Gravitational Waves from Phase Transition in a QCD-like hidden - - PowerPoint PPT Presentation

Gravitational Waves from Phase Transition in a QCD-like hidden sector

Mayumi Aoki (Kanazawa University)

• Sep. 9-13, 2019 TAUP2019 @ TOYAMA

In collaboration with J. Kubo (Toyama U.) Work in progress

MA, Goto, Kubo, PRD 96 (2017)

2

❖ The Higgs boson was discovered at the LHC in 2012.

Introduction

→All particles in the SM had been discovered.

❖ Phenomena in the early universe can also be probed by the GW. ❖ LIGO had made the first observation of the GW in 2015. → A new way to study astrophysical phenomena. ❖ The observation is in agreement with the SM. No signal for BSM at the LHC after the Higgs boson discovery.

3

Origin of Mass

✤ Spontaneous Electroweak Symmetry Breaking

SU(2)L × U(1)Y → U(1)em

VSM = m2

HH†H + λH(H†H)2

hhi = 246 GeV

→ The SM particles get their masses. ❖ The Higgs boson is tightly connected with the mechanism for generating mass in the SM.

3

Origin of Mass

✤ Spontaneous Electroweak Symmetry Breaking

SU(2)L × U(1)Y → U(1)em

VSM = m2

HH†H + λH(H†H)2

hhi = 246 GeV

→ The SM particles get their masses. ❖ The Higgs boson is tightly connected with the mechanism for generating mass in the SM. QCD Dynamical chiral symmetry breaking (DχSB) Higgs EWSB ❖ Mass of the nucleon:

2% + 98%

h¯ qqi

3

Origin of Mass

❖ The EW and QCD phase transitions are crossovers within the SM. They cannot produce the GW background. ❖ In the BSM, observable GW signals associated with a symmetry breaking may be produced and tested.

✤ Spontaneous Electroweak Symmetry Breaking

SU(2)L × U(1)Y → U(1)em

VSM = m2

HH†H + λH(H†H)2

hhi = 246 GeV

→ The SM particles get their masses. ❖ The Higgs boson is tightly connected with the mechanism for generating mass in the SM. QCD Dynamical chiral symmetry breaking (DχSB) Higgs EWSB ❖ Mass of the nucleon:

2% + 98%

h¯ qqi

A Classical Scale Invariance Model

4

❖ The classical scale invariance is one of candidates for the solution

• f hierarchy problem.

×

VSM = m2

HH†H + λH(H†H)2

❖ We study the testability of the GW background produced by the hidden chiral phase transition in the classical scale invariance model.

A Classical Scale Invariance Model

4

❖ The classical scale invariance is one of candidates for the solution

• f hierarchy problem.

×

VSM = m2

HH†H + λH(H†H)2

❖ We study the testability of the GW background produced by the hidden chiral phase transition in the classical scale invariance model. ❖ We consider a classical scale invariance model with the strongly interacting SU(3) Hidden sector by

Holthausen, Kubo, Lim, Lindner, JHEP 1312 (2013).

✤ The chiral phase transition in the hidden sector is of first order.

We study the testability of the GW background produced by the phase transition in the hidden sector.

5

❖ Gauge Symmetry : GSM × SU(3)H

LSM|m2

H→0

S

real singlet scalar

LH

Bµ

S ψi hidden vector-like fermions (i=1-3)

LH = −1 2Tr F 2 + Tr ¯ ψ (i/ ∂ + gH / G + g0Q / B − yS) ψ

❖ Lagrangian of the hidden sector :

VSM+S = λH(H†H)2 − 1 2λHSS2(H†H) + 1 4λSS4

❖ Scalar potential :

Model

Holthausen, Kubo, Lim, Lindner, JHEP 1312 (2013)

5

❖ Gauge Symmetry : GSM × SU(3)H

LSM|m2

H→0

S

real singlet scalar

LH

Bµ

S ψi hidden vector-like fermions (i=1-3)

LH = −1 2Tr F 2 + Tr ¯ ψ (i/ ∂ + gH / G + g0Q / B − yS) ψ

❖ Lagrangian of the hidden sector :

VSM+S = λH(H†H)2 − 1 2λHSS2(H†H) + 1 4λSS4

❖ Scalar potential :

Model

Holthausen, Kubo, Lim, Lindner, JHEP 1312 (2013)

Hidden QCD scale ΛH EW

Explicit χSB Dynamical χSB

EWSB

⌦ ¯ ψψ↵ 6= 0

hSi 6= 0

hhi 6= 0 yS ⌦ ¯ ψψ ↵

λHS hSi2 H†H

• ⌦ ¯

ψψ ↵ ∼ Λ3

H

❖ The DχSB in the hidden sector triggers the EW symmetry breaking.

Model

6

Holthausen, Kubo, Lim, Lindner, JHEP 1312 (2013)

Chiral condensate Hidden mesons

❖ The 8 hidden mesons φa are DM candidates.

SU(3)V flavor symmetry

SU(3)L × SU(3)R → SU(3)V

(Φ)ij = ¯ ψi(1 − γ5)ψj

LH ❖ Nambu—Jona-Lasinio (NJL) Lagrangian

hΦi = 1 4G

• diag.(σ, σ, σ) + i(λa)T φa

❖ The mean-field approximation: ❖ The NJL parameters are obtained by scaling-up the values of GQCD, GDQCD and ΛQCD for the real hadrons.

G = f −2GQCD , GD = f −5GQCD

D

, ΛH = fΛQCD

⌦ ¯ ψψ ↵

LNJL = Tr ¯ ψ(i/ ∂ + g0Q / B − yS)ψ + 2GTr Φ†Φ + GD(det Φ + h.c)

Model

7

❖ The λH and ΛH are chosen to satisfy mh=126 GeV and <h>=246 GeV. the <σ> and <S> can be determined through the minimization of the scalar potential.

Veff = VSM+S + VNJL

VNJL(σ, S; ΛH) = 3 8Gσ2 − GD 16G3 σ3 − 3ncI0(M; ΛH)

❖ For a given set of the free parameters of the model,

: constituent ψ mass.

(λH, λHS, λS, y )

M = σ + yS − GD 8G2 σ2

8

Chiral Phase Transitions

λS = 0.005, λHS = 0, y = 0.001

λS = 0.005, λHS = 0, y = 0.007

T/ΛH

vσ / T vS / T vS / T vσ / T

T/ΛH

DM & S Masses

9

y = 0.001 − 0.00172

λS = 0.001

mh →

allowed by LHC

mS [TeV], mDM [TeV]

λHS

mDM mS

1 2 0.0001 0.01

Ametani, MA, Goto, Kubo, PRD 91 (2015)

for more details, see

Gravitational Wave

10

hϕi 6= 0

hϕi = 0

S3 : the three-dimensional Euclidean action Γ(t) = Γ0(t)e−SE(t)

(per unit volume per unit time)

❖ Probability of the bubble nucleation : ❖ Bubble nucleation:

Γ H4

• t=tn

' 1 , S3(Tn) Tn = 4 ln ✓ Tn H(Tn) ◆

true vacuum

✤ scalar field contribution ✤ sound waves ✤ turbulence

ΩGW = Ωϕ + Ωsw + Ωturb ❖ Sources of GW :

SE(T ) = S3(T )/T

Tn : the nucleation temperature

V (ϕ, T )

ϕ

Tc

Tt

Tn

Gravitational Wave

11

h2Ωpeak

GW

High Tn

Large α, β -1

f peak ∝ (β/H(Tn)) Tn

f

h2ΩGW(f)

∝ α (β/H(Tn))−1

❖ The bubble dynamics can be characterized by α and β.

ρrad: the thermal energy density in the sym. phase.

α = − 1 ρrad ∆V (Tn) + Tn 4 ∂∆V (T ) ∂T

• T =Tn

!

❖ α : Released energy ❖ β-1 : Timescale of the transition β H(tn) = Tn d dT ✓S3(T ) T ◆

• T =Tn

12

Effective Potential

λS = 0.001, λHS = 0, y = 0.00172

Veff/Λ4

H

T/TC = 0.945

Bounce solution ( S3/T=141)

S/ΛH

σ/ΛH

13

α and β

λS = 0.001, λHS = 0

❖ The α(=0.0244) differs only slightly from the pure NJL value. ❖ As the y increases, the β decreases.

Helmboldt, Kubo, Woude, arXiv:1904.07891

βNJL/H = 1.8 × 104

Pure NJL :

β/H

y

0.002 0.0006 2000 10000

❖ We can expect the stronger GW than the pure NJL case.

GW Spectrum

14

❖ Large β case: The sound wave period is shortened.

the root-mean-square four-velocity of the plasma

¯ Uf

R∗

the bubble size at percolation

❖ The result of the numerical simulations of ΩGW might be overestimated.

e.g.) Hindmarsh, Huber, Rummukainen, Weir, PRD 96 (2017)

Ellis, Lewicki, No, JCAP 1904 (2019),

❖ The suppression factor for the SW contribution: h2Ωsw(f) → h2Ωsw(f) × HR∗ ¯ Uf

Ellis, Lewicki, No, Vaskonen, JCAP 1906 (2019)

vw = 1 + p α(2 + 3α) √ 3(1 + α)

❖ Jouguet detonation:

vw > Cs

bubble wall

❖ For α=0.02, we obtain vw=0.6809.

~ 5×10-3 for β/H~104.

HR∗ ¯ Uf

Cs : the speed of sound in the plasma. In a relativistic fluid, Cs =1/√3.

∝ 1/β

Espinosa et al. JCAP 1006 (2010)

v− = cs

v+ = vw ,

The velocity of the plasma in front (+) and behind (−) of the bubble wall in the wall frame.

✤ Wall velocity:

SNRBBO (5yrs)

15

λS = 0.001

✤ Signal to Noise Ratio

SNR = s 2tobs Z fmax

fmin

df  ΩGW(f) Ωnoise(f) 2

mS < mh mS > mh

λHS

y=0.001 y=0.00172 0.0001 0.01

SNRBBO (5yrs)

5 10 15

16

GW Spectrum

f[Hz]

ΩGWh2

SNRthr(5yrs)=5

Summary

17

❖ The strength of the GWs seems to be large for observations at future space-based GW detector. ❖ We have studied the discovery potential of the GW background produced by the chiral phase transition in the hidden sector of a scale invariant extension of the SM. ❖ The Yukawa coupling constant should be sufficiently small to

• btain a first-order chiral phase transition.

❖ The β is sensitive to the Yukawa coupling.