Fast-rolling relaxion KMI, Nagoya University Yutaro Shoji In - - PowerPoint PPT Presentation

Fast-rolling relaxion

KMI, Nagoya University Yutaro Shoji

In collaboration with M. Ibe and M. Suzuki in ICRR, IPMU PPP 2019, YITP, 29 Jul - 2 Aug 2019 1904.02545/hep-ph

Introduction

Little Hierarchy

Photo by Azuma Makoto

New physics

(100GeV)^2 (10TeV)^2 ?

SM

Dynamical solution

(100)^2 (110)^2 (90)^2 Many vacua vacua with different Higgs mass

Photo by Naser Mizban

The EW scale is chosen by dynamics of a field

Relaxion mechanism

V (Φ, X) = (M 2 − ✏X)|Φ|2 − r✏M 2X + Λ4(|Φ|2) cos X f + 4|Φ|4,

Higgs Relaxion

Slope Higgs mass Back reaction

M 2 − ✏X = 0

X

V

Slow-roll [P. W. Graham, D. E. Kaplan, S. Rajendran; ’15] due to inflation

M = O(10TeV)

We assume

Quantum tunneling

dV dX = 0

The relaxion stops classically at Then, it tunnels into lower vacua

τ ⌧ H−1

τ H−1

[P. W. Graham, D. E. Kaplan, S. Rajendran; ’15] Lifetime Lifetime

Timescale of tunneling

τ H−1

γ ⌧ H4

At the last tunneling, Bubble nucleation rate The lifetime of each Hubble patch is τ H3

H4

Inflation lasts until ∆Ne H4

H4

🤕

H4 H4 ?

Too large e-folds

Ne H4 H4 ' 10156 ✓ H 1 MeV ◆4

It is argued that a too large number of e-folds will cause problems in inflation sector e.g.) [K. Choi, S. H. Im; ’16] To avoid fine-tuning, we need (in the context of scanning time)

Ne . 1024

for slow-roll inflation [H. Matsui, F. Takahashi; ’18, K. Dimopoulos ’18,…] Eternal inflation is generically incompatible with the (refined) de Sitter swampland conjecture + Why not multiverse?

Fast-rolling relaxion

Fast-roll

dV dX = 0

The relaxion DOES NOT stop classically at It continues to roll down the potential

τ ⌧ H−1

τ H−1

Stopping mechanism

We need another stopping mechanism ex) particle production with

X f F ˜ F

[A. Hook, G. Marques-Tavares; ’16, …] But, we want something

Model

No extension!

V (Φ, X) = (M 2 − ✏X)|Φ|2 − r✏M 2X + Λ4(|Φ|2) cos X f + 4|Φ|4,

M 2 − ✏X = 0

X

V

Fast-roll

Λ4(|Φ|2) = Λ4 2 + Λ2

h|Φ|2.

Original non-QCD potential It just goes through? [P. W. Graham, D. E. Kaplan, S. Rajendran; ’15]

Higgs homogeneous

• scillation

X

V

• [ / ]

[ ]

Something happens here!

“Gradual” growth of Higgs homogeneous oscillation

Contents

• Introduction
• Edge solution
• Stopping mechanism
• Parameter space
• Summary

Edge solution

Equations of motion

¨ ¯ X + 3H ˙ ¯ X = ✏ ✓ rM 2 + ¯ h2 2 ◆ + Λ4

0 + Λ2 h¯

h2 2f sin ¯ X f , ¯

n ¯ X

)¯ h

: Relaxion homogeneous mode : Higgs homogeneous mode

✓ ◆ ¨ ¯ h + 3H ˙ ¯ h = −(M 2 − ✏ ¯ X)¯ h − 4 ¯ h3 − Λ2

h¯

h cos ¯ X f ,

Terminal velocity

˙ ¯ X ' ✏rM 2 3H

¨ ¯ h + 3H ˙ ¯ h ' (m2 δm2t)¯ h λ 4 ¯ h3 Λ2

hh cos ωt

m2 = M 2 − ✏ ¯ X(0)

m2 = f! = ✏rM 2 3H

Oscillatory solution

¨ ¯ h + 3H ˙ ¯ h ' (m2 δm2t)¯ h λ 4 ¯ h3 Λ2

hh cos ωt

t) = A sn r m2 + λ 8A2t, A2λ 8m2 + A2λ ! ' A sin(m(A)t) ,

¯ h(t)

A :

Amplitude of oscillation

m2(A) = π2(8m2 + A2λ) 32 ⇥ K

• A2λ

8m2+A2λ

⇤2 ' m2 + 3 16λA2

Effective mass

• 1.0
• 0.5

Parametric resonance

¨ ¯ h + 3H ˙ ¯ h ' (m2 δm2t)¯ h λ 4 ¯ h3 Λ2

hh cos ωt

¨ ¯ h ' m2(A)¯ h Λ2

hh cos ωt

Mathieu equation Exponential growth of the amplitude occurs when

ω2 4 ✓ 1 − 3 2 Λ4

h

ω4 ◆ − Λ2

h

2 r 1 − 3 8 Λ4

h

ω4 . m2(A) . ω2 4 ✓ 1 − 3 2 Λ4

h

ω4 ◆ + Λ2

h

2 r 1 − 3 8 Λ4

h

ω4

m2(A)¯ h

Edge solution

¨ ¯ h + 3H ˙ ¯ h ' (m2 δm2t)¯ h λ 4 ¯ h3 Λ2

hh cos ωt

m2 − δm2t

A

Resonance

Edge solution Effective mass Edge of resonance band

m2 δm2t + 3 16λA2 ' ω2 4 ✓ 1 3 2 Λ4

h

ω4 ◆ + Λ2

h

2 r 1 3 8 Λ4

h

ω4

Numerical check

¨ ¯ h + 3H ˙ ¯ h ' (m2 δm2t)¯ h λ 4 ¯ h3 Λ2

hh cos ωt

• ¯

h

m2 δm2t + 3 16λA2 ' ω2 4 ✓ 1 3 2 Λ4

h

ω4 ◆ + Λ2

h

2 r 1 3 8 Λ4

h

ω4

Edge solution (full)

¨ ¯ X + 3H ˙ ¯ X = ✏ ✓ rM 2 + ¯ h2 2 ◆ + Λ4

0 + Λ2 h¯

h2 2f sin ¯ X f , ¯ ✓ ◆ ¨ ¯ h + 3H ˙ ¯ h = −(M 2 − ✏ ¯ X)¯ h − 4 ¯ h3 − Λ2

h¯

h cos ¯ X f ,

• [ / ]

[ ]

m2

Φ + 3

16A2

h ' !2 X

4 + Λ2

h

2 Λ2

h(32Λ4 0 + 17Λ2 hA2 h)

128f 2!2

X

(8Λ2

h 3A2 h)(8Λ2 h A2 h)

512!2

X

9!2

X

4Λ2

h

H2 , !X ' r✏M 2 3Hf A2

h!X

8f 2

• A4

h

128f 2!X + 3A2

h!3 X

16f 2Λ4

h

H2 ,

Analytic expression Hubble friction, Back reactions, …

Inhomogeneous modes

Particle production

X

V

Λ4(|Φ|2) = Λ4 2 + Λ2

h|Φ|2.

Λ0 ∼ Λh

V (Φ, X) = (M 2 − ✏X)|Φ|2 − r✏M 2X + Λ4(|Φ|2) cos X f + 4|Φ|4,

Relaxion particles are created

Particle production

X

V

Relaxion particles are created

• [ / ]

[ ]

Decay into relaxion, Higgs, gauge, … We want to avoid the violation of the homogeneous assumption (see 1904.02545 or ask me later) => Restriction of parameters

Stopping mechanism

Stopping mechanism

X

V

The relaxion accidentally hits the bumps and stops HERE!

• [ / ]

[ ]

• [ / ]

ω / [ ]

Higgs Relaxion velocity

Negative Higgs mass

X

V

Fast-roll

V (Φ, X) = (M 2 − ✏X)|Φ|2 − r✏M 2X + Λ4(|Φ|2) cos X f + 4|Φ|4,

Positive but small Negative Higgs mass

Λ4(|Φ|2) = Λ4 2 + Λ2

h|Φ|2.

Φ

Parameter space

Parameter space

• =
• Λ = Λ []

[]

Successful relaxation Consistency of analysis Experiments

Relaxion mass (GeV)

The lifetime of each vacuum is much longer than the age of the universe

H = 10 GeV, ✏ = 0.8 GeV, r = 0.002, M = 20 TeV.

sin2 θ ' 0.2

Consistency HiggsBounds S u c c e s s f u l r e l a x a t i

• n

Suppression of inhomogeneity

It stops!

★ ★ ★ ★ ★

• Λ = Λ []

[]

• [ / ]

[ ]

Point 1 Point 2 Point 3 Point 4 Point 5

H = 10 GeV, ✏ = 0.8 GeV, r = 0.002, M = 20 TeV.

Summary

• In the original relaxion model, the tunneling phase

requires an unacceptably large number of e-folds.

• The fast-roll relaxion can easily solve this problem, but we

can not use the original stopping mechanism.

• We propose a mechanism to stop the relaxion without

extending the original model.

• The mechanism predicts a relaxion that has a mass of

O(100) GeV and mixes with the Higgs boson. It improves the testability of our mechanism.