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
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Outline Introduction 1 Electroweak Phase Transition 2 3 Hydrodynamics 4 Gravitational Waves Model 5 Results 6 Conclusion 7 Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 2 / 30
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 order 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
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
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 � vh ( T ) Requires � 1 � T � T = Tn 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
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
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Hydrodynamics 1 EWBG ⇒ subsonic v w GWs ⇒ large v w v + instead of v w enters EWBG calculations: v + = 0 . 05 Detonation mode will not work Velocity Profile � � µ 2 2 v ξ = 1 − v ξ − 1 ∂ ξ v 1 − v 2 c 2 s 1 arXiv:1004.4187 Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 7 / 30
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
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Gravitational Waves Full Spectrum h 2 Ω GW = h 2 Ω col + h 2 Ω sw + h 2 Ω turb Sound Wave � H ∗ � � κν α � 2 � 100 � 1 / 3 h 2 Ω sw = 2 . 65 × 10 − 6 β 1 + α g ∗ 3 � � 7 / 3 f 7 × vw 4 + 3 ( f / fsw ) 2 fSW � β � � g ∗ fsw = 1 . 9 × 10 − 5 1 � � T ∗ � 1 / 6 vw H ∗ 100 GeV 100 T ∗ = T n ( 1 + κ T α ) 1 / 4 h 2 Ω col can be neglected � � h 2 Ω GW ( f ) � f max � � 2 � SNR = � δ × T df h 2 Ω exp f min Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 9 / 30
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
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion xSM: SM + S 3 Potential V 0 ( H , S ) = − µ 2 H † H + λ ( H † H ) 2 + a 1 2 H † HS + a 2 2 H † HS 2 + b 2 2 S 2 + b 3 3 S 3 + b 4 4 S 4 √ H T = ( G + , ( v ew + h + iG 0 ) / 2 ) and S = v s + s µ 2 and b 2 replaced by model parameters using minimization condition ( v ew , v s ) Rotate ( h , s ) into physical basis ( h 1 , h 2 ) by mixing angle θ Free parameters of model ⇒ ( v s , m h 2 , θ, b 3 , b 4 ) ′ = V + b 1 S 2 Tadpole basis < S > = 0: V → V 2 arXiv:1701.08774 3 arXiv:0705.2425,1407.5342, and 1701.04442 Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 11 / 30
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Effective Potential 4 V eff = V 0 + V T in high-T expansion V eff ( h , s , T ) = − 1 2 [ µ 2 − Π h ( T )] h 2 + 1 2 [ b 2 + Π s ( T )] s 2 + 1 4 λ h 4 + 1 4 a 1 h 2 s + 1 4 a 2 h 2 s 2 + b 3 3 s 3 + b 4 4 s 4 Thermal Masses Phase Transition Patterns � 2 m 2 W + m 2 z + 2 m 2 � + λ 2 + a 2 t T 2 (a) ( 0 , 0 ) → ( v H � = 0 , v S � = 0 ) Π h ( T ) = 4 v 2 24 (b) ( 0 , 0 ) → ( v H = 0 , v S � = 0 ) → ( v H � = 0 , v S � = 0 ) � a 2 6 + b 4 � (c) ( 0 , 0 ) → ( v H � = 0 , v s = 0 ) → ( v H � = 0 , v S � = 0 ) T 2 Π s ( T ) = 4 4 High-T expansion - arXiv:1101.4665 Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 12 / 30
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
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Constraints Bounded from below � λ > 0 , b 4 > 0 , a 2 ≥ − 2 λ b 4 Stability ∂ 2 V ∂ V = 0 , and > 0 , φ i , j = h , s ∂φ i ∂φ i ∂φ j Higgs Signal Strength Higgs signal strength: µ H = cos 2 θ ⇒ | sin θ | > 0 . 33 Perturbative Unitarity S Matrix Eigenvalues of S greater than ( 1 / 2 × 16 π ) Electroweak Precision Measurements m exp = 80 . 385 ± 0 . 015 GeV W ( θ, m h 2 ) S,T, and U Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 14 / 30
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
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Parameter Space Giving Detectable GW arXiv:1407.5342 Bounded from below: 20 GeV � | v s | � 50 GeV Larger m h 2 preferred W-mass constraint: θ � 0 . 2 Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 16 / 30
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Correlation with Double Higgs Production Searches Γ h 2 = sin 2 θ Γ SM ( h 2 → X SM ) + Γ( h 2 → h 1 h 1 ) σ ( pp → h 1 h 1 ) = σ ( pp → h 2 ) BR ( h 2 → h 1 h 1 ) Large m h 2 ⇒ small Br ( h 2 → h 1 h 1 ) ⇒ small σ ( pp → h 2 → h 1 h 1 ) Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 17 / 30
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Correlation with Double Higgs Production Searches SNR > 50 (red) and 50 > SNR > 10 (green) m h 2 � 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
Introduction Electroweak Phase Transition Hydrodynamics Gravitational Waves Model Results Conclusion Diboson Resonance Searches SNR > 50 (red) and 50 > SNR > 10 (green) Most of h 2 decays in WW, ZZ, and h 1 h 1 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
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 m 2 m 2 h 1 h 1 ∆ L = − 1 v ( 1 + δκ 3 ) h 3 1 − 1 v 2 ( 1 + δκ 4 ) h 4 2 8 1 Correlation given by δκ 4 ≈ ηδκ 3 for η ∈ ( 2 , 4 ) Daniel Vagie U. Oklahoma Collider and Gravitational Wave Complementarity 07 May 2019 20 / 30
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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