Affleck-Dine leptogenesis via multiscalar evolution in a seesaw - - PowerPoint PPT Presentation

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Affleck-Dine leptogenesis via multiscalar evolution in a seesaw model

(ICRR, Univ of Tokyo)

高山 務

共同研究者: 瀬波大土

• Dec. 11. 2007

宇宙線研究所理論研究会「初期宇宙と標準模型を超える物理」 東京大学宇宙線研究所

JCAP11(2007)015 M.Senami, TT

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Outline

２Set-up ・Scalar potential ・initial condition ３Evolution of scalar fields ４Evolution of asymmetry ５Constraints ６Resultant baryon asymmetry ７Summary １Introduction

・

• direction and RH-sneutrino

LHu

・Leptogenesis via Affleck-Dine mechanism: an alternative to thermal leptogenesis in SUSY

˜ N only (Allahverdi & Drees, 2004)

multiscalar

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Standard Model (SM) + Heavy right-handed Majorana neutrino

１. Introduction

possible solution of two unsolved problem of SM 1)

Majorana mass: Dirac mass: lighter mass eigenvalue ∼ m2 M

m¯ LνR

M ¯ νRνR

νR : right-handed neutrino

Origin of small neutrino mass 2) Origin of baryon asymmetry

baryon-to-entropy ratio: nB s = 8.7+0.3

−0.4 × 10−11 (WMAP)

example: thermal leptogenesis

mν O(0.1)eV

seesaw mechanism

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・ -flat direction

１. Introduction

・sufficient baryon asymmetry requires in SUSY, gravitino is overproduced unless TR < 108GeV

alternatives？

Affleck-Dine leptogenesis from right-handed sneutrino

TR > M > 109GeV LHu-flat direction has large vev LHu-flat direction has vanishing vev

      

LHu

many non-thermal leptogenesis scenarios are considered...

AD mechanism in multiscalar evolution (Senami & Yamamoto, 2003)

• flat direction is irrelevant? (Allahverdi & Drees, 2004)

LHu

L = 1 √ 2

• φ
• ,

Hu = 1 √ 2

• φ

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１. Introduction: Affleck-Dine mechanism

complex scalar field with baryon (or lepton) number φ 1

total baryon (or lepton) number in homogeneous condensate of φ

“angular momentum” of φ baryon (lepton) number rotational motion after inflation

Re(φ) Im(φ)

baryon (lepton) number in condensate

φ

• ( -) conserving decay

B L

baryon (lepton) number in SM particles

n = nφ − ¯ nφ = i( ˙ φ∗φ − φ∗ ˙ φ) = 2|φ|2 ˙ θ φ = |φ|eiθ

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１. Introduction

due to interaction with , -flat direction gets large value!

Allahverdi & Drees’s scenario (brief review)

assumption: -direction does not contribute (always )

φ = 0 LHu

LHu ˜ N

・asymmetry is produced via Affleck-Dine mechanism

n ˜

N − n ˜ N∗

tuning is needed (decay at maximum) ・asymmetry is oscillating: n ˜

N − n ˜ N∗ ≃ t−2M −1 N N 2 0 sin(2Bm3/2t)δeff

|B|m3/2 ≃ Γ ˜

N

V ( ˜ N) = m2

0| ˜

N|2 + CIH2| ˜ N|2 + (Bm3/2 ˜ N 2 + h.c.) + (bH ˜ N 2 + h.c.)

・ SM sector lepton number

• violating decay of

CP

˜ N

n ˜

N − n ˜ N∗

• r

SUSY-breaking from thermal effect thermal mass Γ ˜

N→Hu ˜ L = Γ ˜ N→ ¯ ˜ Hu ¯ L

bosonic, fermionic,

∆L = 1 ∆L = −1

  

∆m2

B = 2∆m2 F

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２. Set-up

seesaw mechanism:

·

mν = y2

νv2

MN

２. Set-up of the model: scalar potential

+Vth(φ)

cross term in F-term Hubble-induced SUSY breaking mass term thermal-mass correction

cφ ∼ 1 > 0, cN ∼ 1 > 0

※

, |a| ∼ 1, |b| ∼ 1 V (φ, ˜ N) = y2

ν

4 |φ|4 + MN| ˜ N|2 + y2

ν|φ|2| ˜

N|2 + λ2 M 2

Pl

| ˜ N|6 + yν 2 MNφ2 ˜ N ∗ + yνλ 2MPl φ2 ˜ N ∗3 + λMN MPl ˜ N ˜ N ∗3

• + h.c.
• F-term

+cφH2|φ|2 − cNH2| ˜ N|2 + bH 2 MN ˜ N 2 + ayyν 2 Hφ2 ˜ N + aλλ 4MPl H ˜ N 4

• + h.c.
• Hubble-induced SUSY breaking

A- and B-term ： direction

φ

˜ N ：RH-sneutrino

superpotential: W = WMSSM + yνNLHu + MN

2 N 2 + λ 4MPl N 4

L = 1 √ 2

• φ
• ,

Hu = 1 √ 2

• φ
• LHu

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( case) ( case)

２. Set-up of the model: initial conditions

˜ N : displaced from the origin

・radial direction:

: fixed at the origin due to large effective mass φ meff ∼ yνMGUT during the inflation,

φ has quantum fluctuation around the origin

φhor ∼ H 2π H meff

H ≫ MN

・phase direction can either be

randomly displaced from B-term minima

• r, trapped at B-term minima

  

Hinf MN

Hinf ≫ MN

MGUT

MGUT = 1016GeV ※hereafter,

D-term +Hubble

※ is assumed

MN/λ > 1.2 × 1014GeV

| ˜ N|

NR F-term can not be used to trap ˜

Nini

| ˜ Nini| = MGUT

(Hubble-induced mass and D-term)

F-term

NR F-term +Hubble

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① during inflation:

phase-direction is assumed to be trapped at the minimum of B-term contribution is trapped at the origin

３. Evolution of scalar fields

due to balance between Hubble-induced mass and D-term,

H = Hinf > MN

・ ・

| ˜ N| ∼ MGUT

・

V ˜

N ∼ −cNH2| ˜

N|2 + bH 2 MN ˜ N 2 + h.c.

• + D−term

˜ N φ

φ

Vφ ≃ cφH2|φ|2 + y2

ν| ˜

N|2|φ|2

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３. Evolution of scalar fields

˜ N φ V ˜

N ≃ M 2 N| ˜

N|2 + λMN MPl ˜ N ˜ N ∗3 + h.c.

• ② after inflation: H < MN

Vφ ≃ cφH2|φ|2 + y2

ν| ˜

N|2|φ|2 + yν 2 MNφ2 ˜ N ∗ + h.c.

• ・ oscillates with

˜ N | ˜ N| ∝ H ・ cross term in F-term contribution serves as a source of asymmetry in general, Hubble-induced A- and B-terms are effective only during inflation ※ ・ displacement between B-term and cross term gives -violation CP is trapped at the origin ・ φ

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in general, inflaton: , : oscillating “Hubble-induced” - or -terms A B due to rapid oscillation of , these terms effectively vanish

for example,

δI ∝ δI

δI I = I + δI

K(I, φ) = I†I + φ†φ +

• a

2MPl I†φφ + h.c.

• ※higher order terms of can give effectively non-vanishing - or -terms

however, these terms decrease rapidly

W(I) = I{v2 − gIn/(n + 1)}

  

(new inflation)

V ∋ −aWφφ† eKF ∗

¯ I

MPl + h.c. = aWφφ†eK 2vδI† MPl − aWφφ†eK (δI†)2 MPl + h.c. H2 ≃ 4v2|δI|2 3M 2

Pl

  

∂IW ∝ (δI)2 B A

H2 ≃ m2

I,eff|δI|2

3M 2

Pl

３. Evolution of scalar fields

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３. Evolution of scalar fields

・ ・

˜ N φ V ˜

N ≃ M 2 N| ˜

N|2 + λMN MPl ˜ N ˜ N ∗3 + h.c.

• ③ destabilization:

two minima appear in opposite directions minimize the cross term after and decrease sufficiently, | ˜ N| H ・ position of these minima rotate together with the rotation of these two minima are determined by ˜ N ˜ N Allahverdi & Drees did not consider this process ※

yνMN| ˜ N| ∼ y2

ν| ˜

N|2 + cφH2 Vφ ≃ y2

ν| ˜

N|2|φ|2 + yν 2 MNφ2 ˜ N ∗ + h.c.

• + y2

ν|φ|4/4

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３. Evolution of scalar fields

・ ・

˜ N φ

④ after destabilization: H < MN, yνMN| ˜

N| > y2

ν| ˜

N|2 + cφH2

V ˜

N ≃ M 2 N| ˜

N|2 + y2

ν| ˜

N|2|φ|2 + yν 2 MNφ2 ˜ N ∗ + h.c.

• scillates around the minimum

determined by rotating ˜ N φ

• scillates around one of minima

determined by the cross term φ ・ to which minima falls is determined by quantum fluctuation φ spatially inhomogeneous

Vφ ≃ y2

ν| ˜

N|2|φ|2 + yν 2 MNφ2 ˜ N ∗ + h.c.

• + y2

ν|φ|4/4

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３. Evolution of scalar fields

・ ・

˜ N φ

⑤ after decay of : （friction term dominates the evolution of ） ˜ N

˜ N H < Γ ˜

N = y2 νMN/(4π)

after the condensate of decays, is fixed at the minima ˜ N ˜ N

Vφ,eff ≃ y4

ν

4 |φ|6 M 2

N

+ Vth(φ)

φ

• scillates around the origin

・ the direction of rotation is determined by the rotation of at ② ˜ N

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３. Evolution of scalar fields: numerical result

evolution of scalar fields (numerical calculation)

106 107 108 109 1010 1011 1012 1013 1014 1015 1016 1017 104 105 106 107 108 109 1010 1011 1012 1013

|φ| | ˜ N|

field [GeV]

① ② ③ ④ ⑤

H [GeV]

MN = 1011GeV, yν = 10−1, TR = 2 × 106GeV cφ = cN = 1, λ = 10−4

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３. Evolution of scalar fields: remarks

Allahverdi & Drees did not consider destabilization of φ in ②, must not be trapped at the minima of F-term contribution VN,FNR = M 2

N| ˜

N|2 − 2λMN MPl | ˜ N|4 + λ2 M 2

Pl

| ˜ N|6

˜ N

MN/λ > 1.2 × 1014GeV is needed

we reconsidered this scenario final direction of rotation of is determined by the rotation of in ② non-vanishing is generated after averaging over initial quantum fluctuation of Lφ

φ

※Remarks:

φ

˜ N

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４. Evolution of asymmetry

before is destabilized, does not contribute to asymmetry

φ

left-handed lepton number right-handed lepton number

L ˜

N ≡ −i( ˙

˜ N ∗ ˜ N − ˙ ˜ N ˜ N ∗)

H ∼ MN : is (almost) fixed

L ˜

N

after is destabilized, and oscillate rapidly

φ

L ˜

N

Lφ however, is almost conserved!

Lφ − L ˜

N

※ inherits fraction of

Lφ

after decays, is fixed with

˜ N

Lφ

O(1)

Lφ − L ˜

N

s′ = 4M 2

PlH2/TR

δeff = O(1)

Lφ = 0

d dt L ˜

N

H2

• + Γ ˜

N

L ˜

N

H2 ≃ d dt Lφ H2

• ≃ −yνMN

H2 Im(φ∗2 ˜ N)

(F-term is dominant)

Lφ ≡ i( ˙ φ∗φ − ˙ φφ∗)

φ

|L ˜

N|

s′ ≃ 6λM 4

GUTTR

M 2

NM 3 Pl

δeff homogeneous

d dt |L ˜

N|

H2

• ≃ − 4λMN

MPlH2 Im

• ˜

N 3 ˜ N ∗

cf:

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４. Evolution of asymmetry: numerical result

asymmetry

evolution of asymmetry (numerical calculation)

H [GeV]

10-26 10-24 10-22 10-20 10-18 10-16 10-14 10-12 10-10 10-8 104 105 106 107 108 109 1010 1011 1012 1013

|Lφ − L ˜

N|

s′ |Lφ| s′ |L ˜

N|

s′

① ② ③ ④ ⑤

lepton asymmetry is nonperturbatively transfered to -direction LHu

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because is homogeneous, final averaged over the fluctuation is non-vanishing

４. Evolution of asymmetry: homogeneity of

vanishes on an average over the universe?

Lφ and oscillate rapidly, but conserving L ˜

N

Lφ Lφ − L ˜

N

center of the oscillation of is determined by homogeneous at the destabilization

※potential minima of is determined by homogeneous φ

˜ N

the direction of the rotation of these minima is one definite direction all over the universe

| ˜ N| = 0 | ˜ N| = 0

L ˜

N

Lφ

sgn(Lφ)

Lφ L ˜

N

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isocurvature perturbation of

５. Constraints on this scenario

baryon isocurvature perturbation Ba =

• PS

PR < 0.31

※if the phase minimum is displaced from the minimum of B-term during the inflation, this constraint can be avoided

positive thermal-mass can prevent the destabilization reheating temperature must be sufficiently low: TR < 6.5 × 106GeV × g∗ 100 1

4

mν 0.01eV 1

4

MN 109GeV 5

4

※Allahverdi & Drees’s scenario can work for higher TR

MN < Hinf < 3 × 1012GeV

θ ˜

N

baryon isocurvature perturbation

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parameter region which give (red lines)

６. Resultant baryon asymmetry: constraint on parameters

MN [GeV] TR [GeV]

102 103 104 105 106 107 108 109 1010 108 109 1010 1011 1012 1013

λ = 10−5 10−4 10−3 10−2 mν = 10−2eV 10−4eV 10−6eV destabilization of is prevented above these lines dotted parts are excluded by the condition

nB/s = 8.7 × 10−11

MN/λ > 1.2 × 1014GeV φ

nB s ∼ 8.7 × 10−11 ×

• λ

10−4 MGUT 1016GeV 4 MN 1011GeV −2 TR 6 × 106GeV

• analytically,

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７. Summary

we reconsidered Affleck-Dine leptogenesis in SUSY seesaw model

• flat direction is relevant even if it has positive Hubble-induced mass term

LHu

for higher , Allahverdi & Drees’s scenario can work TR charge asymmetry is generated in condensate, then transfered to -flat direction

˜ N

LHu

sufficient baryon asymmetry can be generated ※this scenario is difficult if | ˜

Nini| < MGUT

(for example, )

| ˜ Nini| = MSU(2)R < MGUT

※small is desirable for this scenario λ ※unlike Allahverdi & Drees, fine tuning is not needed ※only the initial evolution of determines the final baryon asymmetry

˜ N