map (Finkbeiner, 2003)Thermal/Spinning Dust -Emission from vibrating and spinning dust grains; morphology traced by the SFD98 dust map (Schlegel et al.) and the 94 GHz Finkbeiner map

59

_

+

+

+

Syn

chro

tron

Fre

e-f

ree

T &

S

Du

stC

MB

WMAP

= …

22 GHz

22 GHz

After known foregrounds are subtracted, an excess appears in the residual maps within the inner ~20 around the Galactic Center

60

61

Dark Matter and the WMAP Haze

22 GHz•Initial interpretation: thermal bremsstrahlung gas 104-106 K

•Ruled out by the lack of a corresponding H

recombination (X-ray) line

•Appears to be hard synchrotron emission from a new population of energetic electrons/positrons in the inner galaxy -Too hard to be supernovae shocks -Too extended to be a singular event (GRB, etc.)

•Very Difficult to explain astrophysically

•2004 Doug Finkbeiner: WMAP Haze could be synchtrotron from electrons/positrons produced in dark matter annihilations in the inner galaxy

1) Assuming an NFW profile, a WIMP mass of 100 GeV and an annihilation cross section of 3x10-26 cm3/s, the total power in dark matter annihilations in the inner 3 kpc of the Milky Way is ~1.2x1039 GeV/sec

2) The total power of the WMAP Haze is between 0.7x1039 and 3x1039 GeV/sec

Coincidence?

62

Fitting The Haze To The Dark Matter Halo ProfileFitting The Haze To The Dark Matter Halo Profile

•When the effects of diffusion are accounted for,

an NFW halo profile ( R-1)

under produces the WMAP haze at small angles

•Angular distribution of the haze matches that found for a cusped halo profile, with R-1.2

•Although the precise result of this fit depends on the diffusion parameters adopted (magnetic fields, starlight density, etc.), the approximate result (slope of -1.1 to -1.3) is fairly robust

(R) R-1.2

(R) R-1

(NFW)

Significant systematic errorsSignificant systematic errors

63

The Dark Matter Annihilation Cross The Dark Matter Annihilation Cross SectionSection

Hooper, G. Dobler and D. Finkbeiner (2007)

•For a typical 100-1000 GeV WIMP, the annihilation cross section needed is within a factor of 2-3 of the value needed to generate the density of dark matter thermally (3x10-26 cm3/s); No boost factors are required!

b-b+

ZZW-W+

e-e+

-+

-+

For a given annihilation mode, diffusion parameters and halo profile, we can calculate the annihilation cross section needed to normalize the observed intensity of the WMAP Haze

WIMP annihilation cross section (times boost factor) required to produce the intensity of the WMAP haze.

64

Other (OLDER) Claims of Evidence For Dark Other (OLDER) Claims of Evidence For Dark Matter AnnihilationMatter Annihilation

•The HEAT positron excess

•511 keV emission from the galactic bulge

•EGRET’s galactic gamma ray spectrum

•EGRET’s extragalactic gamma ray spectrum

65

The HEAT Positron ExcessThe HEAT Positron Excess•In its 1994-95, 2000 flights, the HEAT balloon-based cosmic ray detector observed an excess of positrons relative to electrons in the 7-30 GeV range

•Measurements from AMS-01 add some support

•Combined statistical significance of several (4-5) sigma, neglecting (likely important, but difficult to evaluate) systematic uncertainties E. Baltz and J. Edsjo,

PRD, astro-ph/9808243

66

The HEAT Positron ExcessThe HEAT Positron ExcessStrengths:

•Fit to data can be easily improved if dark matter component is included

Weaknesses:

•Messy astrophysics

•Requires annihilation boost of ~50 or more (possible, but unlikely), or non-thermal dark matter production

Prospects:

•Confirmed by PAMELA (excess in the 10-100 GeV range) data and by FERMI (extended to about 200 GeV)

67

511 keV Emission from the Galactic Bulge511 keV Emission from the Galactic Bulge

•2003: INTEGRAL/SPI spectrometer observed bright 511 keV emission from the bulge of the Milky Way (1.3 x 1043 positrons injected per second)

•Gaussian, spherically symmetric morphology (FWHM of 8˚)

•Type Ia supernovae are unable to generate the observed injection rate (too few escape)

•Hypernovae (type Ic SNe) or gamma ray bursts could potentially generate enough positrons if high estimates for rates are considered

•Even if the injection rate is sufficient, a mechanism is required to transport from disk to bulge - appears to be somewhat difficult

1-10 MeV dark matter particles annihilating to e+e- could simultaneously generate the measured dark matter relic abundance, and the observed 511 keV emission (particle much lighter than the DM particles in the theoretical most attractive models(Boem et al. 2003, astro-ph/0309686)

68

511 keV Emission and MeV Dark Matter511 keV Emission and MeV Dark Matter

Strengths:

•Challenging to explain 511

signal with non-exotic astrophysics

Weaknesses:

•Somewhat difficult to construct a viable particle physics model with an MeV WIMP

Prospects:

•No clear path to confirmation or exclusion of the MeV dark matter hypothesis (perhaps 511 emission from dwarf galaxies?)

De Cesare et al. (2012) : line from Galactic X-Ray Binaries

1. Although neutralinos should be heavier (by relic abundance considerations) than 20 GeV they can be much lighter in extended supersymmetric models in which light Higgs bosons can mediate neutralino annihilations2. 500 GeV dark matter particles could ∼be collisionally excited to states which are 1 MeV heavier, which produce ∼electron-positron pairs in their subsequent de-excitations to the ground state

INTEGRAL all-sky picture of positronium

gamma line (511 keV) emission

(J. Knödlseder et al., astro-ph/0506026)

69

EGRET’s Galactic Gamma Ray SpectrumEGRET’s Galactic Gamma Ray Spectrum

•EGRET observed an excess of gamma rays above 1 GeV, compared to the the most simple galactic cosmic ray models

•Could be the product of a ~50-100 GeV WIMP (W. de Boer et al, PLB, hep-ph/0511154; Astron.Astrophys, astro-ph/0508617; astro-ph/0408272)

•The same dark matter annihilation spectrum can fit the shape of the GeV excess in all regions of the sky •Problem: To accodomate the required normalization for the annihilation rate in various regions of the Galaxy, however, requires a departure from a simple halo profile

•De Boer, et al. introduce two rings of dark matter near the galactic plane at 4 and 14 kpc from galactic center (8x1010 M tidally disrupted dwarf galaxy? motivated by rotation curves)

(W. de Boer et al, A.A., astro-ph/0508617

70

EGRET’s Galactic Gamma Ray SpectrumEGRET’s Galactic Gamma Ray Spectrum

•Problem: With a standard treatment of cosmic ray diffusion, far too many antiprotons are produced in this scenario

•To reconcile, anisotropic diffusion, strong convection away from (and outside of) the disk and local spatial variations are required

(Bergstrom, Edsjo, Gustafsson and Salati, JCAP, astro-ph/0602632)

Predicted in de Boer model

Prediction from standard secondary cosmic ray production

71

EGRET’s Galactic Gamma Ray SpectrumEGRET’s Galactic Gamma Ray Spectrum

Strengths:

•Consistent with a neutralino

or other EW-scale WIMP(50-

100 GeV WIMP)

•Similar spectral shape over sky

Weaknesses:

•Non-standard dark matter distribution is needed (two rings)

•Conflict with antiprotons unless non-standard comic ray diffusion is invoked

•The GeV excess can plausbily be reduced or eliminated without dark matter by modifying the diffusion model

FERMI data on diffuse gamma rays compared with EGRET data in the mid-latitude range (100 < b < 200)

72

EGRET’s Extragalactic Gamma Ray SpectrumEGRET’s Extragalactic Gamma Ray Spectrum

•EGRET has also detected a diffuse, extragalactic gamma ray signal, which becomes more intense above 1 GeV

•Integrated signal from dark matter annihilations throughout the universe could produce a potentially observable signal (Ullio, Bergstrom,Edsjo 2002)

•Intensity depends critically on DM distribution – cuspy halos and substructure are required

•The EGRET extragalactic diffuse spectrum

can be fit by annihilations from a ~500 GeV

neutralino (or other WIMP)

Elsasser and Mannheim, PRL, astro-ph/0405235

(higgsino mass parameter µ; gaugino mass parameter m2;mass of the cp-odd higgs mA; ratio of the higgs vacuum Expectation values tan ; scalar mass parameter mS and Trilinear soft-breaking parameters for the third generation squarks At and Ab)

___steep power law plus annihilation spectrum

Ψ=boost factor

EGB (Extra Galactic γ-ray Background) spectrum hastwo components: a steep-spectrum power law with index -2.33 (dashed-blue) and a strong bump at a few GeV.

73

EGRET’s Extragalactic EGRET’s Extragalactic Gamma Ray SpectrumGamma Ray Spectrum

Strengths:

•Consistent with a (somewhat heavy) neutralino or other WIMP

Weaknesses:

•Not a particularly distinctive signal, could easily be astrophysical

•High annihilation rate needed; either large degree of very cusped substructure, or a non-thermal WIMP

•Signal from our galactic center would have been seen, unless cusp is removed by tidal effects (S. Ando, PRL, astro-ph/0503006)

74

Summary

• Searches for dark matter signatures in gamma rays from the Milky Way halo and dwarf galaxies exclude canonical thermal relic dark matter annihilation cross-sections for masses less than a few tens of GeV

• Fermi LAT CRE data provide a valuable probe of dark matter models that could explain the measured rise in the local cosmic-ray positron fraction

• More observations are needed