Huaike Guo In collaboration with Wei Chao and Jing Shu ...

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