Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 1'

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Neutralino Dark Matter in the NMSSM

Daniel E. Lopez-Fogliani

Universidad Autonoma de Madrid

Departamento de Fısica Teorica and IFT

D. Cerdeno, C. Hugonie, D. L-F., C. Munoz, A. Teixeira, JHEP 0412 (2004) 048

E. Gabrielli, D. L-F., C. Munoz, A. Teixeira, hep-ph/06?????

IRGAC 2006, Barcelona, 11-15 July

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 2'

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Index

Introduction

Dark Matter in the NMSSM

• The NMSSM

• The DM-Nucleus Cross Section

• Experimental constraints

• Analysis of DM in the NMSSM

Conclusions

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 3'

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The problem of galaxy rotation curves

Far from the center of the galaxy we expect: v =√

GMvis

R∼ 1√

R

But observation gives v ∼ cte

Solution

Dark Matter: Postulated for the first time by Zwicky (1933)

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 4'

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WMAP

Energy composition of the Universe

• Ordinary Matter→ 4 %

• Dark Matter→ 23 %

• Dark Energy→ 73 %

Cold Dark Matter→ 0.094 . Ωh2 . 0.129 WMAP’06

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 5'

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WIMPs

• WIMP’s very promising and exciting DM candidates:

stable, massive, weakly interacting particles;

enough WIMP’s left after Big Bang to acount for observed DM

SUSY

• R parity→ the LSP is absolutely stable

• SUSY provides good candidates to Dark Matter

From SUSY models→ the WIMP by excellence is the lightest Neutralino

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 6'

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WIMP’s Direct Detection

Since 1987 there are a lot of experiments around the world

for direct and indirect detection of WIMP’s

target crystal

recoiling nucleus

scattered particle

• DAMA claim: detection of DM σ ∼ 10−7− 6 × 10−5pb

POLEMIC RESULT

• EDELWEISS, CDMS (Soudan), GEDEON, ......

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 7'

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Why going beyond the MSSM? Why the NMSSM?

Solves a problem of naturalness in the MSSM: the µ problem

Less severe ”Higgs-little fine tuning” problem than in the MSSM

NMSSM

Superpotential

WWW = ǫij

(

Yu Hj2 Qi u + Yd Hi

1 Qj d + Ye Hi1 Lj e

)

− ǫijλλλ S Hi1H

j2 +

1

3κκκS3

Higgs soft terms of the NMSSM

−LLLHiggssoft = m2

HiH∗

i Hi + m2Sm2Sm2S S∗S + (−ǫijλλλAλAλAλSHi

1Hj2 + 1

3κκκAκAκAκ S3 + H.c.)

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 8'

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NMSSM potential

After EW Symmetry breaking: < H01 >= v1, < H0

2 >= v2, < S >= s

µeff = λsµeff = λsµeff = λs

〈V Higgsneutral〉 =

g2

1+g2

2

8

(

|v1|2 − |v2|

2)2

+ |λ|2(

|s|2|v1|2 + |s|2|v2|

2 + |v1|2|v2|

2)

+|κ|2|s|4 + m2H1|v1|

2 + m2H2|v2|

2 + m2S |s|

2

+(−λκ∗v1v2s∗2 − λAλsv1v2 + 1

3κAκs3 + H.c.)

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 9'

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Minimization of the scalar potential

Finding a minimum of V is much harder than in the MSSM ...

From the minimization of the potential with respect to the phases of the VEV’s we have

four combinations of signs for Aκ Aλ, s and k :

(i) sign(s) = sign(Aλ) = −sign(Aκ),

(ii) sign(s) = −sign(Aλ) = −sign(Aκ),

with |Aκ| > 3λv1v2|Aλ|/(−|sAλ|+ κ|s2|). k > 0

(iii) sign(s) = sign(Aλ) = sign(Aκ),

with |Aκ| < 3λv1v2|Aλ|/(|sAλ|+ κ|s2|).

(iv) sign(s) = sign(Aλ) = sign(Aκ),

with |Aκ| > 3λv1v2|Aλ|/(|sAλ| − κ|s2|). k < 0

We must also satisfy the minimization Eqs. for |v|

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 10'

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NMSSM Particle content

NMSSM Spectrum ≡ MSSM +

8

<

:

2Higgs (CP − even, CP − odd)

1Neutralino

Mχ0 =

0

B

B

B

B

B

B

B

@

M1 0 −MZ sin θW cos β MZ sin θW sin β 0

0 M2 MZ cos θW cos β −MZ cos θW sin β 0

−MZ sin θW cos β MZ cos θW cos β 0 −λs −λv2

MZ sin θW sin β −MZ cos θW sin β −λs 0 −λv1

0 0 −λv2 −λv1 2κs

1

C

C

C

C

C

C

C

A

The lightest neutralino:

χ01χ01χ01 = N11B

0 + N12W03 + N13H

01 + N14H

02 + N15S15S15S

The lightest CP-even Higgs:

h01h01h01 = S11H

01 + S12H

02 + S13S13S13S

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 11'

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Dark matter: Direct detection in the NMSSM..

..

~01q ~q ~01q. .

. .~01

q h0i~01qLeff = α3i

¯χ01 χ0

1 qiqi

αh3i =

∑3a=1

1m2

h0a

CiY Re [Ca

HL]

αq3i = −

∑2X=1

14(m2

Xi−m2χ01)Re

[(

CXiR

) (

CXiL

)∗]

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Relic density

Enough χ01 can survive annihilation (and coannihilation) in order to account for observed Ω

For example: χ01 χ0

1⇒

W± W± , Z Z

h0 h0 , a0 a0 , h0 Z

q q , l+ l−

NMSSM similar to MSSM, but additional ”fingerprint”-type processes like.

.

.

.

χ01

χ01

h01

q ( l+)

q (l−)

where χ01 ! singlino; h0

1 ! singlet

BUT! Generating large σ may lead to excessive χ01-annihilation (low Ω)

See also Belanger et al., ’05

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b→ s γ

Experimental data [HFAG ’06]: BR(b→ sγ)= (3.55± 0.27)× 10−4

Theoretical calculation for the SM [Gambino ’05]: BR(b→ sγ)= (3.73± 0.30)× 10−4

SUSY contributions at 1 loop-level

• Charged Higgs H± and up quarks u, c, t

• Chargino χ± and up squarks u, c, t

• Neutralino χ0 and down squarks d, s, b

• gluino g and down squarks d, s, b

In our analysis: dominant H±-mediated contribution! [No flavour mixing other than the VCMK]

⇒ BR(b→ sγ) ∝ 1/m4H± with m2

H± = 2µ2

sin(2β)κλ− v2λ2 + 2µAλ

sin(2β) + m2W

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Constraints on the NMSSM parameter space and computation

Relevant parameters at low scale λ, κ, tanβ, µ, Aλ, Aκ, M1, M2, M3 (M0, A0)

• Minimization of the potential

• Absence of Landau Pole for λ, κ, Yt, and Yb below MGUT

• Computation of the NMSSM spectrum NMHDECAY 2.0

• Experimental constraints from LEP (Ellwanger, Hugonie)

Neutralino

Higgs

Squark

• b → s γ (gµ − 2), rare B and K decays

• Dark Matter Relic density New MicrOMEGAs

• Neutralino Nucleon Cross Section

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 15'

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BR(b→ sγ) in the NMSSM: Results

Motivated by previous analysis of DM direct detection [Cerdeno, Hugonie, L-F, Munoz, Teixeira, ’04]

M1 = 500 GeV, M2 = 1 TeV, Aλ = 200 GeV, Aκ = −200 GeV, µ = 150 GeV, tan β = 3

b→ sγ isocurves ”mimick” mH± isocurves

b→ sγ typically maximal close to tachyon ”border”

Improve b→ sγ: larger (Aλ, µ, tanβ)←→Worsens exclusion by LEP constraints

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 16'

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Phenomenology in the λ-κ plane

For the same parameters as the previous study

M1 = 500 GeV, M2 = 1 TeV, Aλ = 200 GeV, Aκ = −200 GeV, µ = 150 GeV, tan β = 3

blue dots ↔ S213 = 10, 90%; black full ↔ N2

15 = 10%; red dashed ↔ mh0

1

= 114, 75, 25 GeV;

Very light neutral Higgs: mh0

1& 20 GeV; singlet component: 0.9 . S2

13 . 0.95;

Higgsino-singlino LSP ⇒ Very distinct features from expected in MSSM!

LEP constraints: violating h0 → bb bounds

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Dark Matter: Ω and direct detection

For the same parameters as the previous study

M1 = 500 GeV, M2 = 1 TeV, Aλ = 200 GeV, Aκ = −200 GeV, µ = 150 GeV, tan β = 3

Gray → Experimentally excluded Green → Not satisfing WMAP constraints for the relic density

Red → Satisfies all experimental constraints

Large σ→ exchange of light singlet-like higgs

Dominant annihilation channel: χ0 χ0 → ZZ, W+W−

ΩWMAP → vicinity of tachyons ”border”; b→ sγ within 2σ

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NMSSM DM: further examples

M1 = 160 GeV, M2 = 320 GeV, Aλ = 300 GeV, Aκ = −50 GeV, µ = 150 GeV, tan β = 3

⋆ Nearly degenerateM1-µ: Bino-Higgsino-Singlino admixture;

⋆ Compatible with Ω and b → sγ (2σ): mh0 ≈ 70GeV and mχ0

1

≈ 100GeV

⋆ Within CDMS-Soudan range: MSSM-like scenario (heavier h01, Higgsino-like χ0

1)

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NMSSM DM: further examples

M1 = 320 GeV, M2 = 660 GeV, Aλ = 480 GeV, Aκ = −60 GeV, µ = 180 GeV, tan β = 3

⋆ Singlino-like χ01 & singlet-like h0

1; clear NMSSM scenario

⋆ Compatible with Ω and b → sγ (2σ): mh0 ≈ 30GeV and mχ0

1

≈ 25GeV

⋆ Direct detection ross-section: within GEDEON (and CDMS-Soudan) reach

Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 20'

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Conclusions

❶ Systematic analysis of the NMSSM parameter space

Taken into account LEP constraints

BR(b→ s γ) bounds (as well as others)

WMAP data on Ω

Investigated prospects for direct detection of DM

❷ In the NMSSM, large σχ0

1−p can be obtained

Associated to t-channel exchange of very light Higgs (mh0

1

. 70 GeV),

large singlet component (escapes detection)

NMSSM nature is further evidenced in having a singlino-Higgsino LSP

❸ Impact of Ω and BR(b→ s γ)

Ω often relies on the same light-Higgs exchange that gives large σ

large σχ0

1−p↔ excessive annihilation

BR(b→ s γ) typically larger in regions where DM is WMAP-compatible & within

range of present detectors