Gravitational Waves from Hidden QCD Phase T ransition by Hiromitsu - - PowerPoint PPT Presentation

Gravitational Waves from
 Hidden QCD Phase T ransition

by Hiromitsu GOTO


Kanazawa University
 
 in collaboration with
 Mayumi AOKI, Jisuke KUBO
 Based on Phys. Rev. D96 075045, (2017) arXiv:1709.07572
 
 The 21st Regular Meeting of New Higgs Working Group Dec. 22, 2017

EW Scale from
 Classical Scale Invariance Breaking

2

✤ We focus on “Classical Scale Invariant Extension”


• Weakly : Colman-Weinberg Mechanism
• Strongly : Dynamical Generation of Scale e.g. QCD


Direct Transmission 
 
 Indirect Transmission

W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 (1995)

LSM|µ2→0 + Scalar Portal λHS(S†S)(H†H)

⌦ ¯ ψψ ↵ ∼ Λ3

H

yS ⌦ ¯ ψψ ↵

λHS hSi2 H†H

⌦ S†S ↵ ∼ Λ2

H

λHS ⌦ S†S ↵ H†H

Scalar QCD QCD

• T. Hur, D-W. Jung, P. Ko and J-Y. Lee arXiv: 0709.1218, 1103.2571
• J. Kubo, K. S. Lim, M. Lindner arXiv:1403.4262

3

✤ How can we test Indirect Transmutation?

• T. Hur, D-W. Jung, P. Ko and J-Y. Lee arXiv: 0709.1218, 1103.2571

Gauge Symmetry : GSM × SU(Nc)H

LH

h S

ΛH

EW

LSM|µ2→0

SM-singlet 
 Vector-like Fermion

SM-singlet Real Scalar

Nf hSi 6= 0

H ⊃ −yS ¯

ψψ

VSM 1 2λHS hSi2 (H†H)

U(Nf)L × U(Nf)R SU(Nf)V × U(1)V

DχSB

φ

N 2

f − 1

× NG Bosons

— we can obtain the symmetry by accident

B ×…

Hidden Baryon Dynamical Origin :

⌦ ¯ ψψ ↵ 6= 0

Explicit χSB !!

Dark Matter !! = Massive

if y = 0 It may be good way to test it using DM as Hidden Hadron!
 — BUT it becomes hopeless when couplings are too small…

4

✤ Our Target : Hidden Chiral Phase Transition


Explain not only Higgs but also Dark Matter Mass

cross over SM

mu,d ms

∞ ∞

1st-order PT QCD Phase Transition Nf = 2+1 N

f

= 3

Chiral limit 
 (Scale Invariance) Pure SU(3)

In small y (Nc = Nf = 3) 
 realize First-order Chiral PT

• M. Holthausen, J. Kubo, K. S. Lim and M. Lindner, JHEP 1312 (2013) 076 

• Y. Ametani, M. Aoki, HG, J. Kubo Phys Rev D 91(2015)115007

How about GW from Hidden Chiral Phase Transition?
 — Chiral Condensation Not Higgs

⌦ ¯ ψψ ↵

hhi 6

What we have known so far How deal with
 non-perturbative effect?

Direct Calculation e.g. Lattice QCD Effective Theory e.g. sigma model, 
 NJL model,…

✤ NJL Model + U(1)A breaking term (KMT term)


✤ Same Global Symmetry as at Low Energy


Nambu—Jona-Lasinio Model
 for Low Energy Effective Theory

5

(Nf = 3)

4-Fermi 6-Fermi

LNJL = Tr ¯ ψ(i/ ∂ − yS)ψ + 2GTr Φ†Φ + GD(det Φ + h.c)

(Φ)ij = ¯ ψi(1 − γ5)ψj

• cf. mc

where

LH

χSB Pattern

U(3)L × U(3)R → SU(3)V × U(1)V

U(1)A

by KMT term

✤ Self-Consistent Mean Field Approximation

6

LNJL

define “BCS” vacuum |”BCS” > = |σ, φ (π,K,…) >

hΦi = 1 4G

• diag.(σ, σ, σ) + i(λa)T φa

LMFA = Tr ¯ ψ(i/ ∂ − M)ψ + at most quadratic in fermions

¯ ψψ, σ, φ

Interactions

VMFA = 3 8Gσ2 − GD 16G3 σ3+

Through integrating out the internal fermion, 
 we can obtain non-zero <σ> (DχSB) and 
 calculate the mass spectrum for hidden hadrons: M, mσ and mφ.

Internal fermion mass Effective Potential with cutoff ΛH

(Φ)ij = ¯ ψi(1 − γ5)ψj

σ

φ

¯ ψψ ¯ ψγ5λψ

CP 
 Even CP 
 Odd

✤ Mass Spectrum and Dark Matter Annihilation

7

1000 2000 3000 4000 5000 0.001 0.01 0.1 1 y M mS mDM

y

Mass [GeV]

(λH, λHS, λS) = (0.13, 0.01, 0.19)

mφ

mS

M

S

φ φ h

h

S

φ

φ

h

SM SM

mφ < mS mφ > mS

S

φ φ

S

This channel open

• Need 2mφ = mS to obtain correct ΩDM
• At most σSI ~ 10 cm around mφ = 100 GeV
• 48

2

1st-order PT

y ≦ O(10 )

• 3

✤ Hidden Chiral Phase Transition

8

VEFF(S, σ, T ) = V h→0

SM+S(S) + VNJL(S, σ) + VCW(S) + VFT(S, σ, T ) + VRING(S, T )

λH = λS = 0.13 , λHS = 0.02 y=0.007 y=0.006 y=0.005

550 600 650 0.0 0.5 1.0 1.5 2.0 2.5

T [GeV] <M>/T

where

M = σ + yS − GD 8G2 σ2

LH ⊃ −yS ¯

ψψ

Not only σ but also S
 get non-zero VEV 
 in generally y ≦ 0.006.

• Y. Ametani, M. Aoki, HG and J. Kubo, 

• Phys. Rev. D 91 (2015) no.11, 115007

S3(T ) = Z Z Z d3r " Z−1

σ (S, σ, T )

2 ✓dσ dr ◆2 + 1 2 ✓dS dr ◆2 + VEFF(S, σ, T ) # We assume 3D Euclidian Action for mean fields as

Compute at loop level Multi-Fields Tunneling 


• vershot/undershot method does not work

9

Equations of Motion for Multi-Fields Tunneling

d2σ dr2 + 2 r dσ dr = Zσ(S, σ, T ) × " ∂VEFF(S, σ, T ) ∂σ + 1 2 ∂Z−1

σ (S, σ, T )

∂σ ✓dσ dr ◆2# d2S dr2 + 2 r dS dr = ∂VEFF(S, σ, T ) ∂S + 1 2 ∂Z−1

σ (S, σ, T )

∂S ✓dσ dr ◆2

with

ϕi(∞) = 0

ϕ0

i(0) = 0

✤ Bubble Nucleation from Hidden Chiral Tunneling

Compositeness condition 
 guarantee 
 the bounce solution!

T/Λ = 0 T / Λ = . 1 T/Λ = 0.02 T/Λ = 0.03

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.0 0.5 1.0 1.5

σ/Λ Zσ (S/Λ=0,σ/Λ,T/Λ)

G1/2Λ = 1.82, (-GD)1/5Λ = 2.29

Λ Λ Λ Λ

In SCMF approximated NJL 
 σ disappear at symmetric phase
 — Zσ(σ) → 0 as σ → 0

✤ How to Find Multi-Bounce Solution

10

Find initial position (σ0, S0) 
 doubly fine-tuned

d2σ dr2 + 2 r dσ dr = Fσ(σ, S) d2S dr2 + 2 r dS dr = FS(σ, S)

with

ϕi(∞) = 0

ϕ0

i(0) = 0

and

Find tunneling path S(σ) 
 satisfied NS[S(σ)] = 0

d2σ dr2 + 2 r dσ dr = Fσ(σ, S(σ))

NS(S(σ)) ≡ d2S dσ2 ✓dσ dr ◆2 + ✓dS dσ ◆ Fσ(σ, S(σ)) − FS(σ, S(σ))

with

ϕi(∞) = 0

ϕ0

i(0) = 0

— Change the Question ! —

0.00 0.05 0.10 0.15 0.00 0.02 0.04 0.06 0.08 0.10 σ/ΛH S/ΛH

σ(r) S(r) S(σ)

0.00 0.05 0.10 0.15 0.00 0.02 0.04 0.06 0.08 σ/ΛH S/ΛH

More generally C. L. Wainwright arXiv:1109.4189

GW Signal from
 Scale Invariant Hidden QCD PT

✤ HQCD Model Based on Classical Scale Invariance


✤ Strategy to Test HQCD with GW Spectrum


11

Indirect Dimensional Transmission

⌦ ¯ ψψ ↵ ∼ Λ3

H

yS ⌦ ¯ ψψ ↵ λHS hSi2 H†H

Fixed EχSB: DM Mass & PT

DχSB as Origin


• f EWPT & DM

fixes HQCD Scale

(λH, λHS, λS, y)

Model Parameter

NJL

V (σ, S)

NJL (α, ˜ β; Tt)

GW Parameter

ΩGW(f)

GW Spectrum

(mDM, ΛH)

with LISA or DECIGO Test

✤ Benchmark Points — A, B, C and D

12

y ≧ 0.0001
 by hand λHS ≧ 0.0001 
 by hand λHS ≦ 0.12 mh = 125 GeV, <h> = 246 GeV
 mS = 2mDM

(λH, λHS, λS, y)

mc = y hSi

• cf. current mass

Model Parameter

λHS

Large Small Small Large EχSB

✤ GW Spectrums for Benchmark Points

13

“runaway” vw=1

GW signal from this model (ΛH < 200 TeV) may appear in DECIGO.

using parameterization in C. Caprini et al. arXiv:1512.06239

Conclusion

14

✤ Scale Invariant QCD-like Hidden Sector ( Nc = Nf = 3 )


We discussed indirect dimensional transmutation from
 χSB Pattern U(3)R × U(3)L → SU(3)V × U(1)V 
 In mDM < mS case 
 — Need Resonance Effect ( 2mDM = mS )
 — Poor testability in DM search because of small y
 but chiral phase transition become first-order phase transition

✤ GW from Hidden QCD Phase Transitions 


We predict the GW signal using SCMF approximated NJL analysis
 They may appear O(0.01) ~ O(1) Hz region (DECIGO).

Conclusion

15

✤ Analysis of Multi-Fields Tunneling


More interesting if there exist two scale first-order PT
 Method : Path Deformation

✤ Model including Strong Dynamics


Compatible with scale invariant extension and GW Prediction
 — Effective model may be practical approach now…
 — When DM is hidden Baryon, mDM ~ ΛH,
 peak frequency of GW signal corresponds to DM mass directly

Backup Slides

Beyond the Standard Model
 from Higgs Mass term

17

▸ RG Equation for the Higgs Mass


▸ Fine-Tuning Problem

VSM = µ2(H†H) + λH(H†H)2

＊ ONLY Higgs mass term breaks scale invariance ＊ What is the origin of Higgs mass term?

dm2

h

d ln µ = 3m2

h

8π2 ✓ 2λH + y2

t − 3g2 2

4 − 3g2

1

20 ◆

m2

h = (1019 GeV)2 − (1019 GeV)2 = (125 GeV)2

“Fine-T uning Problem”
 from Wilsonian RG Flow

18

• H. Aoki, S. Iso PhysRevD.86.013001

Who put Higgs near the critical line? Broken
 Phase Symmetric
 Phase

λ m2

m2

R > 0

m2

R < 0

m2

R = 0

m2

R = O(Λ2 EW)

m2

R ∼ O(Λ2 pl)

(λ0, m0) @ Planck

Scale Invariant Extension

19

Mpl

EW

VSM = µ2(H†H) + λH(H†H)2

×

QCD

Classical Scale Invariance

No large intermediate scale below the Planck scale

Hidden dynamics in TeV scale
 explain Electroweak symmetry breaking

Low-energy is responsible 
 for the origin of low energy scales

— What is the dynamical origin of Higgs mass?

W.A. Bardeen, FERMILAB-CONF-95-391 (1995)

Phase T ransitions
 in the Standard Model

✤ EW Phase Transition

20

✤ QCD Phase Transition


Higgs Phase

1 s t

• r

d e r P T 75 GeV 110 GeV

mh

T

• K. Kanjantie et al. arXiv: hep-lat/9511992

(Nf = 2+1) cross over SM

mu,d

ms

∞ ∞

1st-order PT

N

f

= 3

Phase Transition in the SM are not first-oder type

Symmetric Phase

H.-T. Ding et al. arXiv: 1111.0185

✤ How deal with non-perturbative effect?


mass spectrum of hadron, coupling…
 
 
 
 Direct Approach 
 Lattice gauge theory
 — but not suitable for scale invariance!
 
 Effective Theory Approach
 Sigma model
 Nambu—Jona-Lasinio (NJL) model 
 AdS/CFT …
 — but additional parameter appear!

Difficulty of
 QCD-like Hidden Sector

21

cross over SM

mu,d

ms

∞ ∞

1st-order PT QCD Phase Transition Nf = 2+1 N

f

= 3

Chiral limit 
 (Scale Invariance) Pure SU(3)

φ φ

SM SM SM SM

B ¯ B B ¯ B

φ

φ

Determination NJL Parameters
 from QCD Hadron Physics

22

Theory(MeV) Experimental value(MeV) mπ 136 140(π±) 135(π0) mK 499 494(K±) 498(K0, ¯ K0) mη 460 548 mη0 960 958 fπ 93 92(π) fK 105 110(K)

Parameter (2GQCD)1/2 (−GQCD

D

)1/5 ΛQCD mu ms Value (MeV) 361 406 930 5.95 163

Γφ(p2 = m2

φ)

= 0

where 
 internal quarks

yS →

M

in

Mu,s

mu,s

=

CP Even Scalar

23

✤ Mass and Mixing (h,S,σ)

h

S

σ

h

S

σ

Γij

@ h S σ 1 A = B @ ξ(1)

1

ξ(2)

1

ξ(3)

1

ξ(1)

2

ξ(2)

2

ξ(3)

2

ξ(1)

3

ξ(2)

3

ξ(3)

3

1 C A @ s1 s2 s3 1 A

For (λH, λHS, λS)=(0.13, 0.01, 0.19) y=0.0052, ξ1 = 0.999 ~ 1 Constraint for mixing

ξ1 > 0.9

(1)

m1 = mh = 125.4 GeV (must be SM-Higgs boson) 
 m2 = mS = 946.4 GeV, m3 = mσ = 6.8 TeV

(1)

Higgs mass 3σ

Only three of (λH, λHS, λS, y) are independent

Stability and Perturbativity
 Below the Planck Scale

24

ΛH g4 ΛS y ΛHS g3 g2 gY

3 5 7 9 11 13 15 17 19 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 logHQê1 GeVL couplings

0.05 0.1 0.15 0.2 0.25

λS(q0)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y(q0)

λHS(q0) = 0.1 λHS(q0) = 0.06 λHS(q0) = 0.02

λH(q0) = 0.135 q0 = 1 TeV αH(q0) = 1

• M. Holthausen, J. Kubo, K. S. Lim and M. Lindner, JHEP 1312 (2013) 076 

• Y. Ametani, M. Aoki, HG, J. Kubo Phys Rev D 91(2015)115007

CP Even Scalar

25

✤ Mass and Mixing (h,S,σ)

@ h S σ 1 A = B @ ξ(1)

1

ξ(2)

1

ξ(3)

1

ξ(1)

2

ξ(2)

2

ξ(3)

2

ξ(1)

3

ξ(2)

3

ξ(3)

3

1 C A @ s1 s2 s3 1 A

For (λH, λHS, λS)=(0.13, 0.01, 0.19) y=0.0052, ξ1 = 0.999 ~ 1 Constraint for mixing

ξ1 > 0.9

(1)

m1 = mh = 125.4 GeV (must be SM-Higgs boson) 
 m2 = mS = 946.4 GeV, m3 = mσ = 6.8 TeV

(1)

Higgs mass 3σ

Only three of (λH, λHS, λS, y) are independent

✤ Accidental Symmetry : 
 ✤ DM Annihilation Process

Dark Matter Candidates

26

S

φ

φ

h

h

S

φ

φ

h

SM SM

S

φ φ

S

SU(3)V × U(1)V

φ

B

Hidden 
 Pion Hidden 
 Baryon

× 8

φ

φ

B

¯ B

B

S S

¯ B

× 8, …

mφ ~ y×ΛH mB ~ 3M ~ ΛH

Strong Coupling


GBBφ ~ 13 


& No Baryon Asym.

∝ y ∝ y 2

We consider only φ as DM
 because ΩB << Ωφ


✤ Hidden QCD Scale

27

λHS=0.001 λHS=0.002

0.001 0.005 0.010 0.050 0.100 10 20 30 40 50

y Hidden QCD Scale ΛH [TeV]

λH=0.13, λS=0.08

Mostly
 sensitive to λHS and y

ΛH

LH

LSM+S

λHS y determined by
 <h> = 246 GeV

small λHS large λHS

✤ Effective Potential

Phase T ransition at Finite Temperature

28

VEFF(S, σ, T ) = V h→0

SM+S(S) + VNJL(S, σ) + VCW(S) + VFT(S, σ, T ) + VRING(S, T )

VNJL(σ, S; ΛH) = 3 8Gσ2 − GD 16G3 σ3 − 3ncI0(M; ΛH) For chiral condensation, GD : η-η’ mixing VFT(S, σ, T) ⊃ −6nc T 4 π2 JF (M 2(S, σ)/T 2) ' 3nc

T 2 12 M 2 + · · ·

where

M = σ + yS − GD 8G2 σ2

Note that — Origin of cubic term is
 — M^2 term causes “ ySσ ” GD

QCD-like Dark Hidden Sector

m ˜

B ∼ ΛH

˜ B

φ

Hidden Mesons = DM Candidates! Hidden Baryons = DM Candidates?

h

λHS

S

CP even
 Scalars

σ

Mpl

EW

⌦ ¯ ψψ↵ 6= 0

Hidden DχSB

hSi 6= 0 hhi 6= 0

with NJL Analysis

Nc = Nf = 3

(λH, λS, λHS, y)

y

x8

ΛH

mφ ∼ y × ΛH

S

φ

φ

h

h

S

φ

φ

h

SM SM

Small y case Large y case

mφ > mS mS ' 2mφ

cosθ < 0.99 S

φ

φ

S Not have Asymmetry

• M. Holthausen, J. Kubo, K-S. Lim and M. Lindner arXiv: 1310.4423

Cosmological 
 Gravitational Wave Sources

✤ GW from Pre-BBN cosmological sources appear as


• Inflation
• Topological defeat
• First-order Phase Transition

30

Stochastic 
 GW background.

— Non localized signal

• A. A. Starobinsky, JETP Lett. 30 (1979) 682
• A. Vilenkin et al. 2000
• E. Witten, Phys. Rev. D 30 (1984) 272

Gravitational Waves
 from First-order Phase T ransition

✤ When bubbles collide, 


they convert part of their kinetic energy into GWs.

31

V (ϕ, T )

ϕ

Tc

Tt

PT occurs via tunneling

hϕi 6= 0

hϕi = 0

1 nucleated bubble
 per Hubble volume at Tt Tunneling 
 = Bubble nucleation

T µν

ϕ

T µν

plasma

vw

• M. Hnimarsh, et al. arXiv: 1504.03291

wall velocity

Bubble Nucleation Rate

Γ = Γ0eβt ' Γ0e−S3(T )/T

— Numerical Simulation —

32

✤ Essential Parameters for GW Prediction : ( α , β ; Tt )

Tt

↵ ≡ ✏/⇢

β−1

Transition
 Temperature Ratio of latent heat 
 and energy density Duration time of
 phase transition

f peak

h2Ωpeak

GW

∝ (β/Ht) Tt

∝ α (β/Ht)−1

Generally High Tt Large α, β -1

∼ O(1) mHz (EWPT)

f

h2ΩGW(f)

• C. Grojean, G Servant arXiv: 0607107

(α, β; Tt)

ΩGWh2(f)

Model-independent Analysis

Detail in 


• C. Caprini et al. arXiv:1512.06239

Parameterization of
 Gravitational Wave Spectrum

33

h2Ωϕ(f) = 1.67 × 10−5 ˜ β−2 ✓ κϕα 1 + α ◆2 ✓100 g∗ ◆1/3 ✓ 0.11v3

w

0.42 + v2

w

◆ 3.8(f/fϕ)2.8 1 + 2.8(f/fϕ)3.8

fϕ = 16.5 × 10−6 ˜ β ✓ 0.62 1.8 − 0.1vw + v2

w

◆ ✓ Tt 100 GeV ◆ ✓ g∗ 100 ◆1/6 Hz

h2Ωsw(f) = 2.65 × 10−6 ˜ β−1 ✓ κvα 1 + α ◆2 ✓100 g∗ ◆1/3 vw(f/fsw)3 ✓ 7 4 + 3(f/fsw)2 ◆7/2

fsw = 1.9 × 10−5v−1

w ˜

β ✓ Tt 100 GeV ◆ ✓ g∗ 100 ◆1/6 Hz

h2Ωturb(f) = 3.35 × 10−4 ˜ β−1 ✓κturbα 1 + α ◆ 3

2 ✓100

g∗ ◆1/3 vw (f/fturb)3 [1 + (f/fturb)]

11 3 (1 + 8πf/ht)

fturb = 2.7 × 10−5v−1

w ˜

β ✓ Tt 100 GeV ◆ ✓ g∗ 100 ◆1/6 Hz

Detail in LISA WG paper C. Caprini et al. arXiv:1512.06239

Scalar Sound Wave Turbulence

Peak : Peak : Peak :

σ(r)/ΛH S(r)/ΛH

100 200 300 400 0.00 0.02 0.04 0.06 0.08 0.10 0.12

rΛH σ(r)/ΛH and S(r)/ΛH Case A, T/ΛH=0.0570

✤ CASE A

• 1. Find Bubble Profiles using Path Deformation Method

T S3(T)/T

T A

t

= 387 GeV

• 2. Compute Tt from S3/T
• 3. Compute α and β at Tt

αA = 0.288

T A

t

= 387 GeV ˜ βA = 8.2 × 102

✤ CASE A

10-4 0.001 0.010 0.100 1 10 100 10-19 10-15 10-11 10-7 10-3

Frequency [Hz] ΩGWh2

ΩGW = Ωϕ + Ωsw + Ωturb = Ωϕ + Ωsw + Ωturb

Energy Budget

A

αA = 0.288

αA

∞ = 0.116

α∞ < α Runaway Bubbel

T A

t

= 387 GeV ˜ βA = 8.2 × 102

vw = 1

• 4. Check Bubble Dynamics
• 5. Assume wall velocity and Parameterize
• J. R. Espinosa et al. arXiv: 1004.4187

Detail in C. Caprini et al. arXiv:1512.06239

α∞ ' 1.09 ⇥ 10−3 " nf ✓2M(hϕii) Tt ◆2 + 3λS ✓hSi Tt ◆2#

In our model

✤ Essential Parameters for benchmark points

36

Case Tt [TeV] α ˜ β A 0.387 0.288 824.33 B 0.306 0.223 1485.56 C 8.731 0.310 714.83 D 9.480 0.232 1328.61

A, C B, D

where ˜

β = β/Ht

mc/ΛH

Small Large α (β/Ht) Small Large Small Large

• 1

Case

High Tt Large α, (β/Ht)

• 1

(α, β; Tt)

ΩGWh2(f)

Model-independent Analysis Ωϕ + Ωsw + Ωturb

Scalar Plasma

Energy Budget 


(Model-dependent)

κ(α)

fraction Linear combination of

• J. R. Espinosa et al. arXiv: 1004.4187

Check Runaway or not?

with assumption of wall velocity (vw)