Sean Bailly LAPTH, Annecy April 5 2011 SB, K. Jedamzik, G. - - PowerPoint PPT Presentation

SLIDE 1

Gravitino, dark matter candidate and BBN

Sean Bailly

LAPTH, Annecy

April 5 2011

SB, K. Jedamzik, G. Moultaka, Phys.Rev.D80:063509,2009. SB, K.Y. Choi, K. Jedamzik, L. Roszkowski, JHEP 0905:103,2009. SB, JCAP 1103:022,2011.

Sean Bailly Gravitino, dark matter candidate and BBN 1/ 40

SLIDE 2

Introduction: composition of Universe

A few questions What is Dark Energy ? What is Dark Matter ?

SUSY particles

How is matter produced in the Early Universe ?

Big Bang Nucleosynthesis Lithium problems

Where is the antimatter ?

Baryogenesis, leptogenesis

Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40

SLIDE 3

Introduction: composition of Universe

A few questions What is Dark Energy ? What is Dark Matter ?

SUSY particles

How is matter produced in the Early Universe ?

Big Bang Nucleosynthesis Lithium problems

Where is the antimatter ?

Baryogenesis, leptogenesis

Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40

SLIDE 4

Introduction: composition of Universe

A few questions What is Dark Energy ? What is Dark Matter ?

SUSY particles

How is matter produced in the Early Universe ?

Big Bang Nucleosynthesis Lithium problems

Where is the antimatter ?

Baryogenesis, leptogenesis

Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40

SLIDE 5

Introduction: composition of Universe

A few questions What is Dark Energy ? What is Dark Matter ?

SUSY particles

How is matter produced in the Early Universe ?

Big Bang Nucleosynthesis Lithium problems

Where is the antimatter ?

Baryogenesis, leptogenesis

Sean Bailly Gravitino, dark matter candidate and BBN 2/ 40

SLIDE 6

Introduction: solving the matter problems

A simple framework Extension of the Standard Model: Supersymmetry Constrained Minimal Supersymmetric Standard Model (CMSSM) Lightest Supersymmetric Particle (LSP): gravitino Conservation of R-parity In this scenario The gravitino is a good candidate for dark matter The decay of the Next-to-LSP to the LSP during BBN can solve the lithium problem However The constraints require low reheating temperature and heavy mass spectrum Non-standard cosmology with a modified Hubble parameter

Sean Bailly Gravitino, dark matter candidate and BBN 3/ 40

SLIDE 7

Table of contents

1

Supersymmetry

2

Dark matter

3

Big Bang Nucleosynthesis

4

Stau NLSP and gravitino LSP

5

Non-standard cosmology

6

Summary

Sean Bailly Gravitino, dark matter candidate and BBN 4/ 40

SLIDE 8

Table of contents

1

Supersymmetry

2

Dark matter

3

Big Bang Nucleosynthesis

4

Stau NLSP and gravitino LSP

5

Non-standard cosmology

6

Summary

Sean Bailly Gravitino, dark matter candidate and BBN 5/ 40

SLIDE 9

Supersymmetry

Symmetry between bosons and fermions Q |fermion = |boson Q |boson = |fermion New particles with same mass as SM partners Broken symmetry No observation of superpartners SUSY breaking mechanism is unknown Explicit breaking terms included in effective SUSY lagrangian CMSSM: m1/2, m0, A0, tan β, sgn µ R-parity conservation PR = (−1)3B+L+2S The lightest SUSY particle is stable

Sean Bailly Gravitino, dark matter candidate and BBN 6/ 40

SLIDE 10

Gravitino

Supergravity If supersymmetry is a broken local symmetry: supergravity Graviton and its superpartner, the gravitino ˜ G (3/2-spin particle) Super-Higgs mechanism: ˜ G becomes massive m3/2 = F √ 3MPl where √ F is the SUSY breaking scale

0.1 keV

GMSB

100 GeV

CMSSM

10 TeV

AMSB m3/2 =

F √ 3Mpl

But here we will take the gravitino mass as a free parameter. Gravitino interactions Gravitational interactions ∝ m2

soft

F ∝ m2

soft

m3/2MPl

Sean Bailly Gravitino, dark matter candidate and BBN 7/ 40

SLIDE 11

Table of contents

1

Supersymmetry

2

Dark matter

3

Big Bang Nucleosynthesis

4

Stau NLSP and gravitino LSP

5

Non-standard cosmology

6

Summary

Sean Bailly Gravitino, dark matter candidate and BBN 8/ 40

SLIDE 12

Evidence for dark matter

First observations: F. Zwicky (1933) Study of galactic rotation curves:

• V. Rubin (1970’s)

Other observations Large scale structure formation Gravitational lensing CMB Bullet Cluster . . . WMAP five-year data giving at 3σ Komatsu et al. (2008) ΩDMh2 = 0.1099 ± 0.0124

Sean Bailly Gravitino, dark matter candidate and BBN 9/ 40

SLIDE 13

Relic density calculation

The Boltzmann equation ˙ nX + 3HnX = − σv

• n2

X − neq X 2

In a radiation dominated universe dY dx = −

• π

45G g1/2

∗

mX x2 < σv >

• Y 2 − Yeq

2

with x = mX/T and Y = nX/s The relic density reads: ΩXh2 = 2.742 × 108 mX 1 GeV

• Y(T0)

Sean Bailly Gravitino, dark matter candidate and BBN 10/ 40

SLIDE 14

Gravitino dark matter candidate and non-thermal production

Good candidate No charges Super Weakly Interacting Massive Particle SUSY LSP with R-parity conservation: stable Gravitino production Non-thermal production Thermal production Non-thermal production from NLSP decay All SUSY particles decay to NLSP NLSP freeze-out NLSP decays to LSP ΩNTP

3/2 h2 = m3/2

mNLSP ΩNLSPh2

Sean Bailly Gravitino, dark matter candidate and BBN 11/ 40

SLIDE 15

Gravitino dark matter: thermal production

During reheating, gravitinos can be produced in scattering processes

Bolz et al. (2001), Pradler & Steffen (2007)

g + g → ˜ g + ˜ G q + g → ˜ q + ˜ G q + q → ˜ g + ˜ G . . . YPS(TBBN) =

3

• α=1
• 1 +

M2

α

3m2

3/2

• yαg2

α ln

kα gα TR 1010 GeV

• Thermal contribution to relic density

ΩTP

3/2h2 ≃ 0.32

10 GeV m3/2 m1/2 1 TeV 2 TR 108 GeV

• Gravitino relic density

Ω3/2h2 = ΩTP

3/2h2 + ΩNTP 3/2 h2

Sean Bailly Gravitino, dark matter candidate and BBN 12/ 40

SLIDE 16

Table of contents

1

Supersymmetry

2

Dark matter

3

Big Bang Nucleosynthesis

4

Stau NLSP and gravitino LSP

5

Non-standard cosmology

6

Summary

Sean Bailly Gravitino, dark matter candidate and BBN 13/ 40

SLIDE 17

Big Bang Nucleosynthesis : SBBN (1/5)

Before 1 s : weak interactions n + e+ → p + ¯ νe Weak interaction freeze-out n/p = e−Q/Tf ∼ 1/6 → 1/7 Deuterium bottleneck p + n → γ + D γ + D → p + n Deuterium production starts at 200 s D + p → 3He + γ, D + 3He → 4He + p

4He: most stable element, absorbs all

neutrons Yp = 2n p + n ≃ 0.25

t(s) 1 10

2

10

3

10

4

10 Abundances

• 14

10

• 13

10

• 12

10

• 11

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 10

Li

7

Li

6

n

p

Y He

3

D

No stable element at A = 5 and A = 8 Small abundances of 6Li, 7Li

Sean Bailly Gravitino, dark matter candidate and BBN 14/ 40

SLIDE 18

Big Bang Nucleosynthesis : predictions (2/5)

SBBN has only one free parameter Measurement by WMAP η = nb nγ = (6.225 ± 0.170) × 10−10

Sean Bailly Gravitino, dark matter candidate and BBN 15/ 40

SLIDE 19

Big Bang Nucleosynthesis : observations (3/5)

Element SBBN Observations D

H

• (2.60 ± 0.16) × 10−5

(2.68+0.27

−0.25) × 10−5

3He

H

• (1.05 ± 0.04) × 10−5

(1.1 ± 0.2) × 10−5 Yp 0.2487 ± 0.0006 0.242 ± 0.002 6Li

H

• 10−14 − 10−15

(3 − 5) × 10−12 7Li

H

• (4.26+0.91

−0.86) × 10−10

(1.2 − 1.9) × 10−10

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SLIDE 20

Big Bang Nucleosynthesis : lithium-7 (4/5)

Spite plateau points to a primordial abundance which disagrees with SBBN Possible origin of discrepancy Nuclear rates (re-examined and restricted by solar neutrino flux

Coc et al. (2003), Cyburt et al. (2003))

Stellar depletion Richard et al. (2004),

Korn et al. (2006)

Star temperature scale Melendez &

Ramirez (2004)

Particle decay during BBN Moroi et

• al. (1993), Feng et al. (2003), Cerdeno et al.

(2005)

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SLIDE 21

Big Bang Nucleosynthesis : lithium-6 (5/5)

log (6Li/H), log (Li/H)

Li/H

6Li/H

[Fe/H]

Rollinde et al. (2006)

Debate on the existence of plateau ? Origin Cosmic rays in the galactic formation Suzuki & Inoue (2002) Cosmic rays from Pop III stars

Rollinde et al. (2006)

Particle decay during BBN

Sean Bailly Gravitino, dark matter candidate and BBN 18/ 40

SLIDE 22

Decay of relic particles

Massive unstable particle X with lifetime τX ∼ 102 − 106 s Decay to Standard Model particles Injection of photons and nucleons: photodisintegration, 4He spallation. . .

6Li production: n(4He, pn)3H(α, n)6Li 7Li destruction: 7Be(n, p)7Li(p, α)4He

Abundance change is constrained by observations

Sean Bailly Gravitino, dark matter candidate and BBN 19/ 40

SLIDE 23

Catalyzed BBN

Negatively charged X particles: bound state formation Reactions catalyzed Pospelov (2006)

Li

6

He

4

He

4

Li

6

D γ D X− X ( − )

σCBBN ≃ 108 × σSBBN Important production of lithium-6 for τ 3000 s The BBN code developed by K. Jedamzik (2006) takes all CBBN effects into account (CBBN reaction rates Kamimura et al. (2008))

Sean Bailly Gravitino, dark matter candidate and BBN 20/ 40

SLIDE 24

Table of contents

1

Supersymmetry

2

Dark matter

3

Big Bang Nucleosynthesis

4

Stau NLSP and gravitino LSP

5

Non-standard cosmology

6

Summary

Sean Bailly Gravitino, dark matter candidate and BBN 21/ 40

SLIDE 25

Stau NLSP and gravitino LSP

The two-body decay dominates Γ(˜ τ → τ ˜ G) = 1 48π m5

˜ τ

M2

Plm2 3/2

• 1 −

m2

3/2

m2

˜ τ

4

˜ G τ ˜ τ

(GeV)

• m

3

10

4

10 lifetime (s)

• 2

10

• 1

10 1 10

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

10

10

10

11

10 (GeV)

G ~

m

3

10

2

10

1

10 1

• 1

10

• 2

10

Sean Bailly Gravitino, dark matter candidate and BBN 22/ 40

SLIDE 26

EM cascade

The lepton τ decay processes: mesons : τ → π−ντ, τ → π−π0ντ leptons : τ → e−¯ νeντ, τ → µ−¯ νµντ For stau lifetimes < 100 s, the mesons interact hadronically inducing charge exchange reactions n ↔ p with an increasing ratio n/p. The impact

• n BBN is an increased 4He abundance strongly constrained by
• bservations.

For stau lifetimes > 100 s, the mesons decay electromagnetically. In a good approximation, the two body decay of the stau induces dominantly an electromagnetic cascade. Bem = 1 − Bhad ≃ 1 and Eem = α

• m2

NLSP − m2 3/2

2mNLSP

• α ≃ 1

2

Sean Bailly Gravitino, dark matter candidate and BBN 23/ 40

SLIDE 27

Hadronic cascade: four-body decay (1/3)

First approach : Bhad(˜ τ → τ ˜ Gq¯ q) = Bhad(˜ τ → τ ˜ GZ)B(Z → q¯ q) Feng (2003) A more general calculation Steffen (2006) Bhad(˜ τ → τ ˜ Gq¯ q; mcut

q¯ q) = Γ(˜

τ → τ ˜ Gq¯ q) Γtot with the 4-body decay width Γ(˜ τ → τ ˜ Gq¯ q; mq¯

q) =

m ˜

τ −m3/2−mτ

mq¯

q

dmq¯

q dΓ(˜

τ → τ ˜ Gq¯ q) dmq¯

q ˜ τ ˜ τ ˜ τ ˜ τ q q q q ˜ τ ¯ q ¯ q ¯ q ¯ q τ τ τ τ ˜ G ˜ G ˜ G ˜ G

γ/Z γ/Z γ/Z

τ ˜ χ0 γ/Z ˜ τ q ντ ˜ G

W

˜ τ q ¯ Q ντ ˜ G q ˜ τ ντ ˜ G ¯ Q

W

˜ χ+

W

¯ Q τ Sean Bailly Gravitino, dark matter candidate and BBN 24/ 40

SLIDE 28

Hadronic cascade: four-body decay (2/3)

(GeV)

• m

2

10

3

10 (GeV)

• 13

10

• 12

10

• 11

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1

/Z

• W

h

(GeV)

• m

2

10

3

10 (GeV)

• 13

10

• 12

10

• 11

10

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1

/Z

• W

h

Sean Bailly Gravitino, dark matter candidate and BBN 25/ 40

SLIDE 29

Hadronic cascade: four-body decay (3/3)

Hadronic energy Steffen (2006) Ehad = 1 Γ(˜ τ → τ ˜ Gq¯ q) m ˜

τ −m3/2−mτ

mq¯

q

dmq¯

q mq¯ q dΓ(˜

τ → τ ˜ Gq¯ q) dmq¯

q

Realistic calculation Use of CalcHEP (event generation) + PYTHIA (realistic neutron distribution)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 1e-06 1e-05 1e-04 0.001 0.01 0.1 1 "help1.dat" using 1:2 "fort.33" using 1:2 "help.dat" using 1:2

Li

7

−60 −40 −20 20 40 60 H

2

−60 −40 −20 20 40 60

Sean Bailly Gravitino, dark matter candidate and BBN 26/ 40

SLIDE 30

Results (1/2)

: 6Li solution : 7Li solution : 6Li and 7Li solution

Sean Bailly Gravitino, dark matter candidate and BBN 27/ 40

SLIDE 31

Results (2/2)

(GeV)

1/2

m

3

10 (GeV)

3/2

m

• 1

10 1 10

2

10

Gravitino not LSP Li6/Li7 > 0.66 Li6/Li7 < 0.015

• 1

10 × Li7/H > 2.5 SBBN

• 5

10 × D/H < 5.3

N T P

5

=10

R

T

6

=10

R

T

7

=10

R

T

8

=10

R

T

9

=10

R

T =10 β =80 GeV tan m <100 s

N L S P

τ

(GeV)

1/2

m

3

10 (GeV)

3/2

m

• 1

10 1 10

2

10

The red region solves both problems simultaneously for m1/2 = [3 − 5] TeV corresponding to stau masses m˜

τ = [1 − 1.8] TeV and gravitino masses

m3/2 = 60 − 120 GeV

Sean Bailly Gravitino, dark matter candidate and BBN 28/ 40

SLIDE 32

Results: drawbacks

Matter-antimatter asymmetry To explain η = nb − n¯

b

nγ = (6.225 ± 0.170) × 10−10 A possible scenario is the thermal leptogenesis A requirement for this model is TR > 2 × 109 GeV Our scenario: requires lower reheating temperature TR 107 GeV has quite heavy masses (above LHC range)

Sean Bailly Gravitino, dark matter candidate and BBN 29/ 40

SLIDE 33

Table of contents

1

Supersymmetry

2

Dark matter

3

Big Bang Nucleosynthesis

4

Stau NLSP and gravitino LSP

5

Non-standard cosmology

6

Summary

Sean Bailly Gravitino, dark matter candidate and BBN 30/ 40

SLIDE 34

A scenario with a modified Hubble parameter

Addition of a dark component in the early Universe Arbey & Mahmoudi (2008) ρD(T) = ρD(TBBN) T TBBN nD with TBBN = 10 MeV As we require a radiation dominated era for BBN, we introduce the parameter κD = ρD(TBBN) ρrad(TBBN) ≪ 1 where the radiation density ρrad(T) = geff(T) π2

30 T 4

Modified Hubble parameter H2 = 8πG 3 (ρm + ρrad + ρD)

Sean Bailly Gravitino, dark matter candidate and BBN 31/ 40

SLIDE 35

Non-thermal production (1/4)

Since the Hubble parameter is larger as in the standard scenario, the NLSP freeze-out occurs earlier Boltzmann equation dY dx = −

• π

45 g1/2

∗

mNLSP x2

• 1 +

ρD(T) ρrad π2

30 T 4

−1/2 σeffv

• Y 2 − Y 2

eq

• The NLSP abundance is higher, same for the gravitino relic density

ΩNTP

3/2 h2 = m3/2

mNLSP ΩNLSPh2

Sean Bailly Gravitino, dark matter candidate and BBN 32/ 40

SLIDE 36

Non-thermal production (2/4)

Sean Bailly Gravitino, dark matter candidate and BBN 33/ 40

SLIDE 37

Non-thermal production (3/4)

Sean Bailly Gravitino, dark matter candidate and BBN 34/ 40

SLIDE 38

Non-thermal production (4/4)

D

n 1 2 3 4 5 6 7 8 9

D

Κ

• 10
• 8
• 6
• 4
• 2

2

• 1

10 1 10

D

n 1 2 3 4 5 6 7 8 9

D

Κ

• 10
• 8
• 6
• 4
• 2

2 = 1 G e V

3/2

m =10 GeV

3/2

m

2

h

τ ∼

Ω

=10 β =100 GeV, tan =1000 Gev, m

1/2

m

Sean Bailly Gravitino, dark matter candidate and BBN 35/ 40

SLIDE 39

Thermal production (1/2)

Y3/2(TBBN) =

3

• α=1
• 1 +

M2

α

3m2

3/2

• y

′

αg2 α ln

kα gα TR

TBBN

dT

• 1 + κD
• T

TBBN

nD−41/2 For κD, we recover the standard value YPS nD = 4 Y3/2(TBBN) = 1 1 + κD YPS(TBBN) nD > 4 Y3/2(TBBN) = YPS(TBBN) × 2F1

• 1/N, 1/2; 1 + 1/N; −κD

TR TBBN N Relic density ΩTP

3/2h2 = 2.742 × 108

m3/2 1 GeV

• Y3/2(TBBN)

The thermal contribution is suppressed compared to the standard scenario

Sean Bailly Gravitino, dark matter candidate and BBN 36/ 40

SLIDE 40

Thermal production (2/2)

(GeV)

R

T

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

10

10

10

11

10

12

10

13

10

2

h

TP 3/2

Ω

• 10

10

• 9

10

• 8

10

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 10

2

10 =1 GeV

3/2

=1 TeV m

1/2

m

WMAP standard =4

D

n

• 8

=10

D

κ =5,

D

n

• 5

=10

D

κ =5,

D

n

• 2

=10

D

κ =5,

D

n

• 8

= 1

D

κ = 7 ,

D

n

• 5

= 1

D

κ = 7 ,

D

n

• 8

=10

D

κ =8,

D

n

• 8

=10

D

κ =6,

D

n

• 5

=10

D

κ =6,

D

n

• 2

=10

D

κ =6,

D

n

• 5

=10

D

κ =8,

D

n

• 2

=10

D

κ =7,

D

n

(GeV)

R

T

2

10

3

10

4

10

5

10

6

10

7

10

8

10

9

10

10

10

11

10

12

10

13

10

2

h

TP 3/2

Ω

• 10

10

• 9

10

• 8

Sean Bailly Gravitino, dark matter candidate and BBN 37/ 40

SLIDE 41

Results on gravitino relic density

Sean Bailly Gravitino, dark matter candidate and BBN 38/ 40

SLIDE 42

Results

For a given mass, more NLSP particles decay during BBN

(GeV)

1/2

m

3

10 (GeV)

3/2

m

• 1

10 1 10

2

10

Gravitino not LSP Li6/Li7 > 0.66 Li6/Li7 < 0.015

• 10

10 × Li7/H > 2.5 SBBN

• 5

10 × D/H < 5.3

NTP

7

=10

R

T

8

=10

R

T

9

=10

R

T

10

=10

R

T

11

=10

R

T

12

=10

R

T =5

D

n

• 5

=10

D

κ =80 GeV m < 1 s

N L S P

τ

(GeV)

1/2

m

3

10 (GeV)

3/2

m

• 1

10 1 10

2

10 (GeV)

1/2

m

3

10 (GeV)

3/2

m

• 1

10 1 10

2

10

Gravitino not LSP

L i 6 / L i 7 > . 6 6 L i 6 / L i 7 < . 1 5

• 10

10 × Li7/H > 2.5

SBBN

• 5

10 × D/H < 5.3 NTP =8

D

n

• 5

=10

D

κ =80 GeV m

< 1 s

NLSP

τ

(GeV)

1/2

m

3

10 (GeV)

3/2

m

• 1

10 1 10

2

10

Sean Bailly Gravitino, dark matter candidate and BBN 39/ 40

SLIDE 43

Conclusion

Dark matter Gravitino good cadidate Non-thermal production and thermal production Lithium problems Scenario to solve the lithium problems SBBN puts constraints on the model Modified Hubble parameter Solution for the reheating temperature Lighter mass spectrum Constraints on the pre-BBN era

Sean Bailly Gravitino, dark matter candidate and BBN 40/ 40