[PPT] - We also know MSSM (plus gauge singlets) is compelling effective PowerPoint Presentation

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Mixed axion/axino cold dark matter in SUSY: with implications for LHC

Howard Baer University of Oklahoma OUTLINE

⋆ old ideas from 1970s ⋆ strong CP problem and PQWW solution ⋆ the PQMSSM ⋆ axion/axino CDM ⋆ mSUGRA (CMSSM) ⋆ Effective SUSY ⋆ Yukawa-unified SUSY

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Old ideas from the dawn of time: (1970s)

⋆ renormalizable gauge theories ⋆ QCD ⋆ the Standard Model ⋆ supersymmetry ⋆ GUTs ⋆ superstrings ⋆ see-saw neutrinos ⋆ PQ strong CP solution

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Origin of strong CP problem

⋆ QCD ∋ U(2)V × U(2)A global symmetry (2 light quarks) ⋆ U(2)V = SU(2)I × U(1)B realized; U(2)A broken spontaneously ⋆ expect 4 Goldstone bosons: πs and η, but instead mη ≫ mπ: QCD does not

respect somehow U(1)A (Weinberg)

⋆ t’Hooft resolution: QCD θ vacuum ⇒ theory not U(1)A symmetric, and

mη ≫ mπ explained

⋆ Generate additional term to QCD Lagrangian: L ∋ θ g2

s

32πF µν A ˜

FAµν

violates P and T; conserves C

⋆ In addition, weak interactions ⇒ L ∋ Arg detM g2

s

32πF µν A ˜

FAµν

¯

θ = θ + Arg detM

⋆ experiment: neutron EDM ⇒ ¯

θ

<

∼ 10−10

⋆ How can this be? The strong CP problem

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Solutions to the strong CP problem

⋆ Anthropic: ¯

θ luckily small

⋆ Spontaneously broken CP: induced ¯

θ is small (loop level)

⋆ a new chiral symmetry UP Q(1) exists (Peccei-Quinn); UP Q(1) spontaneously

broken at scale fa (∼ 109 − 1012 GeV)

⋆ Goldstone boson field a(x), the axion must exist (Weinberg, Wilczek) ⋆ L ∋ − 1

2∂µa∂µa + ξ a fa g2

s

32π2 F µν A ˜

FAµν + Lint

⋆ Veff ∼ −(1 − cos(¯

θ + ξ a

fa ))

⋆ axion field settles to minimum of potential: a = − fa

ξ ¯

θ

⋆ strong CP problem solved! ⋆ m2

a = ∂2Veff ∂a2 Howie Baer, GGI LHC mini workshop, June 10, 2010

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Axion cosmology

⋆ Axion field eq’n of motion: θ = a(x)/fa

– ¨ θ + 3H(T) ˙ θ +

1 f 2

a

∂V (θ) ∂θ

= 0 – V (θ) = m2

a(T)f 2 a(1 − cos θ)

– Solution for T large, ma(T) ∼ 0: θ = const. – ma(T) turn-on ∼ 1 GeV

⋆ a(x) oscillates,

creates axions with p ∼ 0: production via vacuum mis-alignment

⋆ Ωah2 ∼ 1

2

6×10−6eV

ma

7/6 θ2

i h2

⋆ astro bound: stellar cooling ⇒ fa

>

∼ 109GeV

10

5

10

4

10

3

ma (eV)

10

5

10

4

10

3

10

2

10

1

10

Ωah

2 (vacuum mis-alignment)

10

9

10

11

10

12

fa /N (GeV)

WMAP 5: ΩCDMh

2 = 0.110 ± 0.006

Howie Baer, GGI LHC mini workshop, June 10, 2010

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We also know MSSM (plus gauge singlets) is compelling effective theory between Mweak and MGUT

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Most analyses work in mSUGRA (CMSSM) model

m0, m1/2, A0, tan β, sign(µ)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Results of χ2 fit using τ data for aµ:

mSugra with tanβ = 10, A0 = 0, µ > 0

250 500 750 1000 1250 1500 1750 2000 1000 2000 3000 4000 5000 6000

mSugra with tanβ = 10, A0 = 0, µ > 0

250 500 750 1000 1250 1500 1750 2000 1000 2000 3000 4000 5000 6000

2

2 4 6 8

m0 (GeV) m1/2 (GeV) ln(χ/DOF)

No REWSB Ζ

~ 1 not LSP

mh=114.1GeV LEP2 excluded SuperCDMS CDMSII CDMS mSugra with tanβ = 54, A0 = 0, µ > 0

250 500 750 1000 1250 1500 1750 2000 1000 2000 3000 4000 5000 6000

mSugra with tanβ = 54, A0 = 0, µ > 0

250 500 750 1000 1250 1500 1750 2000 1000 2000 3000 4000 5000 6000 2 4 6 8 10 12 14

m0 (GeV) m1/2 (GeV) ln(χ2/DOF)

No REWSB Ζ

~ 1 not LSP

mh=114.1GeV LEP2 excluded SuperCDMS CDMSII CDMS

HB, C. Balazs: JCAP 0305, 006 (2003)
numerous recent χ2, MCMC fits to find preferred regions

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Ω e

Z1h2 as surface in m0 vs. m1/2 space

tan β = 10, A0 = 0, µ > 0 (HB, A. Box)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Fine-tuning in mSUGRA with neutralino CDM

⋆ contours of Ω e

Z1h2

⋆ regions of fine-tune: ∆ ≡

∂ log Ω e

Z1h2

∂ log ai

: (HB, A. Box)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Fine-tuning zoomed in stau-co-annihilation

⋆ contours of Ω e

Z1h2

⋆ regions of fine-tune: ∆ ≡

∂ log Ω e

Z1h2

∂ log ai Howie Baer, GGI LHC mini workshop, June 10, 2010

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General scan over 19 param. MSSM

⋆ dimensionful param’s defined at MGUT

mQ1, mU1, mD1, mL1, mE1 : 0 → 3500 GeV
mQ3, mU3, mD3, mL3, mE3 : 0 → 3500 GeV
M1, M2, M3 : 0 → 3500 GeV
At, Ab, Aτ : −3500 → 3500 GeV
mHu, mHd : 0 → 3500 GeV
tan β : 2 → 60

⋆ mf

W1 > 103.5 GeV

⋆ mf

W1 > 91.9 GeV (wino-like)

⋆ mh > 111 GeV

Howie Baer, GGI LHC mini workshop, June 10, 2010

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400 800 1200 1600

mZ1

~

10

4

10

2

10 10

2

10

4

10

6

10

8

Ωh

2 Bino Wino Higgsino Mixed

Howie Baer, GGI LHC mini workshop, June 10, 2010

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General MSSM 19 param. scan

histogram of models vs. Ω e

Z1h2

10

3 10
2 10
1 10

0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8

Ωh

2

200 400 600 800

Total Number of Models

Bino Wino Higgsino Mixed

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Why WIMP miracle really is a miracle for SUSY

histogram of models vs. Ω e

Z1h2 with m e Z1 < 500 GeV

10

3 10
2 10
1 10

0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8

Ωh

2

100 200 300

Total Number of Models

Bino Wino Higgsino Mixed

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Gravitinos: spin-3

2 partner of graviton

gravitino problem in generic SUGRA models: overproduction of ˜

G followed by late ˜ G decay can destroy successful BBN predictions: upper bound on TR (see Kawasaki, Kohri, Moroi, Yotsuyanagi; Cybert, Ellis, Fields, Olive)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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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 predictions: (see Kawasaki, Kohri, Moroi, Yotsuyanagi)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Various leptogenesis scenarios

Upper bound on TR from BBN is below that for successful thermal

leptogenesis: need TR

>

∼ 1010 GeV (Buchmuller, Plumacher)

Alternatively, one may have non-thermal leptogenesis where inflaton

φ → NiNi decay (Lazarides, Shafi; Kumekawa, Moroi, Yanagida)

additional source of Ni in early universe allows lower TR:

nB s ≃ 8.2 × 10−11 ×

TR

106 GeV 2mN1 mφ mν3 0.05 eV

δeff

(1)

Also, AD leptogenesis in φ =

√ Hℓ D-flat direction: TR ∼ 106 − 108 GeV allowed (Dine, Randall, Thomas; Murayama, Yanagida)

WMAP observation: nb/s ∼ 0.9 × 10−10 ⇒ TR

>

∼ 106 GeV

Howie Baer, GGI LHC mini workshop, June 10, 2010

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PQMSSM: Axions + SUSY ⇒ Axino ˜ a dark matter

axino is spin- 1

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

– Raby, Nilles, Kim – Rajagopal, Wilczek, Turner

m˜

a model dependent: keV→ GeV

Z1 → ˜ aγ

non-thermal ˜

a production via Z1 decay:

axinos inherit neutralino number density
ΩNT P

˜ a

h2 =

m˜

a

m e

Z1 Ω e

Z1h2:

– Covi, Kim, Kim, Roszkowski

50 60 70 80 90

mχ

~

1 0 (GeV)

10

5

10

4

10

3

10

2

10

1

10 10

1

τ (s)

f

a

/N = 10

9

GeV f

a

/N = 10

1

GeV f

a

/N = 10

1 1

GeV f

a

/N = 10

1 2

GeV

Howie Baer, GGI LHC mini workshop, June 10, 2010

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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:

ΩT P

˜ a

h2 ≃ 5.5g6

s ln

1.108 gs 1011 GeV fa/N 2 m˜

a

0.1 GeV TR 104 GeV

(2)

10

9

10

11

10

12

fa /N (GeV) 10

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

TR (GeV)

Ωa

~ TPh 2 = 0.001 (solid), 0.01 (dashed), 0.1 (dashed-dotted)

ma

~ (GeV) = 0.0001 (purple), 0.01 (green), 1 (maroon)

m

a ~

= 0.0001 (GeV), Ω

a ~ T P

h

2

= 0.1 m

a ~

= 0.01 (GeV), Ω

a ~ T P

h

2

= 0.01

Howie Baer, GGI LHC mini workshop, June 10, 2010

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mSUGRA model with mixed axion/axino CDM: m˜

a fixed

⋆ (m0, m1/2, A0, tan β, sgn(µ)) = (1000 GeV, 300 GeV, 0, 10, +1) ⋆ Ωah2 + ΩT P

˜ a

h2 + ΩNT P

˜ a

h2 = 0.11

⋆ model with mainly axion CDM seems favored!

10

9

10

11

10

12

fa /N (GeV) 10

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

10 Ωh

2

10

9

10

11

10

12

fa /N (GeV) 10

2

10

3

10

4

10

5

10

6

10

7

TR (GeV)

WMAP ΩCDMh

2

Ωah

2

Ωa

~ NTPh 2

Ωa

~ TPh 2

ma

~ = 100 keV (solid), 1 MeV (dashed)

(a) (b)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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mSUGRA p-space with mainly axion cold DM

⋆ contours of log10 TR: mSUGRA w/ tan β = 10, A0 = 0 ⋆ TR

>

∼ 106 consistent with non-thermal leptogenesis

⋆ most dis-favored mSUGRA regions with neutralino DM are most favored by

mSUGRA with mainly axion DM! (HB, Box, Summy)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Axion/axino relic density in mSUGRA

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Fine-tuning for mainly axion CDM in mSUGRA

⋆ a). contours of Ω e

Z1h2

⋆ regions of fine-tune: ∆ ≡

∂ log Ω e

Z1h2

∂ log ai Howie Baer, GGI LHC mini workshop, June 10, 2010

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supersymetric SO(10): synopsis

⋆ SO(10) is a rank-5 Lie group which contains the SM gauge symmetry.

SO(n) (except n = 6) are naturally anomaly-free, thus explaining the

seemingly fortuitous anomaly cancellation in the SM and in SU(5).

matter unification in spinorial 16: The 16 contains all the matter in a

single generation of the SM, plus a RHN state ˆ N c: see-saw ν-masses

Higgs unification: explains why 2 Higgs doublets in MSSM
Explains R-parity conservation: only matter-matter-Higgs couplings
Expect t − b − τ Yukawa unification in simplest models

⋆ These features have convinced many theorists that the main features of

SUSY SO(10) are surely right!

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Yukawa unification in SUSY: assumptions

some form of 4-d or x-d SO(10) SUGRA-GUT valid at Q > MGUT
SUGRA breaking via superHiggs mechanism: will find m ˜

G ∼ 10 TeV so soft

SUSY breaking terms ∼ 10 TeV

SO(10) breaks to MSSM or MSSM plus gauge singlets at Q ≃ MGUT either

via Higgs mechanism (4-d) or x-d compactification

MSSM (or MSSM plus ˆ

N c) is correct effective theory between MSUSY and MGUT

EWSB broken radiatively due to large mt
we will require that t − b − τ Yukawa couplings unify at Q = MGUT

Howie Baer, GGI LHC mini workshop, June 10, 2010

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lots of previous work!

B. Ananthanarayan, G. Lazarides and Q. Shafi, PRD44 (1991)1613 and

PLB300 (1993)245;

V. Barger, M. Berger and P. Ohmann, PRD49 (1994)4908;
M. Carena, M. Olechowski, S. Pokorski and C. Wagner, NPB426 (1994)269;
B. Ananthanarayan, Q. Shafi and X. Wang, PRD50 (1994)5980;
L. Hall, R. Rattazzi and U. Sarid, PRD50 (1994)7048;
R. Rattazzi and U. Sarid, PRD53 (1996)1553;
T. Blazek, M. Carena, S. Raby and C. Wagner, PRD56 (1997)6919; T. Blazek

and S. Raby, PLB392 (1997)371 and PRD59 (1999)095002; T. Blazek,

S. Raby and K. Tobe, PRD60 (1999)113001 and PRD62 (2000)055001;

Howie Baer, GGI LHC mini workshop, June 10, 2010

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more recent work

HB, Diaz, Ferrandis, Tata, PRD61 (2000) 111701
HB, Brhlik, Diaz, Ferrandis, Mercadante, Quintana, Tata, PRD63

(2001)015007;

HB, Ferrandis, PRL87 (2001) 211803;
Blazek, Dermisek and Raby, PRL88 (2002) 111804 and PRD65 (2002)

115004; Tobe and Wells, NPB663 (2003) 123

Auto, HB, Balazs, Belyaev, Ferrandis, Tata, JHEP0306 (2003) 023
Dermisek, Raby, Roszkowski, Ruiz de Austri, JHEP0304 (2003) 037 and

JHEP0509 (2005) 029

HB, Kraml, Sekmen, Summy, JHEP0803 (2008) 056
HB, Kraml, Sekmen, JHEP0909 (2009) 005

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Yukawa unification requires precision calculation of SUSY spectrum:

need full 2-loop RGE running
full threshold corrections calculated at optimized scale

– applies especially to b-quark self-energy: include ˜ g˜ bi, Wi˜ tj, · · · loops – Hall, Rattazzi, Sarid; Pierce, Bagger, Matchev, Zhang

off-sets Yukawa coupling RG trajectory
minimize scalar potential away from unstable Q = MZ; use

Q = MSUSY ≡ √m˜

t1m˜ t2 instead

we elect to use Isajet/Isasugra spectrum generator

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Yukawa unification in MSSM+RHN model via Isajet

Q (GeV)

3

10

5

10

7

10

9

10

11

10

13

10

15

10

17

10

f

0.4 0.5 0.6 0.7 0.8 0.9 1

t

f

b

f

τ

f

ν

f

Howie Baer, GGI LHC mini workshop, June 10, 2010

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SUSY SO(10) parameter space:

m16, m10, M 2

D, m1/2, A0, tan β, sign(µ)

Here, M 2

D parametrizes D-term splitting of scalar soft terms at MGUT :

m2

Q = m2 E = m2 U

= m2

16 + M 2 D

m2

D = m2 L

= m2

16 − 3M 2 D

m2

˜ νR

= m2

16 + 5M 2 D

m2

Hu,d

= m2

10 ∓ 2M 2 D,

⋆ Two cases:

– “Just-so Higgs splitting” (HS model) – Full D-term splitting plus RHN plus 3rd gen. splitting (DR3 model)

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Top-down scan of HS model with µ > 0

Auto, HB, Balazs, Belyaev, Ferrandis, Tata; HB, Kraml, Sekmen, Summy
R = max(ft, fb, fτ)/min(ft, fb, fτ) at Q = MGUT

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Correlation of SSB terms for YU models

A0 ∼ −2m16
m10 ∼ 1.2m16
tan β ∼ 50
m16 ∼ 10 TeV
m1/2 small

⋆ Earlier work: Bagger, Feng, Polonsky, Zhang derived A2

0 = 2m2 10 = 4m2 16

with m1/2 tiny and Yukawa unified couplings: (RIMH model) – Reconcile naturalness with decoupling via m ˜

f3 ≪ m ˜ f1,2

⋆ Characteristic spectrum for Yukawa unified SUSY:

m˜

q,˜ ℓ(1, 2) ∼ 10 TeV

m˜

t1, mA, µ ∼ 1 − 2 TeV

m˜

g ∼ 300 − 500 GeV Howie Baer, GGI LHC mini workshop, June 10, 2010

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SO(10) sparticle spectra ⇒ trouble for neutralino DM!

⋆ use IsaReD (part of Isajet) to compute relic density ⋆ large m ˜

f1,2 suppresses neutralino annihilation

⋆ Ω e

Z1h2 too large by 103 − 105! Howie Baer, GGI LHC mini workshop, June 10, 2010

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Cold axion and cold/warm axino DM in the universe

Given Ω e

Z1h2 and m e Z1 and ΩNT P ˜ a

h2 can calculate m˜

a.

Given ΩT P

˜ a

h2, m˜

a and fa/N, can calculate re-heat temperature of universe

⋆ Four cases:

1. Take fa/N = 1011 GeV so Ωah2 = 0.017. Bulk of DM must be thermally

produced ˜

a. Take ΩT P

˜ a

= 0.083 and ΩNT P

˜ a

= 0.01

2. Take fa/N = 4 × 1011 GeV so Ωah2 = 0.084. (Bulk of DM is cold axions.)

Take ΩT P

˜ a

= ΩNT P

˜ a

= 0.013

3. Take fa/N = 1012 GeV and lower mis-align error bar so Ωah2 = 0.084. (Bulk
f DM is cold axions.) Take ΩT P

˜ a

= ΩNT P

˜ a

= 0.013

4. Take fa/N = 1012 GeV but allow accidental near vacuum alignment so

Ωah2 ∼ 0. Bulk of DM must be thermally produced axinos. Take ΩT P

˜ a

= 0.1 and ΩNT P

˜ a

= 0.01

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Consistent cosmology for SO(10) SUSY GUTs with mixed a/˜ a DM

Happily, TR falls into the right range to give cold axion/axino DM with a

small admixture of warm axino DM, preserve BBN predictions and have non-thermal leptogenesis!

See HB and H. Summy, PLB666, 5 (2008)
HB, Kraml, Haider, Sekmen and Summy, JCAP0902 (2009) 002

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Howie Baer, GGI LHC mini workshop, June 10, 2010

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Best Yukawa unification favors light gluino!

Possible to see at Tevatron p¯

p collider? m˜

g ∼ 440 GeV! HB, Kraml, Lessa,

Sekmen and Summy, arXiv:0910.2988

Possible to see in year 1 of LHC? m˜

g ∼ 640 GeV! HB, Kraml, Sekmen and

Summy, JHEP0810 (2008) 079; HB, Kraml, Lessa, Sekmen, arXiv:0911.4739

Howie Baer, GGI LHC mini workshop, June 10, 2010

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LHC during year 1 with √s = 7 TeV

using multi-bjet final state, can see m˜

g ∼ 400 GeV with just 0.2 fb−1, even

without using ET !

with ∼ 1 fb−1 and ET , can see m˜

g ∼ 630 GeV

In HS and DR3 model, distinct m(µ+µ−) mass edge

Howie Baer, GGI LHC mini workshop, June 10, 2010

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50 100 150

m(ll) (GeV)

1 2 3 4 5 6

dσ/dm (fb/GeV)

BG HSb + BG DR3b + BG HS (mg

~ = 522 GeV)

DR3 (mg

~ = 526 GeV)

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

mz

~

2-mz

~

1

Howie Baer, GGI LHC mini workshop, June 10, 2010

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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

Howie Baer, GGI LHC mini workshop, June 10, 2010

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Need for broader, deeper axion searches

⋆ axion param. space: Gondolo & Visinelli, 2009 study

we have only begun · · ·

White dwarfs cooling time Tensor modes

Θi1 Θi0.1 Θi3.14 Θi0.01 Θi0.001 Θi0.0001

a CDM a CDM

ADMXI ADMXII CARRACK PLANCK PLANCK

fa TGH Axion isocurvature fluctuations

104 106 108 1010 1012 1014 108 1010 1012 1014 1016 1018 103 106 109 1012 HI GeV fa GeV ma eV Howie Baer, GGI LHC mini workshop, June 10, 2010

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Conclusions

⋆ neutralino CDM: usually too much or too little ⋆ neutralino CDM with Ω e

Z1h2 ∼ 0.1 fine-tuned

⋆ PQ strong CP solution + SUSY: why not both? ⋆ expect mixed axion/axino CDM if ˜

a is LSP

⋆ then low fine-tuning of Ωa˜

ah2

⋆ TR ∼ 106 − 108 possible:

solve gravitino problem if m ˜

G >

∼ 5 TeV

allow for non-thermal leptogenesis

⋆ Neutralino CDM dis-favored models now allowed

Effective SUSY
Yukawa-unified SUSY

Howie Baer, GGI LHC mini workshop, June 10, 2010