Supersymmetric Dark Matter: Direct, Indirect and …baer/okstate.pdf⋆ Part 2: models/implications – MSSM, SUGRA, GMSB, AMSB, ··· – dark matter density/detection ⋆ Part 3:

Supersymmetric Dark Matter:

Direct, Indirect and Collider Searches

Howard Baer

University of Oklahoma

OUTLINE

⋆ The Standard Model

⋆ Inconsistencies

⋆ Supersymmetry

⋆ Dark matter (DM)

• neutralino, axion/axino, gravitino

⋆ The Hunt for DM at LHC

⋆ direct DM searches

⋆ indirect DM searches

Howie Baer, Oklahoma State University colloquium, April 16, 2009 1

The Standard Model of Particle Physics

⋆ gauge symmetry: SU(3)C × SU(2)L × U(1)Y ⇒ g, W±, Z0, γ

⋆ matter content: 3 generations quarks and leptons

u

d

L

uR, dR;

ν

e

L

, eR (1)

⋆ Higgs sector ⇒ spontaneous electroweak symmetry breaking:

φ =

φ+

φ0

(2)

⋆ ⇒ massive W±, Z0, quarks and leptons

⋆ L = Lgauge + Lmatter + LY uk. + LHiggs: 19 parameters

⋆ good-to-excellent description of (almost) all accelerator data!


Shortcomings of SM

Data

⋆ neutrino masses and mixing

⋆ baryogenesis (matter anti-matter asymmetry)

⋆ cold dark matter

⋆ dark energy

Theory

⋆ quadratic divergences in scalar sector ⇒ fine-tuning

⋆ origin of generations

⋆ explanation of masses/ mixing angles

⋆ origin of gauge symmetry/ quantum numbers

⋆ unification with gravity


The supersymmetry alternative

Supersymmetry: bosons⇔ fermions

⋆ SUSY is a space-time symmetry!

⋆ space-time xµ ⇒ (xµ, θi) i = 1, · · · , 4 superspace

⋆ fields ψ ⇒ φ ∋ (φ, ψ) superfields

⋆ gauge fields Aµ ⇒ W ∋ (λ, Aµ) gauge superfields

⋆ superfield formalism ⇒ general form for Lagrangian of (globally)

supersymmetric gauge theory: quadratic divergences cancel!

⋆ SUSY can be broken by soft SUSY breaking terms: maintain cancellation of

quadratic divergences


Weak Scale Supersymmetry

HB and X. Tata

Spring, 2006; Cambridge University Press

⋆ Part 1: superfields/Lagrangians

– 4-component spinor notation for exp’ts

– master Lagrangian for SUSY gauge theories

⋆ Part 2: models/implications

– MSSM, SUGRA, GMSB, AMSB, · · ·– dark matter density/detection

⋆ Part 3: SUSY at colliders

– production/decay/event generation

– collider signatures

– R-parity violation


Minimal Supersymmetric Standard Model (MSSM)

⋆ Adopt gauge symmetry of Standard Model

• spin 1

2gaugino for each SM gauge boson

⋆ SM fermions ∈ chiral scalar superfields: ⇒ scalar partner for each SM

fermion helicity state

• electron ⇔ eL and eR

⋆ two Higgs doublets to cancel triangle anomalies

⋆ add all admissible soft SUSY breaking terms

⋆ resultant Lagrangian has 124 parameters!

⋆ Lagrangian yields mass eigenstates, mixings, Feynman rules for scattering and

decay processes

⋆ predictive model!


Supergravity (SUGRA)

⋆ eiαQ with α(x): local SUSY transformation

• forces introduction of spin 2 graviton and spin 3

2gravitino

• resultant theory ⇒ General Relativity in classical limit!

⋆ rules for Lagrangian in supergravity gauge theory: Cremmer et al. (1983)

⋆ fertile ground: supergravity ∪ grand unification: LE limit of superstring?

⋆ minimal supergravity model (mSUGRA)

⋆ m0, m1/2, A0, tan β, sign(µ)

• m0 = mass of all scalars at Q = MGUT

• m1/2 = mass of all gauginos at Q = MGUT

• A0 = trilinear soft breaking parameter at Q = MGUT

• tanβ = ratio of Higgs vevs

• µ = SUSY Higgs mass term; magnitude determined by REWSB!


Some successes of SUSY GUT theories

⋆ SUSY divergence cancellation maintains hierarchy between GUT scale

Q = 1016 GeV and weak scale Q = 100 GeV

⋆ gauge coupling unification!


Gauge coupling evolution






⋆ Lightest Higgs mass mh<∼ 135 GeV as indicated by radiative corrections!


Precision electroweak data and the Higgs mass:

160 165 170 175 180 185mt [GeV]

80.20

80.30

80.40

80.50

80.60

80.70

MW

[GeV

]

SM

MSSM

MH = 114 GeV

MH = 400 GeV

light SUSY

heavy SUSY

SMMSSM

both models

Heinemeyer, Hollik, Stockinger, Weber, Weiglein ’08

experimental errors 68% CL:

LEP2/Tevatron (today)

Tevatron/LHC

S. Heinemeyer et al.







⋆ radiative breaking of EW symmetry if mt ∼ 100 − 200 GeV!


Soft term evolution and radiative EWSB







⋆ radiative breaking of EW symmetry if mt ∼ 100 − 200 GeV!

⋆ dark matter candidate: lightest neutralino Z1

⋆ stablize neutrino see-saw scale vs. weak scale

⋆ SO(10) SUSY GUT: baryogenesis via leptogenesis

⋆ can give dark energy via CC Λ (but need huge fine-tuning...)

• SUGRA = low energy limit of superstring?

• stringy multiverse: anthropic selection of small CC?


Evidence for dark matter in the universe

⋆ binding of galactic clusters (Zwicky, 1930s)

⋆ galactic rotation curves

⋆ large scale structure formation

⋆ inflation ⇒ Ω = ρ/ρc = 1

⋆ gravitational lensing

⋆ anisotropies in cosmic MB (WMAP)

⋆ surveys of distant galaxies via SN (DE)

⋆ Big Bang nucleosynthesis

• ΩΛ ≃ 0.7

• ΩCDM ≃ 0.25

• Ωbaryons ≃ 0.045 (dark baryons ∼ 0.040)

• Ων ≃ 0.005


Dark matter versus dark energy


SUSY dark matter

⋆ R-parity conservation⇒ conserved B and L ⇒ proton stability

• R(particle) = 1; R(sparticle) = −1

⋆ Naturally occurs in SO(10) SUSY GUT theories

⋆ Some consequences:

• Sparticles are produced in pairs

• Sparticles decay to other sparticles

• Lightest SUSY particle (LSP) is absolutely stable (good candidate for dark

matter)

⋆ LSP must be charge, color neutral (bound on cosmological relics)

⋆ Sneutrino would have been detected in direct detection experiments

⋆ lightest neutralino Z1 is LSP in wide range of models

⋆ Z1 is weakly interacting, massive particle (WIMP)


Calculating the relic density of neutralinos

⋆ At very high T , neutralinos in thermal equilibrium with cosmic soup

⋆ As universe expands and cools, expansion rate exceeds interaction rate

(freeze-out)

⋆ number density is governed by Boltzmann eq. for FRW universe

• dn/dt = −3Hn− 〈σvrel〉(n2 − n20)

• Ω eZ1h2 = s0

ρc/h2

(45

πg∗

)1/2xf

mP l

1

〈σv〉

• ΩCDMh2 ∼ 0.1 ⇒ 〈σv〉 ∼ 0.9 pb!

• 〈σv〉 = πα2/8m2 ⇒ m ∼ 100 GeV

• “The WIMP miracle!”: cosmic motivation for new physics at weak scale

⋆ SUSY: 1722 annihilation/co-annihilation reactions; 7618 Feynman diagrams

⋆ IsaReD program (HB, A. Belyaev , C. Balazs)


Results of χ2 fit using τ data for aµ:

mSugra with tanβ = 10, A0 = 0, µ > 0

0

250

500

750

1000

1250

1500

1750

2000

0 1000 2000 3000 4000 5000 6000


0

250

500

750

1000

1250

1500

1750

2000

0 1000 2000 3000 4000 5000 6000

-2

0

2

4

6

8

m0 (GeV)

m1/

2 (G

eV)

ln(χ

/DO

F)

No REWSB

Ζ~

1 no

t LSP

mh=114.1GeV LEP2 excluded

SuperCDMS CDMSII CDMS


0

250

500

750

1000

1250

1500

1750

2000

0 1000 2000 3000 4000 5000 6000


0

250

500

750

1000

1250

1500

1750

2000

0 1000 2000 3000 4000 5000 6000

0

2

4

6

8

10

12

14

m0 (GeV)m

1/2

(GeV

)

ln(χ

2 /DO

F)

No REWSB

Ζ~

1 no

t LSP

mh=114.1GeV LEP2 excluded

SuperCDMS CDMSII CDMS

HB, C. Balazs: JCAP 0305, 006 (2003)


Axions

⋆ PQ solution to strong CP problem in QCD

⋆ pseudo-Goldstone boson from

PQ breaking at scale fa ∼ 109 − 1012 GeV

⋆ non-thermally produced

via vacuum mis-alignment as cold DM

• ma ∼ Λ2QCD/fa ∼ 10−6 − 10−1eV

• Ωah2 ∼ 1

2

[6×10

−6eVma

]7/6

h2

• astro bound: stellar cooling ⇒ ma < 10−1eV

• a couples to EM field: a− γ − γ coupling (Sikivie)

• axion microwave cavity searches

10-5

10-4

10-3

ma (eV)

10-5

10-4

10-3

10-2

10-1

100

Ωah2 (

vacu

um m

is-a

lignm

ent)

109

1010

1011

1012

fa

/N (GeV)

WMAP 5: ΩCDM

h2 = 0.110 ± 0.006


Axion microwave cavity searches

⋆ ongoing searches: ADMX experiment

• Livermore⇒ U Wash.

• Phase I: probe KSVZ

for ma ∼ 10−6 − 10−5 eV

• Phase II: probe DFSZ

for ma ∼ 10−6 − 10−5 eV

• beyond Phase II:

probe higher values ma


Axions + SUSY ⇒ Axino a dark matter

• axino is spin-1

2element of axion supermultiplet (R-odd; can be LSP)

• ma model dependent: keV→ GeV

• Z1 → aγ

• non-thermal a production via Z1 decay:

• axinos inherit neutralino number density

• ΩNTPa h2 = ma

m eZ1

Ω eZ1

h2:50 60 70 80 90

mχ~1

0 (GeV)

10-5

10-4

10-3

10-2

10-1

100

101

τ (s

)

fa /N = 10

9 GeV

fa /N = 1010

GeV

fa /N = 10

11 GeV

fa /N = 10

12 GeV


Thermally produced axinos

⋆ If TR < fa, then axinos never in thermal equilibrium in early universe

⋆ Can still produce a thermally via radiation off particles in thermal equilibrium

⋆ Brandenberg-Steffen calculation:

ΩTPa h2 ≃ 5.5g6

s ln

(1.108

gs

)(1011 GeV

fa/N

)2 ( ma

0.1 GeV

) (TR

104 GeV

)(3)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

ma~ (GeV)

104

105

106

107

108

109

1010

TR (

GeV

)

fa /N = 10 12

GeVfa /N = 10 11

GeVfa /N = 10 10

GeV

hot warm cold

NT leptogenesis


Gravitinos: spin-3

2partner of graviton

• gravitino problem in generic SUGRA models: overproduction of G followed by

late G decay can destroy successful BBN predictons: upper bound on TR

(see Kawasaki, Kohri, Moroi, Yotsuyanagi; Cybert, Ellis, Fields, Olive)


Gravitinos as dark matter: again the gravitino problem

• neutralino production in generic SUGRA models: followed by late time

Z1 → G+Xdecays can destroy successful BBN predictons:

(see Kawasaki, Kohri, Moroi, Yotsuyanagi)


Gravitino dark matter: if one can avoid gravitino problem

⋆ mG = F/√

3M∗ ∼ TeV in Supergravity models

• if G is LSP, then calculate NLSP abundance as a thermal relic: ΩNLSPh2

• Z1 → hG, ZG, γG or τ1 → τG possible

∗ lifetime τNLSP ∼ 104 − 108 sec

∗ also produce G thermally (depends on re-heat temp. TR)

∗ DM relic density is then ΩG =mG

mNLSPΩNLSP + ΩTP

G

∗ Feng et al.; Ellis et al.; Brandenberg+Steffen; Buchmuller et al.

• G undetectable via direct/indirect DM searches

• unique collider signatures are possible:

∗ τ1=NLSP: stable charged tracks

∗ can collect NLSPs in e.g. water (slepton trapping)

∗ monitor for NLSP → G decays


Production of sparticles at CERN LHC


Sparticle cascade decays

400

600

800

1000

1200

1400

1600

1800

2000

10-2

10-1

1 10 102

Br (%)

Mas

s s

cale

(G

eV)

g~ (2060)

q ~

L (≈1857)

q ~

R (≈1770)

b ~

2 (1690) t

~

2 (1689) b

~

1 (1619)

t ~

1 (1449)

W ~ ±

2 (1067) Z

~ 4 (1066)

Z ~

3 (1056)

W ~ ±

1 (754) Z

~ 2 (754)

τ ~

2 (726) ν

~

τ (712)

τ ~

1 (442) Z

~ 1 (395)

Z ~

1 qq (27.0 %)

Z ~

1 τνWbb (12.1 %)

Z ~

1 ττWWbb (8.4 %)

Z ~

1 WWbb (7.4 %)

Z ~

1 τνqq (5.9 %)

Z ~

1 τνWWWbb (4.1 %)

Z ~

1 ττbb (2.9 %)

Z ~

1 ττqq (2.9 %)

Z ~

1 τνZWbb (2.8 %)

Z ~

1 τνhWbb (2.6 %)


Event generation for sparticles

~

~

~Z1

~Z1

g

Hadrons

Remnants

q

p

p

1

23

4

5

Event generation in LL - QCD

1) Hard scattering / convolution with PDFs

2) Intial / final state showers

3) Cascade decays

4) Hadronization

5) Beam remnants


Isajet v7.79 for sparticle event generation

⋆ Isajet (1979), by F. Paige and S. Protopopescu

⋆ Isajet 7.0 (1993) -7.75: FP, SP, HB and X. Tata

• Isasugra subprogram: SUGRA models (and others)⇒ sparticle masses,

mixings, decay rates

⋆ SUSY and SM event generation for hadron colliders

⋆ e+e− colliders

• polarized beams

• bremsstrahlung/ beamstrahlung

⋆ IsaTools: Ω eZ1h2, (g − 2)µ, BF (b→ sγ), BF (Bs → µ+µ−), σ(Z1p)

⋆ Les Houches event output: 7.78


Simulated sparticle production event at LHC

S. Abdullin Oct.2000

GEANT figure

mSUGRA : m 0 = 1000 GeV, m 1/2 = 500 GeV, A 0= 0, tan β = 35, µ > 0

m g ~ = 1266 GeV

m u ~ = 1450 GeV

m t ~ = 1026 GeV

m

~ = 410 GeV 1

L

Z 2

m ~ = 214 GeVZ

1

m h = 119 GeV

g ~

t ~

1 t -

W -

+ b -

T = 113 GeV)

s + c -

~W +

2 + b ~W +

1 + Z ν ν-

( jet4, E

T = 79 GeV) ( jet5, E

T = 536 GeV)( jet3, E

~Z

1 W +

+ τ e ν

+ +

u ~

L ~Z

2 + u T = 1196 GeV)( jet6, E

~Z

1 + h

b -

T = 320 GeV)( jet2, ET = 206 GeV)( jet1, E b

ν

S.

Abd

ullin

, A

. Nik

iten

ko

b-jet 1

b-jet 2 Z 1

Z 1

b-jet 3

b-jet 4

jet 5

jet 6

E T

miss= 380 GeV

~

~

5


e+e− → W+

1 W−

1 → (qq′Z1) + (eνeZ1) at linear collider


Sparticle reach of all colliders with relic density

200

400

600

800

1000

1200

1400

1600

0 1000 2000 3000 4000 5000 6000 7000 8000


m0 (GeV)

m1/

2 (G

eV)

LHC

Tevatron

LC 500

LC 1000

Ωh2< 0.129

LEP2 excluded

200

400

600

800

1000

1200

1400

1600

0 1000 2000 3000 4000 5000 6000 7000

mSugra with tanβ = 45, A0 = 0, µ < 0

m0 (GeV)m

1/2

(GeV

)

LHC

Tevatron

LC 500

LC 1000

Ωh2< 0.129

LEP2 excluded

HB, Belyaev, Krupovnickas, Tata: JHEP 0402, 007 (2004)


Early SUSY discovery at LHC with just 0.1 fb−1?

• To make 6ET cut, complete knowledge of detector needed

– dead regions

– “hot” cells

– cosmic rays

– calorimeter mis-measurement

– beam-gas events

• Can we make early discovery of SUSY at LHC without 6ET ?

• Expect SUSY events to be rich in jets, b-jets, isolated ℓs, τ -jets,....

• These are detectable, rather than inferred objects

• Answer: YES! See HB, Prosper, Summy, arXiv:0801.3799


D0 saga with missing ET


Simple cuts: ≥ 4 jets plus isolated leptons

• 6ET not really necessary

0 5# of Isolated Leptons

0.1

1

10

100

1000

10000

1e+05

1e+06

1e+07

σ (f

b)

SO10ptA(9202.87,62.498,-19964.500,49.1,171)QCD JetsttW+jetsZ+jetsWW, WZ, ZZSum of Backgrounds

No. of Isolated LeptonsCuts C1a


Cuts C1′ plus ≥ 2 OS/SF ℓ

0 50 100 150m

ll (GeV)

0

10

20

30

40

dσ/d

mll (

fb/G

eV)

SO10ptA + BGQCD JetsttW+jetsZ+jetsWW, WZ, ZZSum of Backgrounds

Cuts C1a


Precision measurements at LHC: Atlas and CMS

• Meff = 6ET + ET (j1) + · · · + ET (j4) sets overall mg, mq scale

• m(ℓℓ) < meZ2−meZ1

mass edge

• m(ℓℓ) distribution shape

• combine m(ℓℓ) with jets to gain m(ℓℓj) mass edge: info on mq

• further mass edges possible e.g. m(ℓℓjj)

• Higgs mass bump h→ bb likely visible in 6ET + jets events

• in favorable cases, may overconstrain system for a given model

⋆ methodology very p-space dependent

⋆ some regions are very difficult e.g. HB/FP


International linear e+e− collider (ILC)

⋆ A linear e+e− collider with√s = 0.5 − 1 TeV is highest priority project for

HEP beyond LHC! Why?

• All beam energy ⇒ collision (aside from brem/beamstrahlung losses)

• beam energy known

• clean collision environment

• low (electroweak) background levels

• adjustable beam energy (threshold scans)

• e− and possibly e+ beam polarization

⋆ ILC will be ideal machine to perform precision spectroscopy of any new (EW

interacting) matter states (provided they are kinematically accessible)!

⋆ timeline: decision-2012; ready-2025?


Precision sparticle measurements at a e+e− linear collider


Direct detection of SUSY DM

⋆ Direct search via neutralino-nucleon scattering


Direct detection of neutralino DM: the race is on!

WIMP Mass [GeV/c2]

Cro

ss-s

ectio

n [p

b] (

norm

alis

ed to

nuc

leon

)

080418114601

http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini

101

102

103

10-10

10-9

10-8

10-7

10-6

10-5

080418114601Baer et. al 2003XENON1T (proj)LUX 300 kg LXe Projection (Jul 2007)XENON100 (150 kg) projected sensitivitySuperCDMS (Projected) 25kg (7-ST@Snolab)WARP 140kg (proj)SuperCDMS (Projected) 2-ST@SoudanCDMS Soudan 2007 projectedXENON10 2007 (Net 136 kg-d)CDMS: 2004+2005 (reanalysis) +2008 GeCDMS 2008 GeWARP 2.3L, 96.5 kg-days 55 keV thresholdDAMA 2000 58k kg-days NaI Ann. Mod. 3sigma w/DAMA 1996Edelweiss I final limit, 62 kg-days Ge 2000+2002+2003 limitDATA listed top to bottom on plot


Indirect detection (ID) of SUSY DM: ν-telescopes

⋆ Z1Z1 → bb, etc. in core of sun (or earth): ⇒ νµ → µ in ν telescopes

• Amanda, Icecube, Antares


ID of SUSY DM: γ and anti-matter searches

• Z1Z1 → qq, etc.→ γ in galactic core or halo

• Z1Z1 → qq, etc.→ e+ in galactic halo

• Z1Z1 → qq, etc.→ p in galactic halo

• Z1Z1 → qq, etc.→ D in galactic halo


Direct and indirect detection of neutralino DM

200

400

600

800

1000

1200

1400

1600

0 1000 2000 3000 4000 5000 6000 7000 8000

mSUGRA, A0=0 tanβ=10, µ>0

m0(GeV)

m1/

2(G

eV)

LEP

no REWSB

Z~

1 no

t LS

P

Φ(p-)=3x10-7 GeV-1 cm-2 s-1 sr-1

(S/B)e+=0.01

Φ(γ)=10-10 cm-2 s-1

Φsun(µ)=40 km-2 yr-1

0<Ωh2<0.129

mh=114.4 GeV

σ(Z~

1p)=10-9 pb

LHC

LC1000

LC500

TEV

µD

D

200

400

600

800

1000

1200

1400

1600

0 1000 2000 3000 4000 5000

mSUGRA, A0=0, tanβ=50, µ<0

m0 (GeV)m

1/2

(GeV

)

LEP

no REWSB

Z~

1 no

t LS

P

Φ(p-) 3e-7 GeV-1 cm-2 s-1 sr-1 (S/B)e+=0.01

Φ(γ)=10-10 cm-2 s-1 Φsun(µ)=40 km-2 yr-1

0< Ωh2< 0.129

mh=114.4 GeV

Φearth(µ)=40 km-2 yr-1 σ(Z~

1p)=10-9 pb

LHC

LC1000

LC500

µ

DD

HB, Belyaev, Krupovnickas, O’Farrill: JCAP 0408, 005 (2004)


Impact of DM direct/indirect detection on LHC program

• Extend reach in σSI ∼ 10−9 − 10−10 pb

– explore thoroughly region of MHDM, possibly MWDM

• after discovery, extract mwimp?

– meZ1sets absolute mass scale for SUSY particles-

– combine with LHC mass edges to gain LHC absolute sparticle masses

– learn if Z1 is absolutely stable: R-conservation

• IceCube turn-on can discover/verify especially MHDM

• knowledge of LHC spectra, σSI , σSD combined with possible gamma ray

signals may allow map of dark matter distribution in the galaxy

• role of p, e+, D signals


Models beyond mSUGRA

⋆ Normal scalar mass hierarchy

– split scalar generations m0(1) ≃ m0(2) ≪ m0(3)

– resolves BF (b→ sγ) and (g − 2)µ

⋆ Non-universal Higgs scalars

– motivated by SO(10) and SU(5) SUSY GUTs

– allow A-funnel at low tan β; higgsino DM at low m0

– enhanced DD/ ID rates

⋆ DM in models with t− b− τ Yukawa unification (SO(10))

⋆ Mixed wino DM

⋆ Bino-wino co-annihilation (BWCA) DM

⋆ Low M3 mixed higgsino DM

⋆ KKLT mixed moduli/AMSB DM


Conclusions

⋆ Supersymmetry is very compelling BSM theory

⋆ Irrefragable case for CDM has emerged

⋆ Some reach for SUSY at Tevatron

⋆ Huge reach for SUSY at CERN LHC

⋆ Possible early SUSY discovery at LHC: leptons instead of 6ET

⋆ e+e− LC necessary for precision sparticle spectroscopy

⋆ Direct search for WIMP/axion DM is underway

⋆ Indirect search for WIMP DM via Icecube ν telescope

⋆ Indirect search via γ, p, e+, D detection from galactic core/halo WIMP

annihilations

⋆ Solution of mystery of CDM is near if CDM =lightest SUSY particle!


Documents

Supersymmetric Dark Matter: Direct, Indirect and …baer/okstate.pdf⋆ Part 2: models/implications – MSSM, SUGRA, GMSB, AMSB, ··· – dark matter density/detection ⋆ Part 3: