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.