Gravitational Wave Signals of Electroweak Phase TransitionTriggered by Dark Matter

Huaike GuoIn collaboration with Wei Chao and Jing Shu,

(arXiv:1702.02698)

ITP-CAS

May 15, 2017

Huaike Guo | May 15, 2017 1 / 16

Baryon Asymmetry and Dark Matter

Atoms 4.9%

Dark Matter 26.6%

Dark Energy 68.5%

Planck, 2013. Astron.Astrophys. (2014)

Huaike Guo | May 15, 2017 2 / 16

Electroweak Baryogenesis: The Standard Picture

ϕ

V

T>Tc

T=Tc

T<Tc

T ≈ 100GeV ≈ 1015K

Gravitational Waves (mHz level)

Huaike Guo | May 15, 2017 3 / 16

Minimal Extensions of the SM: Dark Matter and EWPT

SM + S (stringent experimental tension)

s

h

SM + S + S

Huaike Guo | May 15, 2017 4 / 16

SM + DM + Scalar: Model at T = 0

A simplified Z2 × Z2 symmetric potential:

V0 = −1

2µ2

ΦΦ2 +1

4λΦΦ4 −

1

2µ2SS

2 +1

4λSS

4

−µ2H†H + λ(H†H)2 + λ1S2H†H + λ2Φ2H†H

+λ3S2Φ2,

• vS = 0 ⇒ s is stable

• h, φ mix: h = cθh+ sθφ, φ = −sθh+ cθφ. (cθ > 0.86 at 95% CL)

Physical Parameters:

µΦ, µS µ, λΦ, λS , λ, λ1, λ2, λ3

vH , mH , vΦ, mφ, mS , λS , θ, λ1, λ3

7 free parameters

Huaike Guo | May 15, 2017 5 / 16

Dark Matter: Turn Off SI Scattering at Tree Level

DM-Nucleaon scattering cross section:

σn =µ2m2

n

πv2EWm2

S

∣∣∣∣∣∣ cθahm2h

−sθaφ

m2φ

∣∣∣∣∣∣22

9+

7

9

∑q=u,d,s

fnTq

2

Two sets of diagrams:

ah : s2h : 2λ3vφsθ + λ1vHcθ

aφ : s2φ : 2λ3vφcθ − λ1vHsθ

Zoomin to the parameter space with a negligible direct detection signal:

λ3 =vHλ1(m2

htan θ +m2

φcot θ)

2vΦ(m2h−m2

φ)

⇒ 6 free parameters

Huaike Guo | May 15, 2017 6 / 16

Effective Potential: Gauge Dependence

VTeff(φ) = V

T=0(φ) + V

T=0CW (φ)

+T4

2π2

∑scalars

JB(M2(ξ)

T2) + 3

∑gauge

JB(µ2

T2)−

∑gauge

JB(ξµ2

T2)− 4

∑fermions

nfCJF (

m2f

T2)

,ξ: Gauge fixing parameter in Rξ-gauge.

O(T 2) terms are ξ-independent & Equivalent to including thermal masses at tree level:

Πh =

3g2 + g′2

16+λ

2+ht

4+λ1 + λ2

12

T 2,

Πs =

λs

4+λ1

3+λ3

6

T 2,

Πφ =

λφ

4+λ2

3+λ3

6

T 2.

More on this topic: H.Patel, M. Ramsey-Musolf, JHEP 1107 (2011) 029.

Huaike Guo | May 15, 2017 7 / 16

Analysis of O(T 2) Terms

Generic Form:

V Teff(φ) = Dh(T 2 − T 2h )h2 + Λhh

4

+ Dφ(T 2 − T 2φ)φ2 + Λφφ

4

+ Ds(T2 − T 2

s )s2 + Λss4

+ δhφh2φ2 + δhsh

2s2 + δφsφ2s2

• Basics: Λh > 0, Λφ > 0, Λs > 0, δhφ > 0, Λhs > 0, Λφs > 0.

• Symmetry Restoration: Dh > 0, Dφ > 0, Ds > 0, T 2h > 0, T 2

φ > 0, T 2s > 0,

• Two minima: (0, 0, s) and (h, φ, 0) (Hessian Positive Definite)

• DM develops a vev first: Ts > Th, Ts > Tφ

• EW minimum (h, φ, 0) stable at T = 0

I These two minima will cross at some T (≡ Tc) in the phase diagram.

Huaike Guo | May 15, 2017 8 / 16

Phase History: A Benchmark Point

vΦ = 65GeV, mφ = 82GeV, mS = 71GeV, λS = 0.015, θ = 0.12, λ1 = 0.046 and λ3 = 0.57

0 50 100 150

-1.2×108

-1.0×108

-8.0×107

-6.0×107

-4.0×107

-2.0×107

0

T(GeV)

V(GeV4) (h,ϕ,0)

(0,0,s) (0,0,0)vh (TC)

TC=2.6

Ts =150GeV

TC=78.8GeV

Th =108GeV

100 150 200 250 300

0

20

40

60

80

h

ϕ

Th

TC

T=0

The first step could also be a 1st order phase transition with a more complete Veff.

Huaike Guo | May 15, 2017 9 / 16

Avoid Baryon Washout

Γsym ≈ 6× (18± 3)α5WT 4, Γbrok ∼ T 4exp(−

Esph

T)

130 140 150 160 170T / GeV

-45

-40

-35

-30

-25

-20

-15

-10

log Γ

/Τ4

standardmulticanonicalfitperturbative

pure gauge

log[αH(T)/T]

Sphaleron rate from lattice in SM,Phys.Rev.Lett,113, 141602 (2014).

Strongly first order EWPT criteria:vh(TC)

TC> 1 (ξ-dependence)

Huaike Guo | May 15, 201710 /

16

A Survey of Parameter Space

80 100 120 140 160 180

0.00

0.01

0.02

0.03

0.04

0.05

mS(GeV)

λ1

-0.4 -0.3 -0.2 -0.1 0.0

0.00

0.01

0.02

0.03

0.04

0.05

0.06

θ

λ1

All gives previous EWPT pattern and no SI DM detection signal at tree level.

• Ωch2 ∈ (0.03, 0.12)

• Ωch2 ∈ (0.03, 0.12) and

vh(TC)

TC> 1

Huaike Guo | May 15, 201711 /

16

Gravitational Waves: Experimental

C J Moore et al. Class. Quantum Grav. 32 (2015) 015014.

Huaike Guo | May 15, 201712 /

16

Gravitational Waves: A Benchmark Point

ΩGWh2 ' Ωφh2 + Ωswh

2 + Ωturbh2

Three sources:

Bubble Collision

Sound Waves

Turbulence

Tn: bubble nucleation temperatureα: strength of phase transitionβ: inverse duration of phase transition

10-5

10-4

0.001 0.010 0.100 1

10-18

10-13

10-8

f(Hz)

ΩGWh2

collision

turbulence

soundwaves

All

N2A5M5L6

N2A1M5L6

N2A2M5L4

N1A1M2L4

ALIA

DECIGOUltimate-DECIGOBBO

Huaike Guo | May 15, 201713 /

16

Higgs Couplings

λhhh = −3m2

h

vH[1−

3θ2

2+O(θ3)]

0.6 0.8 1.0 1.2 1.4

0

20

40

60

80

100

120

λhhh/λhhhSM

TC(GeV)

30%

λhhhh = −3m2

h

v2H

[1 + (m2φ

m2h

− 3)θ2 +O(θ3)]

-1 0 1 2 3

0

20

40

60

80

100

120

λhhhh/λhhhhSM

TC(GeV)

150%

• Ωch2 ∈ (0.03, 0.12) and

vh(TC)

TC> 1

• GW benchmark point.

Huaike Guo | May 15, 201714 /

16

Conclusion

• Dark matter itself could have experienced a phase transition.

• Dark matter might have played a role in EWPT.

• Gravitational waves thus produced can be probed by LISA, etc,.

• Higgs self-couplings measurement serves as a complementary test.

Huaike Guo | May 15, 201715 /

16

Thanks

Huaike Guo | May 15, 201716 /

16