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Dark Matter candidate
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What will we learn today?
What kind of Dark Matter do we „need“?
Baryonic Dark Matter?- Why not?- Primordial Nucleosynthesis
Particle Dark Matter:- Axions- WIMPs: thermal production – the „WIMP miracle“
SUSY and the neutralino(Extra Dimensions: Kaluza-Klein particles)
- sterile neutrinos
This lecture is to learn about the models that predict Dark Matter candidates→ lots of theoretic ideas
CDM ModelThe Standard Model of Cosmology(„Concordance Model“)
Describes the Universe since the Big Bang with a few parameters only (6)
Uses Friedmann equation to describe evolution of Universesince Inflation
Agrees with the most important cosmological observations: CMB Fluctuation Large Scale Structures Accelerated Expansion (SN observations) Distribution of H, D, He, Li Ingredients:
Cosmological ConstantCDM Cold Dark Matter
Cold vs. Hot Hot: particle moving with relativistic speed
at the time when galaxies could just start to form
Cold: moving non-relativistically at that time
Important implication for structure formation
Hot Dark Matter cannot cluster on galaxy scales untilit has cooled down to non-relativistic speeds and sogives rise to a considerably different primordial fluctuation spectrum
We are looking for Cold Dark Matter:
InvisibleCold (v < 10-8 c)CollisionlessStable
Do we have to invent something new?
Baryonic Matter in the Universe
Centaurus A
Remember: Baryonic Matter might also be „dark“ in the optical...
BUT we are looking for something without e/m interaction
Why not Baryonic Matter?
b < 0.05
too little: b < 0.05
Big Bang Nucleosynthesis fixes
b quite precisely (+CMB)
(1940s: Gamov, Alpher, Herman)
- abundances of light elements depend on number of baryons - D production is most sensitive
not collisionless
not found in microlensing searches
Black Holes? → No
Baryonic Candidates
main class: MACHOs – massive compact halo objects
Brown Dwarfs: H/He spheres with m < 0.08 M⊙
(too light, H-burning will never start)
Jupiters: similar but with m < 0.001 M⊙
Black Holes with m ~ 100 M⊙
could be remnants of an early generation of stars whichwere massive enough so that not many heavy elementswere dispersed when they exploded as supernovae
Less popular: fractal or specially placed clouds of molecular hydrogen
EROS, MACHO, OGLE
Microlensing with OGLE
Polish project started 1992 telescope located in Chile main targets: GMC and galactic bulge some MACHOs and 14 extrasolar planets found so far
Primordial Black Holes
Carr et al, PRD 81, 104019 (2010)
Fraction of the Universe's masswhich could be in form of a
primordial black hole
BUT
some of the dark matter must be baryonic!
We expect b~0.05 (nucleosynthesis, CMB) but what we see (stars, gas, dust) only accounting for lum~0.01
It seems that there are way too many MACHOs to explain the discrepancy
Why not Neutrinos?
Neutrinos are a part of the SM
collisionless
massive ( -oscillations)
produced in the early Universe: decouple at kT ~ 3 MeV
n ~ 115 cm-3
compare with critical density
crit = 5.1 GeV/m3
= 5100 eV/cm3
→ neutrinos can make up the entire energy content of the Universe if
much too large!
Large Scale StructuresBUT: neutrinos move too far and too fast(decoupling at kT=3 MeV)
⇒ hot Dark Matter
The smallest scale with „clumpy“ structuresets a lower limit on the particle mass:
low mass→ high speed (if created thermally)→ travels large distances→ scale on which density perturbations
are washed out
Probing small scale structures at z~3: mDM 2 keV
0.63 eVFrom direct e mass limit; oscillations;WMAP data
Back to Particle Physics?
the Standard Model provides an excellent description of allexperimental observations...
BUT it is incomplete...
H
The Standard Model
H
> 18 free parameters
No grand unification
No gravity
Why P and CP violation?
Why three particle generations?
Strong CP problem
Hierarchy Problem (mH ≪ m
P l)
⇒ Not the fundamental theory
Popular extensions:Supersymmetry (SUSY) → WIMPExtra Dimensions → LKPPeccei-Quinn Theory → Axion... and many, many more
stolen from Gianfranco Bertone
Non baryonic DM: new particles or „old“ particles with non-standard properties
(Some) Dark Matter Candidates
Axion
WIMPs - Neutralino - (LKP)
sterile neutrinos
mass
cros
s se
ctio
n
DM ProductionTwo production mechanisms:
Thermal Production Non thermal production
In thermal equilibrium with Production in a the Universe („freeze out“) Phase Transition
→ WIMPs → Axions
Candidates for non-baryonic DM must be
stable on cosmological time scales (otherwise they would have been decayed by now)
must interact very weakly (otherwise would not be considered as Dark Matter)
must have the right relic density (=amount of DM)
Note: There is a 3rd production mechanism at very large T, soon after or soon before inflation. These particles are usually superheavy, e.g. Wimpzillas
The Axion in a Nutshell
The strong CP-Problem:
BUT: no neutron EDM found (< 3x10-2 6 e cm) → no CP violation in QCD ( < 10-1 0 ) → Question: Why is so small? Naturalness Problem
Peccei, Quinn (1977): Add new global symmetry spont. broken U(1) → make a dynamical variable
Weinberg, Wilzcek (1978): Theory contains a new particle: Axion
DM candidate: cosmological E density
cold Dark Matternon-thermal production
CP violating term
Va ~ 10 -- 1 7 c
+
Effective Axion Potential
very high E spontaneous symmetrybreaking; the axion fieldrelaxes somewhere in
the potential
QCD epoch: vacuum(instanton) effects tiltthe potential, explicitlybreaking the symmetry axion gets mass CP symmetry restored
A Pooltable Analogy
stolen from P. Sikivie, arXiv:hep-ph/9506229
We live on a pool-table whichis perfectly flat (such that wecan play pool properly...)
<10 – 9
CP seems to be a perfectsymmetry in strong interactions
A Pooltable Analogy
stolen from P. Sikivie, arXiv:hep-ph/9506229
At some point we jump off thetable an realize that it is standingon a non-flat room floor
→ why is the table so remarkably flat?
<10 – 9
It is strange that CP is conservedin strong interactions while it isviolated in weak interactions
→ Why is so small (or zero)?
A Pooltable Analogy
stolen from P. Sikivie, arXiv:hep-ph/9506229
The easiest way to makeevery pool table perfectly flat is to build it on a postthan can pivot on an axle,countered by a weight.→ then gravity does the adjustment
<10 – 9
The Peccei-Quinn mechanismmakes a dynamic field.Non-perturbative QDC effectsthen pull to zero.
A Pooltable Analogy
stolen from P. Sikivie, arXiv:hep-ph/9506229
One can try to test thishypothesis by inducingoscillations in the pool table.
The oscillation frequencydepends on the lever arm L
<10 – 9
The axion is the quantum of oscillation of the parameterin QCD.
Its properties depend in the axiondecay constant f ∝ ma– 1
L
A Pooltable Analogy
Assume the pool table wasbrought from outer space (no gravity) and the initial anglewas –*
Depending on how gravity startedto act (when the spaceship landed)there might be relic oscillations whichdepend on the initial misalignment angle *
Depending on how the QCDeffects appear at kT~1 GeV thereare initial coherent axion field oscillations. If f is large, thesemight constitute an axion relicenergy density.→ dark matter candidate„vacuum misalingnment mechanism“non thermal DM production
L
*
Axion Searches / Limits
Current Axion Limits (... from 2010)
Generalized Formalism for Dark Matter Candidates
most „new physics“ models need to have a mechanism to make the lightest new particle stable→ Dark Matter Candidate
this is usually achieved by introducing a multiplikative discrete D-symmetry (D=Dark) with
D=+1 standard model sectorD=−1 new particle sector
D is a multiplikative quantum number→ particles in the D=−1 sector can only be pair-annihilated or -produced→ the lightest particle with D=−1 is stable
if the particle is electrically neutral→ Dark Matter Candidate
WIMPs
Weakly Interacting Massive Particles
Some of the best motivated candiates from „new“ physics
WIMPs interact only via gravity and weak interactions
WIMPs are somewhat similar to neutrinos, but far more massive (>GeV) and slower
sub-GeV WIMPs could be Light Dark Matter
Why weak scale masses/interactions?
The Planck Scale
Mpl2 = ℏc/G ≈ 101 9 GeV → Planck mass
At this scale, the strength of gravity becomes similar to the other forces→ „natural“ scale for gravity interactions
Compton wavelength is about the size of a Schwarzschild radius of a black hole → QFT breaks down
Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension, but it would be massive enough to immediately become a black hole → Quantum gravity is needed(here string theory comes into play)
Early universe (right after the Big Bang) is governed by Planck scale dynamics
Expansion and the Temperatureof the early Universe(radiation dominated):
Thermal WIMP Production
„The WIMP Miracle“
suppose WIMP candidates can be created/annihilated in pairs
assume that the 's are in thermal eq. with all light particles
number density n follows the Boltzmann equation:
when T < m, pair creation needs from tail of v-distribution→ in equilibrium, number density falls exponentially
Thermal WIMP Production II
O(1) when A~10-- 3 6 cm² → weak scale
ThermalEquilibrium
Freeze Out
When the annihilation rate nannv⟩ < expansion rate H, the probability for to find a partner for annihilation becomes small
expanding Universe: „freeze out“WIMPs fall out of equilibrium, cannot annihilate anymore
→ non relativistic when decoupling from thermal plasma→ constant DM relic density→ relic density depends on
A
WIMP relic density:
Supersymmetry
top
stop
Solving the hierarchy problem:
Minimal Supersymmetric SM
Incorporating SUSY in the Standard Model requires doubling the particle content(no SM particle can be the SUSY partner of another one)
New particle → new possible interactions
MSSM (1981: Georgi/Dimopulos)simplest possible SUSY model consistent with the SM
minimal field content: the only new fields (arranged in supermultiplets with the SM particles) are the ones required by SUSY
minimal choice of interactions: only SUSY generalization of SM
Underlying dynamics of theory is supersymmetric, but the ground state does not respect the symmetry (no light SUSY particles)→ SUSY is broken spontaneously
R-Parity Appears in most versions of low E SUSY
Removes unwanted superpotential terms from the theory
Avoids excessive Baryon/Lepton number violating processes(e.g. proton decay via )
R-parity, a multiplikative new quantum number
R=+1 for ordinary particlesR=−1 for SUSY particles
SUSY particles can only be created/annihilated in pairs with ordinary particles
The lightest SUSY particle (LSP) is stable since there is nokinematically allowed state with R=−1
What could be the LSP in MSSM? LSP electrically charged or strongly interacting
→ would bind to conventional matter→ detectable as anomalous heavy nucleus („Bohr“ radius of LSP atom would be less than nuclear radius)BUT: excluded by experiments down to levels much below the expected abundance of the LSP
Therefore: LSP is neutral and has only weak interactions(= missing energy signature in HE physics)
3 Dark Matter Candidates in the MSSM
1. sneutrino (spin 0)would have relatively large coherent i/a with nucleidirect DM expts exclude sneutrinos between a few GeV and several TeV
2. neutralino (spin ½) → the favourite
3. gravitino (spin 3/2)
The Neutralino LSP that is considered most often
4 neutralinos, each of them a linear superposition of the R=1 neutral fermions: wino, bino, two Higgsinos (SUSY partners of the neutral gauge bosons/Higgs bosons):
the Dark Matter particle is the lightest neutralino
In different regions of SUSY parameter space, the LSP can be more wino-, bino-, or Higgsino-like
in much of the parameter space of interest (correct relic density etc.) the is bino
it is a Majorana fermion → it's own anti-particle
don't forget: multitude of SUSY models→ properties vary from model to model
A Plethora of Parameters
A disadvantage of a full supersymmetric model (even making the particle content minimal, MSSM) is that the number of free parameters is excessively large - of the order of 100 (128 to be exact).
Therefore, most treatments have focused on constrained models, where one has the opportunity to explain electroweak symmetry breaking by radiative corrections caused by running from a unification scale down to the electroweak scale.
Let's have a look at this... →
MSSM expectation for S I
Vast range! No predictive power!
WIMP mass
WIM
P c
ross
se c
tion
Add grand Unification...
use this to get relations between parameters in order to reduce them dramatically
most MSSM parameters are associated with SUSY breaking(the E scale at which we get non-SUSY physics from the SUSY model)
now: assume that these parameters are universal at some input scale (here: the GUT scale MGUT = 2 x 101 6 GeV)
→ Constrained MSSM (CMSSM)
Unification of forces
Renorm. group evolution
The CMSSM… the benchmark model for the LHC
CMSSM global scan
CMSSM: typical Plots
for given values of tan, A0, sgn(µ), the parameter space yielding an acceptable relic density and satisfies other constrains can be displayed in the (m1/2, m0) plane
Occasionally CMSSM is also called mSUGRA (minimal supergravity)
However, models based on mSUGRA should have 2 more constraints, further reducing the number of parameters
A0=0 A0=0
Cosmologically preferred region
not the LSP
g-2 favoured
SUSY Overview
Kinematics Couplings (F) to leptons LAnd the Higgs field
Majorana mass term:NI is SU(3)xSU(2)xU(1) inv.→ consistent with the SM symmetry
Sterile NeutrinosMotivation:
We know that neutrinos exits, and that they have a mass→ the only solid lab evidence for beyond SM physics
Maybe this is a sign for existence of a new E scale (GUT?)
Assume - masses come from existence of new unseen particles- complete theory is a renomalizable extension of the SM
Introduce sterile neutrinos or heavy neutral leptons NI
(=singlet [w. respect to the SM gauge group] Majorana fermions → no weak i/a)
Number of singlet fermions unknown → choose 3 in SM analogy
MSM: neutrino minimal SM
The Seesaw Mechanism mechanism to explain why the known neutrino
masses are so extremely small ≪m(e)
seesaw: one mass goes up, the other down
Heavy neutrino(Dark Matter candidate)
Very light neutrino(as observed)
The MSM No new scale introduces since MI ~ EW scale
Alternative to SUSY approach to hierarchy problem
Can explain Baryogenesis, baryonic/dark matter production
Natural DM Candidate: sterile neutrino with mass O(10 keV)
Sterile neutrinos - interact gravitationally- do not interact through standard weak interactions but communicate with the rest of the sector through fermion mixing
Sterile neutrino would be warm Dark Mattersome beneficial effects on some aspects of the CDM scenario such as - absence of predicted cusp in the central regions of some galaxies- lack of substructure in Dwarf Galaxies bound to the Milky Way (→ last issue seems to be not there anymore after new SDDS + Keck data)
Drawbacks: - some fine tuning is necessary to achieve all this- some/many other problems are not addressed
Neutrino Summary
It seems that it is very plausible that neutrinos („standard“ and sterile) make up some of the Dark Matter in the universe (given the experimental results on neutrino oscillations), but most of the dark matter is probably of some other form.
Particle physics o ers several other ffpromising candidates for this.
Another Approach: Unification
EW Scale
GUT Scale
Planck Scale
Kaluza Klein Theory: Extra Dimensions
Originally, Kaluza and Klein invented this theory to unite gravity and electromagnetism
1921: Kaluza proposed to add a 5t h dimension to GR; the equations could be separated in the Einstein equation and Maxwell's equations+ an extra field (the „radion“) → new particle
this approach was forgotten until the 1970-1980s (strings)
1998: it was proposed to lower the scale of quantum gravity M*to the TeV scale by localizing the SM on a 3+1 dim surface in a higher dimensional spacetime (extra dimensions) → „ADD“ model
the n extra dimensions are compactified into a large volume Rn that effectively dilutes the strength of gravity from the fundamental scale (TeV → solves Hierarchy problem) to the Planck scale:
„Gravity is not weak but some of is flux is lost in the extra-dimensions“
Extra Dimensions: Visualization
Extra Dimensions are compactified
In the original 1998 theory (ADD), only gravity propagates in the extra dimensions → very weak constraint R < 1mm ~ meV – 1
In other models, also SM particles can propagate in the extra dimensions→ KK partners of ordinary particles not seen→ energy scale E~1/R > few hundred GeV→ R < 10 – 1 7 cm (microscopic extra dim)
The law of gravity changes with n extradimensions of size d:
F∝1/r2 + n for r≪dF∝1/r2 for r≫d
The Kaluza Klein Tower Basic Idea: Every multidimensional field corresponds to a
Kaluza-Klein tower of 4dim particles with increasing masses
Assume one circular spatial extra dimension of radius R→ QM: expect standing waves in the compactified extra dim
The invariant mass of the standing waves is
expect a comb-like particle spectrum
If SM particles „live“ in extra dimensions → KK excitations for all particles → DM candidates if stable
All SM fields propagate universally in flat toroidal extra dimensionsADD: only gravity in extra dimension and SM on 3+1 membrane
Discrete symmetry: KK parity (−1)n
n=0 SM particlesn=1 KK state
symmetry ensures that interactions with one KK state and 2 SM particles are forbidden(KK-parity corresponds to the symmetry of reflection about the midpoint in the extra dimension)
As a result, the lightest KK particle (LKP) cannot decay and is stable
In UED, the LKP is likely to be associated with the first KK excitation of the hypercharge gauge boson B0(1 )
Universal Extra Dimensions
Lightest Kaluza-Klein Particle (LKP) KK parity makes the LKP stable
Assume - TeV-1 sized extra dimensions (the original suggestion)
- an electrically neutral LKP - with weak scale interactions→ The LKP is a WIMP!
WMAP: ΩCDM h2 = 0.1131 ± 0.0034 → mass of DM candidate B0(1 ) : ~0.5 – 1 TeV
unknown KK parameter space is rather small (compared to SUSY) and will be entirely scanned by the LHC
good direct detection prospects
The 10 Points Test for new Particles
stolen from Gianfranco Bertone, arXiv:0711.4996
Test Results
arXiv:0711.4996
Backup
The strong CP problem more formal:
there are CP violating terms in the QCD Lagrangian that arise from the (non-trivial) QCD vacuum structure
since no strong CP violation is observed, must be very small or zero
however, it could take any value [expect O(1)]
Strong CP Problem („Naturalness Problem“):
Why is so small?
Gluon Dynamics Quark Masseskinetic Quark termsfrom QDC vacuum;CP violating
Reminder: Spontanous Symmetry Breaking Spontaneous Symmetry Breaking: The equations of the system
exhibit a symmetry that is not present in the ground state.
Example: Consider a scalar field
the Lagrangian has a kinetic and a potential term
When the potential has the form
the symmetry of the system is spont. broken
The theory is symmetric around = 0,but has many degenerate states of minimal E:
Goldstone Theorem: Theories with spontaneously broken symmetryhave a massless Nambu-Goldstone boson
[Nb: If the theory has gauge symmetry, the gauge bosons „eat“ the Goldstone bosons,become massive, and the Goldstone boson provides the longitudinal polarization.]
Peccei-Quinn Mechanism and Axion introduce the global Peccei-Quinn Symmetry U(1)PQ
this symmetry is spontaneously broken at some large E scale
this leads to a dynamical interpretation of the angle :
a is the axion field, fa the decay constant
now, the QCD Lagrangian reads:
non-perturbative effects induce a potential for a with the minimum
This cancels the terms and restores CP symmetry
Weinberg and Wilczek realized, that this theory has a pseudo-scalarboson (the axion) which is the Pseudo-Nambu-Goldstone bosonof the spontaneously broken PQ symmetry.
Primakoff Process Properties of axion are closely related to those of neutral pions
(= pseudo Nambu-Goldstone bosons of the QCD)
one of the most important axion processes
describes the axion's two-photon interaction
F is the electromagnetic field strength tensor
The Primakoff Effect plays the key role in most axion searches
it predicts the interaction of axions with magnetic fields
the axion also couples to gluons, fermions, ...
any new boson that couple to charge can coupleto 2 photons via triangle diagrams.Hence searches are not limited to „standard“ PQ axions
Gravitino The LSP in SuperGravity models (combining GR and SUSY)
Supersymmetric partner of the (still hypothetic) graviton
Spin 3/2 fermion
the gravitino is the fermion mediating supergravity interactions, just as the photon is mediating electromagnetism
the gravitino aquires mass when the SUSY is spontaneously broken in SuperGravity theories;the mass is the SUSY breaking scale
naturally, this scale would be the Planck scale
SUSY breaking scale is pushed down to O(TeV) to solve the- hierarchy problem (smallness of Higgs mass)- allow unification of the forces→ Gravitino gets a ~TeV mass
hierarchy Problem: why is SUSY breaking scale << Planck scale?
Gravitino Dark Matter Only gravitational strength interactions → no thermal production
Could be produced in HE collisions or via decay of heavier SUSY particles in the early universe
Next-to-lightest SUSY particle (NLSP, stau? stop? neutralino?) would be important source of gravitinos and metastable (gravitational strength decay rate)→ important cosmological constraints on m, of NLSP(from agreement of BB nucleosynthesis with abservations)
NLSP has a higher detection chance at the LHC
Limits as Gravitino being the DM particle come from abundance of light elementsthe NLSP can form bound states, e.g. with 4He; then the NLSP catalyzes reaction such as 4He(D,)6Li
Favoured by observation
Cosmological Gravitino Problems… when the Gravitino has a TeV mass:
Assume conserved R-parity:
Gravitino could be LSP → Dark Matter Candidate
BUT: the calculation shows that the gravitino density would exceed the Dark Matter density
Assume Gravitino is instable:
It would decay away → no Dark Matter candidate
Gravitino lifetime = mPl2/m3 (nat. units)
with m~TeV, this gives ~ 105 seconds (longer than nucleosynthesis era after Big Band)
Daugthers (, e, µ) from decay would be so energetic that they would distroy nuclei → strong impact on nucleosynthesis; no star formation (which is not observed)
Possible ways out... Split SUSY:
Gravitino mass scale is much higher than TeV,but other fermionic SUSY partners of SMparticles appear there
Slightly violated R-parity:gravitino is the LSP → almost all SUSY particles in the early Universe decay into SM particles via R-parity violating interactions well before the synthesis of primordial nuclei
a small fraction however decay into gravitinos, whose half-life is orders of magnitude greater than the age of the Universe due to the suppression of the decay rate by the Planck scale and the small R-parity violating couplings
BUT: The Gravitino only interacts gravitationally→ seems impossible to detect it in experiments(maybe via decays → a line in the HE spectrum)
