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.)
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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
)∗]
Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 12'
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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
Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 13'
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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)
Neutralino Dark Matter in the NMSSM, D. E. Lopez-Fogliani. 19'
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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