Post on 24-Jan-2021
MSSM flat directionsin the universe
Shinta KasuyaKanagawa University
KEK Theory Meeting 2005, March 4, 2005 @ KEK
DarkEnergy
73%
CDM22.4% baryon
4.6%
WMAP-only + prior (H0 >50 km/s/Mpc)0.98 < Ωtot < 1.08
Spergel et al. [WMAP collaboration] (03)
H0 = 72 ± 5 km/s/MpcΩmh2 = 0.14 ± 0.02
Ωbh2 = 0.024 ± 0.001WMAP-only, flat universe
ns = 0.99 ± 0.04
inflation+
ΛCDM model
Cosmological parameters
Structure formation
Baryogenesis
Density Perturbation
What’s the source?
What is cold dark matter?
What is the seed?
How to createBaryon asymmetry?
curvaton
Affleck-Dine field
Q ball
What is dark energy?
Quintessence
Some scalar fieldsinflaton
Structure formation
Baryogenesis
Density Perturbation
What is cold dark matter?
What is the seed?
How to createBaryon asymmetry?
curvaton
inflaton
Affleck-Dine field
Q ball
What is dark energy?
Quintessence
MSSMFlat direction
What’s the source?
Why considering MSSM ?
MSSM is the Minimal Supersymmetric Standard Model.
Why considering flat directions ?
The potential of the flat direction is very flat.
the “known” physics
Necessary for cosmology
May obtain information from collider experiments.
e.g. inflaton, Affleck-Dine field, etc.
Today’s plan
1. Introduction
2. What is MSSM flat direction?
3. MSSM flat direction as curvatonEnqvist, SK, Mazumdar (03), Enqvist, Jokinen, SK, Mazumdar(03)SK, Kawasaki, Takahashi(04)
5. MSSM flat direction as Affleck-Dine field and Q balls
6. Summary
4. MSSM flat direction as inflatonSK, Moroi, Takahashi (04)
SK, Kawasaki (00),(00),(00),(01)SK, Kawasaki, Takahashi (03)
The flat direction is a (complex) scalar field whose potential vanishes along that direction.
†
DA = F+T AFD-term F-term
†
FF =∂W∂F
,
†
V (F) = 12
DA DA + FF2
flat direction = D-flat and F-flat
i.e.,
†
DA = 0 &
†
FF = 0
is made of squarks, sleptons, and maybe higgs.
†
F
2.What is MSSM flat direction?
scalar potential
QQQLQuQdQuLeuude
MSSM flat directions
LHuHuHduddLLeQdL
dddLLuuueeQuQueQQQQu(QQQ)4LLLeuudQdQd
Dine, Randall, Thomas (96)Gherghetta, Kolda, Martin (96)
Flat directions lifted by Wren are:
†
Wren = yuQHuu + ydQHd d + ylLHde
†
Q = 13
F
0Ê
Ë Á
ˆ
¯ ˜ , L =
13
0F
Ê
Ë Á
ˆ
¯ ˜ , d =
13
FQLd LHu
†
L = 12
F
0Ê
Ë Á
ˆ
¯ ˜ , Hu =
12
0F
Ê
Ë Á
ˆ
¯ ˜
Parametrization of flat directions(examples)
lift up of flat direction
• SUSY breaking soft mass term• Non-renormalizable operator higher order terms
where m = O(TeV) , †
V (F)
†
F
†
Fm
Dine, Randall, Thomas (96)Gherghetta, Kolda, Martin (96)
QQQLQuQdQuLeuude
LHuHuHduddLLeQdL
dddLLuuueeQuQueQQQQu(QQQ)4LLLeuudQdQd
†
WNR =lFn
MPn
n=4
n=6 n=4n=4n=4n=4
n=6n=4
n=4
n=7n=4n=9n=4
n=4
n=4
3. MSSM flat direction as curvatonEnqvist, SK, Mazumdar (03), Enqvist, Jokinen, SK, Mazumdar(03)SK, Kawasaki, Takahashi(04)
Curvaton : a light scalar field which creates curvature (adiabatic) perturbation other than inflaton.
Inflaton (1) Exponential expansion
(2) Density perturbation
(3) Origin of matter: reheating
Inflation model is constrained by observation.e.g., WMAP, SDSS, …
In usual picture
3. MSSM flat direction as curvatonEnqvist, SK, Mazumdar (03), Enqvist, Jokinen, SK, Mazumdar(03)SK, Kawasaki, Takahashi(04)
Curvaton : a light scalar field which creates curvature (adiabatic) perturbation other than inflaton.
Inflaton (1) Exponential expansion
(2) Density perturbation
(3) Origin of matter: reheatingCurvaton+
Curvaton scenario may relax the condition for successful construction of inflation model.
In curvaton scenario
Dimopoulos, Lyth (04), Moroi, Takahashi, Toyoda (05)
Curvaton mechanism
Conversion of isocurvature to curvature perturbations
†
f decays into ordinary (SM) radiationAdiabatic fluctuations
is necessary to account observation.
Lyth, Wands (02), Enqvist, Sloth (02), Moroi, Takahashi (01)
†
rf
curvatonOrigin of matter:reheating
curvatonDensity perturbation
inflatonExponential expansion
Decay product is naturally (MS)SM degrees of freedom.
Inflaton couples to SM degrees of freedom.
Inflaton does not couple to SM degrees of freedom.
Completely hidden inflaton scenario
Inflaton lives in a completely hidden sector, and hence does not couple to the SM degrees of freedom at all.
(except gravitationally)Enqvist, SK, Mazumdar (03), Enqvist, Jokinen, SK, Mazumdar(03)
For successful curvaton mechanism
(1) During inflation, non-negligible fluctuation.
†
mf ,eff
Energy dominance
†
HEQ > Gd ª f2mf
†
(ph = wrh )
†
f <mfMP
Ê
Ë Á
ˆ
¯ ˜
1n-2
È
Î
Í Í Í
˘
˚
˙ ˙ ˙
1+w2w
Curvaton decays after it dominates the universe.
n=9 direction is ok.
allowed
QuQue lifted by QuQuQuHdee
Fluctuation Production
During inflation,
†
mf ,eff2 ≡ V ' '(f) = b 2H*
2
†
b
Evolution of fluctuations
†
˙ ̇ f + 3H ˙ f + V '(f) = 0
†
d˙ ̇ f k + 3Hd ˙ f k +k 2
a2dfk + V ' '(f)dfk = 0 k 0 superhorizon mode
†
xf ≡dff
dff
Ê
Ë Á
ˆ
¯ ˜
i
ªffi
Ê
Ë Á
ˆ
¯ ˜
n-42
†
˜ d = xfd ª10-5
†
d ª10-3, H* ª 5 ¥1013
After inflation, it evolves as:
Density perturbation
This is achieved, e.g., for n=9 with
†
f* ª 5 ¥1016GeV, GeV.
Decay temperature Reheating temperature in (MS)SM radiation
†
fd ª f2MP
†
Hd ª f2mf £10
-10 mf
†
f £mfMP
Ê
Ë Á
ˆ
¯ ˜
1 3
ª10-5 because
†
ffd £ mf
†
Td ª 3¥105 GeV
Baryogenesis may take place at the electroweak phase transition.CDM may be LSPs thermally produced.
Thus,
4. MSSM flat direction as inflatonSK, Moroi, Takahashi (04) For earlier attempts, Connors, Deans, Hagelin (89),(93)
ΔT/T ~ 10-5
m~10 GeV for V= m Φ 13 2 21
2_
λ~10 for -13
mΦ~TeV V= mΦ Φ is not suitable for inflation. 221
2_
Q1Huu1 direction may be the inflaton with . V= Φ 4_
4λ
λ can be 10-13 if up-quark mass is radiatively generated from supersymmetric loop diagrams.
Seeking for the possibility MSSM flat direction is an inflaton.
λV= Φ 4_
4
†
l =13
yu2, yu =
muv sinb
ª8.6 ¥10-6
sinbmu
1.5MeVÊ
Ë Á
ˆ
¯ ˜ a bit larger
Loop correction to up-quark mass
Relevant part of SUSY breaking terms
where
is on the verge.
Comparison with observation
nS = 1 - ≈ 0.953
N+3/2
r = ≈ 0.2416
N+3/2
Spectral index
Tensor-to-scalar ratio
e-folding number N ≈ 64, irrespective of TRH.
Tegmark et al. [SDSS collaboration] (04)
Curvature perturbation (adiabatic fluctuation) is created.
_λV= Φ 4
4
5. MSSM flat direction as Affleck-Dine field and Q ballsSK, Kawasaki (00),(00),(00),(01), SK, Kawasaki, Takahashi (03)
†
Q = d3xÚ f 2 ˙ q
Affleck-Dine mechanism
(2) Rotation in the potential.
Baryon number production
(3) Affleck-Dine field decays into quarks.
(1) Large vev during inflation.
Affleck, Dine (85)
†
F = f exp(iq) / 2
†
F possesses baryon number.
MSSM flat direction is a perfect candidate. Affleck, Dine (85), Dine, Randall, Thomas (85)
Q-ball formation
All the baryon numberis absorbed into Q balls
†
f†
V (f)
m-1
Homogeneous condensate
Spatial instabilities
Q balls
m (Φ) Φ is shallower than φ .2 2 2
Gauge-mediation
Q ball: Emin configuration of a scalar field with Q=fixed.
Coleman (85)
Kusenko, Shaposhnikov (98)
SK, Kawasaki (00)
Affleck-Dine field (Flat direction)
Q-ball formation
Stable Unstable
Q balls
decay
LSP
Evaporationbaryon
Gauge-mediation Gravity-mediation
B &DM1
(for/against decay into nucleon)
M = m Q3/4
M /Q > GeV
M = m QQM /Q < GeVQ Q
Q
Ω ~ Ω is naturally obtained.B DM
Dark matter Dark matterbaryon
Relation between baryon and dark matter.
Affleck-Dine field (Flat direction)
Q-ball formation
Stable Unstable
Q balls
decay
LSP
Evaporationbaryon
Gauge-mediation Gravity-mediation
B &DM2
(for/against decay into nucleon)
M = m Q3/4
M /Q > GeV
M = m QQM /Q < GeVQ Q
Q
Ω ~ Ω is naturally obtained.B DM
Dark matter Dark matterbaryon
Relation between baryon and dark matter.
detectable
SU(3)c(1) inside the Q ball
p q q q (surface layer)+ 1 GeV energy release
soft pions
Quarks are absorbed into the condensate
heavy gluino exchange
q
q
q
q(2) Observables
Flux:F < F ~DM2
Cross section: ρDM~ 0.3 GeV/cm , v ~ 10 c3 -3
σ~ πRQQ
ρDM v4πM
Detection
SK dataTakenaga et al. [SK collaboration] (05)
Kusenko et al. (98)Arafune et al. (00)SK, Kawasaki (01)
6. Summary
MSSM flat direction may play the important roles in the early universe.