Dark Matter Candidates

Dark Matter Candidates

Astroparticlephysics, UZH, Spring 2012

Marc Schumann [email protected] 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 Model

The 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 Universe since 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 Constant CDM 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 until it has cooled down to non-relativistic speeds and so gives rise to a considerably different primordial fluctuation spectrum We are looking for Cold Dark Matter:

Invisible Cold (v < 10-8 c) Collisionless Stable

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?

● too little:  < 0.05 b ● Big Bang Nucleosynthesis  < 0.05 fixes  quite precisely (+CMB) b b (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 which were massive enough so that not many heavy elements were 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

Fraction of the Universe's mass which could be in form of a Carr et al, PRD 81, 104019 (2010) 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 Structures

BUT: neutrinos move too far and too fast (decoupling at kT=3 MeV)

From direct e 0.63 eV mass limit;  oscillations; WMAP data ⇒ hot Dark Matter

The smallest scale with „clumpy“ structure sets 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 Back to Particle Physics?

the Standard Model provides an excellent description of all experimental observations... H BUT it is incomplete... The Standard Model

> 18 free parameters

No grand unification No gravity Why P and CP violation? Why three particle generations? Strong CP problem

Hierarchy Problem (m ≪ m ) H P l

⇒ Not the fundamental theory

Popular extensions: Supersymmetry (SUSY) → WIMP H Extra Dimensions → LKP Peccei-Quinn Theory → Axion ... and many, many more

Non baryonic DM: new particles or „old“ particles with non-standard properties

stolen from Gianfranco Bertone (Some) Dark Matter Candidates

● Axion

n

o ●

i

t WIMPs

c e - Neutralino

s

s s - (LKP)

o

r c ● sterile neutrinos

mass DM Production

Two 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:

CP violating term + 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 Matter V ~ 10 -- 1 7 c non-thermal production a Effective Axion Potential

very high E spontaneous symmetry QCD epoch: vacuum breaking; the axion field (instanton) effects tilt relaxes somewhere in the potential, explicitly the potential breaking the symmetry  axion gets mass  CP symmetry restored A Pooltable Analogy

<10 – 9

We live on a pool-table which CP seems to be a perfect is perfectly flat (such that we symmetry in strong interactions can play pool properly...)

stolen from P. Sikivie, arXiv:hep-ph/9506229 A Pooltable Analogy

<10 – 9

At some point we jump off the It is strange that CP is conserved table an realize that it is standing in strong interactions while it is on a non-flat room floor violated in weak interactions

→ why is the table so remarkably flat? → Why is  so small (or zero)?

stolen from P. Sikivie, arXiv:hep-ph/9506229 A Pooltable Analogy

<10 – 9

The easiest way to make The Peccei-Quinn mechanism every pool table perfectly makes  a dynamic field. flat is to build it on a post Non-perturbative QDC effects than can pivot on an axle, then pull  to zero. countered by a weight. → then gravity does the adjustment stolen from P. Sikivie, arXiv:hep-ph/9506229 A Pooltable Analogy

<10 – 9

L One can try to test this The axion is the quantum of hypothesis by inducing oscillation of the  parameter oscillations in the pool table. in QCD.

The oscillation frequency Its properties depend in the axion depends on the lever arm L decay constant f ∝ ma– 1

stolen from P. Sikivie, arXiv:hep-ph/9506229 A Pooltable Analogy

*

L Assume the pool table was Depending on how the QCD brought from outer space effects appear at kT~1 GeV there (no gravity) and the initial angle are initial coherent axion field was –* oscillations. If f is large, these might constitute an axion relic Depending on how gravity started energy density. to act (when the spaceship landed) → dark matter candidate there might be relic oscillations which „vacuum misalingnment mechanism“ depend on the initial misalignment angle * non thermal DM production 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 sector D=−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 Expansion and the Temperature gravity becomes similar to the other forces of the early Universe → „natural“ scale for gravity interactions (radiation dominated):

● 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 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

When the annihilation rate nannv〉 < expansion rate H, the probability for  to find a partner for annihilation becomes small expanding Universe: „freeze out“ WIMPs fall out of equilibrium, cannot Thermal Freeze Out annihilate anymore Equilibrium

→ non relativistic when decoupling from thermal plasma → constant DM relic density → relic density depends on  A

WIMP relic density:

O(1) when  ~10-- 3 6 cm² → weak scale A Supersymmetry

Solving the hierarchy problem:

top

stop 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 particles R=−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 no kinematically 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 nuclei direct 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

n

o

i

t

c

e

s

s

s

o

r

c

P

M

I

W

WIMP mass

Vast range! No predictive power! Add grand Unification...

Renorm. group evolution

Unification of forces

● 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) The CMSSM … the benchmark model for the LHC

CMSSM global scan CMSSM: typical Plots

A0=0 A0=0

Cosmologically preferred region

g-2 favoured

 not the LSP

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

SUSY Overview Sterile Neutrinos Motivation:

● 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

Majorana mass term: Kinematics Couplings (F) to leptons L And the Higgs field  NI is SU(3)xSU(2)xU(1) inv. → consistent with the ● MSM: neutrino minimal SM SM symmetry The Seesaw Mechanism

● mechanism to explain why the known neutrino masses are so extremely small ≪m(e)

Heavy neutrino (Dark Matter candidate)

Very light neutrino (as observed) ● seesaw: one mass goes up, the other down 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 Matter some 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 off ers several other promising candidates for this. Another Approach: Unification

Planck Scale

GUT Scale

EW 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

The law of gravity changes with n extra dimensions of size d:

F∝1/r2 + n for r≪d F∝1/r2 for r≫d

● 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 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 Universal Extra Dimensions

● All SM fields propagate universally in flat toroidal extra dimensions ADD: only gravity in extra dimension and SM on 3+1 membrane

● Discrete symmetry: KK parity (−1)n

n=0 SM particles n=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 ) 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

Gluon Dynamics from QDC vacuum; kinetic Quark terms Quark Masses CP violating

● 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? 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 symmetry have 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-scalar boson (the axion) which is the Pseudo-Nambu-Goldstone boson of 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 couple to 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 Favoured by observation ● Limits as Gravitino being the DM particle come from abundance of light elements the NLSP can form bound states, e.g. with 4He; then the NLSP catalyzes reaction such as 4He(D,)6Li 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

2 3 ● Gravitino lifetime  = mPl /m (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 SM particles 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)