huaike guo in collaboration with wei chao and jing shu
TRANSCRIPT
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