Level Crossing between QCD Axion and ALP collaboration with Naoya - - PowerPoint PPT Presentation

Level Crossing between QCD Axion and ALP

collaboration with Naoya Kitajima & Fuminobu Takahashi

Ryuji Daido Tohoku Univ.

1505.07670 1510.06675

@TeVPa 2015 Kashiwa, Japan

Axions

shift symmetry discrete shift symmetry

Non-perturbative effect

・Axion Like Particles (e.g. String theory)

a → a + C

V = const

a

V ' Λ4  1 cos ✓ a Fa ◆

a

・QCD axion (solves the strong CP)

L ⊃ θ 32π2 F ˜ F, |θ| . 10−10

1/11

a

aH

Mixing

mH ≡ Λ2

H

FH/nH

VQCD = ma(T)2F 2

a

 1 − cos ✓ a Fa ◆

mixing

VH = Λ4

H

 1 − cos ✓ nH aH FH + na a Fa ◆ mH

ma(T)

mH < ma(T = 0)

ma(T) = 8 < : 4.05 × 10−4 Λ2

QCD

Fa

⇣

T ΛQCD

⌘−3.34 3.82 × 10−2 Λ2

QCD

Fa

T > 0.26ΛQCD T < 0.26ΛQCD

temperature dependent

2/11

ma(T = 0)

Level Crossing

• Time

Mass

level crossing

m1 m2

mH

ma(T)

mH < ma(T = 0) Level crossing takes place!

3/11

VQCD = ma(T)2F 2

a

 1 − cos ✓ a Fa ◆ VH = Λ4

H

 1 − cos ✓ nH aH FH + na a Fa ◆

Hill, Ross, NPB 311, 253 (1988), Kitajima, Takahashi, 1411.2011

High temperature Low temperature

heavy light

4/11

Level Crossing

Time evolution of the potential

VQCD = ma(T)2F 2

a

 1 − cos ✓ a Fa ◆ VH = Λ4

H

 1 − cos ✓ nH aH FH + na a Fa ◆

ALP Q C D a x i

• n

ALP Q C D a x i

• n

θ ≡ a Fa θH ≡ aH FH θ ≡ a Fa θH ≡ aH FH

global minima

Timing of level crossing

Hlc ⌧ Hosc (ⅰ)

(The axion starts to oscillate well before the level crossing.)

The resonant transition occurs like the MSW effect.

(ⅱ) Hlc ∼ Hosc

The axion exhibits non-trivial behavior!

5/11

The potential changes adiabatically.

The adiabaticity is broken.

Kitajima, Takahashi, 1411.2011 RD, Kitajima, Takahashi, 1505.07670 RD, Kitajima, Takahashi, 1510.06675

Hlc Hosc = O(0.1 − 1)

1.Kicked into different directions.

• 1
• 0.5

0.5 1 2 4 6 8 10 n2a2/2πf2 n1a1/2πf1

• 2.Initial energy is greater

than the barrier. @ oscillation

θ θH

Two conditions satisfied, the axion passes through many crests and troughs of the potential.

Axion roulette! π −π

6/11

Axion roulette

ALP Q C D a x i

• n

crest trough

RD, Kitajima, Takahashi, 1505.07670 RD, Kitajima, Takahashi, 1510.06675

ρosc > Λ4

0.5 1 1.5 2 2.5 3

• 1500
• 500

500 1500 i (H+5)f

The final value is highly sensitive to θi

2.00000 2.00005 2.00010

• 20

20 40 i (H+5)f

7/11

θi

Numerical Results

ALP (final value) QCD axion (initial value)

(nHθH)f

(nHθH)f

The ALP takes different value even for .

δθi ∼ 10−5 .

θi = ai Fa

θi

Numerical Results

8/11

Fa = 1012 GeV, θi = 2.5, na = 5

• 1000

Θf

100 10 10 1000 100

Hlc Hosc . 0.1

10−8

10−7

10−6

ALP mass mH[eV]

• 109

1010 1011 1012

decay constant FH/nH[GeV]

Hlc Hosc & 1 Hlc Hosc = O(0.1 − 1)

(nHθH)f

ρosc > Λ4

ρosc < Λ4

If the axion roulette occurs, domain walls without cosmic strings are likely to be formed. It is cosmologically problematic.

Solution 1

9/11

Domain wall problem

Diluting the domain wall by inflation.

It is unlikely that inflation continues until the QCD phase transition.

ALP mass decay constant

However, in our situation,..

Domain wall problem

Solution 2

Introduce a bias term and makes the domain wall unstable.

2π ・If the axion is trapped in identical minima, we cannot introduce bias.

ALP mass decay constant

10/11

However, please note that.. ・ determines identical minima.

nH

nH = 3

θH

・Bias can be introduced if

nH 1

• r

the spatial variation of .

(θH)f < 2π

・We studied level crossing between QCD axion and ALP.

11/11

Summary

・We found that the axion roulette occurs if the timing of level crossing is close to that of oscillation. ・We determined the parameter region where the axion roulette takes place.

10−7eV . mH . 5 × 10−6eV, FH/nH . 109GeV

10−8eV . mH . 5 × 10−7eV, FH/nH . 1011GeV

Fa = 1012GeV Fa = 1010GeV

for for

・Stable domain wall is likely to be formed by the axion roulette. ・Bias can be introduced if nH 1 the spatial variation of .

• r

(θH)f < 2π