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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Collider and Gravitational Wave Complementarity in Exploring the Singlet Extension of the Standard Model Daniel Vagie University of

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Collider and Gravitational Wave Complementarity in Exploring the Singlet Extension of the Standard Model

Daniel Vagie

University of Oklahoma

based on arXiv:1812.09333 [JHEP] with Alexandre Alves, Tathagata Ghosh, Huai-Ke Guo, Kuver Sinha

07 May 2019

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 1 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Outline

1

Introduction

2

Electroweak Phase Transition

3

Hydrodynamics

4

Gravitational Waves

5

Model

6

Results

7

Conclusion

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 2 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Introduction

The Higgs potential is still largely unknown New scalars may provide an insight into the EWPT in the early universe Baryogensis through a strongly first

  • rder EWPT ⇒ SM + S

GWs produced by bubble nucleation and expansion Complementarity between GWs and colliders

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 3 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Electroweak Phase Transition

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 4 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

EWPT

Essential step in EWBG by providing an out of equilibrium environment Electroweak symmetry restoration at high T Strongly first order phase transition proceeds through bubble nucleation

Requires

vh(T) T

  • T=Tn

1

Dynamics of nucleated bubbles in the plasma will generate GW

2nd Order PT 1st Order PT

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 5 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Hydrodynamics

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 6 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Hydrodynamics 1

EWBG ⇒ subsonic vw GWs ⇒ large vw v+ instead of vw enters EWBG calculations: v+ = 0.05 Detonation mode will not work Velocity Profile 2 v ξ = 1 − vξ 1 − v2

  • µ2

c2

s

− 1

  • ∂ξv

1arXiv:1004.4187 Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 7 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Gravitational Waves

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 8 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Gravitational Waves

Full Spectrum h2ΩGW = h2Ωcol + h2Ωsw + h2Ωturb Sound Wave

h2Ωsw = 2.65 × 10−6 H∗ β κν α 1 + α 2 100 g∗ 1/3 × vw   f fSW   3 7 4 + 3(f/fsw )2 7/3 fsw = 1.9 × 10−5 1 vw β H∗ T∗ 100 GeV g∗ 100 1/6

T∗ = Tn (1 + κT α)1/4 h2Ωcol can be neglected SNR =

  • δ × T

fmax

fmin

df h2ΩGW (f) h2Ωexp 2

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 9 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Model

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 10 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

xSM: SM + S 3

Potential V0(H, S) = −µ2H†H + λ(H†H)2 + a1 2 H†HS + a2 2 H†HS2 + b2 2 S2 + b3 3 S3 + b4 4 S4 HT = (G+, (vew + h + iG0)/ √ 2) and S = vs + s µ2 and b2 replaced by model parameters using minimization condition (vew, vs) Rotate (h, s) into physical basis (h1, h2) by mixing angle θ Free parameters of model ⇒ (vs, mh2, θ, b3, b4) Tadpole basis < S >= 0: V → V

′ = V + b1S 2 2arXiv:1701.08774 3arXiv:0705.2425,1407.5342, and 1701.04442 Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 11 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Effective Potential 4

Veff = V0 + VT in high-T expansion Veff (h, s, T) = − 1 2[µ2 − Πh(T)]h2 + 1 2[b2 + Πs(T)]s2 + 1 4 λh4 + 1 4 a1h2s + 1 4 a2h2s2 + b3 3 s3 + b4 4 s4 Thermal Masses

Πh(T) =

  • 2m2

W + m2 z + 2m2 t

4v2 + λ 2 + a2 24

  • T 2

Πs(T) = a2 6 + b4 4

  • T 2

Phase Transition Patterns

(a) (0, 0) → (vH = 0, vS = 0) (b) (0, 0) → (vH = 0, vS = 0) → (vH = 0, vS = 0) (c) (0, 0) → (vH = 0, vs = 0) → (vH = 0, vS = 0)

4High-T expansion - arXiv:1101.4665 Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 12 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Results

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 13 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Constraints

Bounded from below

λ > 0, b4 > 0, a2 ≥ −2

  • λb4

Stability

∂V ∂φi = 0, and ∂2V ∂φi ∂φj > 0, φi,j = h, s

Higgs Signal Strength

Higgs signal strength: µH = cos2 θ ⇒ | sin θ| > 0.33

Perturbative Unitarity S Matrix

Eigenvalues of S greater than (1/2 × 16π)

Electroweak Precision Measurements

mexp

W

= 80.385 ± 0.015 GeV S,T, and U    (θ, mh2 )

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 14 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

EWPT and GW

EWPT Type: (A) 99 %, (B) 1 %, (C) 0 % LISA: SNR < 10 (blue - 28 %), 10 < SNR < 50 (green - 50%),and SNR > 50 (red - 22 %) Larger α and smaller β ⇒ larger SNR

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 15 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Parameter Space Giving Detectable GW

arXiv:1407.5342

Bounded from below: 20 GeV |vs| 50 GeV Larger mh2 preferred W-mass constraint: θ 0.2

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 16 / 30

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Correlation with Double Higgs Production Searches

Γh2 = sin2 θΓSM(h2 → XSM) + Γ(h2 → h1h1) σ(pp → h1h1) = σ(pp → h2)BR(h2 → h1h1) Large mh2 ⇒ small Br(h2 → h1h1) ⇒ small σ(pp → h2 → h1h1)

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 17 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Correlation with Double Higgs Production Searches

SNR > 50 (red) and 50 > SNR > 10 (green) mh2 500 GeV can be probed by both 3 ab−1 (13 TeV) HL-LHC and space-based GW detectors

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 18 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Diboson Resonance Searches

SNR > 50 (red) and 50 > SNR > 10 (green) Most of h2 decays in WW, ZZ, and h1h1 channels HL-LHC will probe large fraction of parameter space in ggF and VBF channels

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 19 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Higgs Cubic and Quartic Couplings

arXiv:1711.03978

SNR > 50 (red) and SNR > 10 (green) Precise measurements can be used to reconstruct the Higgs potential ∆L = − 1

2 m2

h1

v (1 + δκ3)h3 1 − 1 8 m2

h1

v2 (1 + δκ4)h4 1

Correlation given by δκ4 ≈ ηδκ3 for η ∈ (2, 4)

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 20 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Conclusion

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 21 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Conclusion

Electroweak Phase Transitions lead to a GW spectrum Singlet-extended SM Higgs sector offers a wide range of parameter space with large SNR at LISA Di-Higgs searches can probe lighter masses at HL-LHC Weak diboson resonance searches can probe a large fraction of the parameter space Modification to Higg’s cubic and quartic couplings Main features of the parameter space: 20 GeV |vs| 50 GeV, θ 0.2, δκ4 ≈ (2 − 4)δκ3, and large mh2 preferred for SNR

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 22 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

Some References

W-mass: arXiv:1203.0275 Higgs signal strength: arXiv:1606.02266, and arXiv:1801.00794 Sound waves: arXiv:1504.03291

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 23 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

EWPT Definitions

Key parameters: Tc, Tn, α, β, and vw Bubble Nucleation Rate

Γ ∼ A(T)e−S3/T

Euclidean Action of the critical bubble

S3( φ, T) = 4π

  • r2dr

  1 2

  • d

φ(r) dr 2 + V( φ, T)   d φ(r) dr

  • r=0 = 0,
  • φ(r = ∞) =

φout

Bubble Nucleation

tn ΓVH(T)dt = ∞

Tn

dT T 2ξMpl T 4 e−S3/T = O(1) S3(T) T ≈ 140

Inverse time duration of PT

β = HnTn d(S3/T) dT

  • Tn

Vacuum energy released from PT

α = ∆ρ ρR = 1 ρR

  • −V(

φb, T) + T ∂V( φb, T) ∂T

  • T=Tn

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 24 / 30

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Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion

W-mass Constraint

arXiv:1406.1043v2

W mass calculated from experimentally measured values of GF , mZ , and α(0) Functions relating these parameters depends on the loop calculations to the vector boson self-energies

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 25 / 30

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Feynman Diagrams for Double Higgs Production and Weak Boson Pairs

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 26 / 30

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Double Higgs Production Channels

CMS 35.9 fb−1 at 13 TeV di-Higgs decay channels: b¯ bγγ, b¯ bτ +τ −, b¯ bb¯ b, and b¯ bWW/ZZ arXiv:1811.09689 for recent combination ATLAS 36.1 fb−1 at 13 TeV Di-Higgs decay channels: γγb¯ b, b¯ bτ +τ −, b¯ bb¯ b, WW ∗WW ∗, and b¯ bWW ∗ "Combination of searches for Higgs boson pairs in pp collisions at 13 TeV with the ATLAS experiment." for recent combination Cross sections calculated at NNLO-NNLL for gluon fusion

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 27 / 30

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Diboson-Resonances

ATLAS combined results at 13 TeV with 36 fb−1 data VBF at NNLO ggF at NNLO-NNLL Decay channels: WZ → qqqq, lνqq, lνll, WW → qqqq, lνqq, lνlν, ZZ → qqqq, ννqq, llqq, llνν, llll, and WH → qqbb, lνbb, ZH → qqbb, ννbb, llbb, and lν, ll arXiv:1808.02380

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 28 / 30

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Higgs Cubic and Quartic Deviations at Lepton Colliders

(Higgsstrahlung): e+e− → hZ (WW-fusion): e+e− → ν¯ νh (WW-pair production): e+e− → WW Higgs decays into ZZ ∗, WW ∗, γγ, Zγ, gg, b¯ b, c¯ c, τ +τ −, and µ+µ− Global Analysis: arXiv:1711.03978

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 29 / 30

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Perturbative Unitarity S-Matrix

Eleven 2 → 2 channels Charge neutral channels (h1h1, h2h2, h1h2, h1Z, h2Z, ZZ, W +W −) Charge-1 channels (h1W +, h2W +, ZW +) Charge-2 channels (W +W −) Leading partial wave amplitudes of these scatterings are given collectively by a symmetric matrix S = S0 S1 S2

Daniel Vagie

  • U. Oklahoma

Collider and Gravitational Wave Complementarity 07 May 2019 30 / 30