Multistep Single-Field Strong Phase Transitions from New Fermions Peisi Huang University of Nebraska-Lincoln @Searching for new physics- Leaving no stone unturned! University of Utah, Aug 9, 2019 Based on work with Andrei Angelescu, 1812.08293, PRD
What do we really know about the Higgs? • We have discovered the Higgs boson and measured its properties with precisions. • However, we know very little about the Higgs potential. V(Φ) vev, measured from G F Φ v ' 246 GeV 1
What do we really know about the Higgs? • We have discovered the Higgs boson and measured its properties with precisions. • However, we know very little about the Higgs potential. V(Φ) vev, measured from G F m h ' 125 GeV Higgs mass measured at the LHC Φ v ' 246 GeV 2
What do we really know about the Higgs? • We have discovered the Higgs boson and measured its properties with precisions. • However, we know very little about the Higgs potential. Completely specify the Higgs V(Φ) potential in the SM, but NOT directly measured m h ' 125 GeV ��� V = − µ 2 H † H + λ h ( H † H ) 2 ��� Φ ��� ��������� ������ �� ��� ��� � ��� ���� ���� µ 2 = M 2 ��������� ������ �� ��� ��� � h / 2 ' (88 GeV) 2 ���� ���� v ' 246 GeV ��� ��� λ h = M 2 h / (2 v 2 ) ' 0 . 13 ��� 3 ��� ��� ��� ��� ��� ��� ��� ��� ��� � �� ��� ��� ��� ��� ��� ��� � �� ��� ��� ��� ��� ��� ��� ����� ����� �� ��� ����� ����� �� ���
What do we really know about the Higgs? • We have discovered the Higgs boson and measured its properties with precisions. • However, we know very little about the Higgs potential. V(Φ) 8 ] σ Significance [ ATLAS Preliminary 7 Simulation and Projections from Run 2 data -1 s = 14 TeV, 3000 fb 6 Systematic uncertainties included b b b b 5 b b m h ' 125 GeV γ γ 4 b b τ τ Combination Φ 3 2 1 v ' 246 GeV 0 2 0 2 4 6 8 − κ λ Self coupling, Limited sensitivity at HL-LHC 4
What do we want to know about the Higgs? • The shape of the Higgs potential is closely related to the electroweak phase transition. V(Φ) V(Φ) ? T=0 T >> 100 GeV Φ Φ Know nothing beyond v, and m h EW symmetry restored 5
Electroweak Phase Transitions V(Φ) • First Order? • In the SM, the EW symmetry is broken by a smooth cross over. T • v (T) changes smoothly • No energy barrier; no bubbles; • no cosmological relics Φ 6
Electroweak Phase Transitions ⇠ � ⇠ � V = µ 2 H † H � λ ( H † H ) 2 + f − 2 ( H † H ) 3 8 ] σ Significance [ ATLAS Preliminary 7 Simulation and Projections from Run 2 data -1 s = 14 TeV, 3000 fb 6 Systematic uncertainties included • For a first order phase transition, b b b b 5 b b γ γ ' 4 b b τ τ Combination 5 3 3 < κ λ < 3 ( 2 1 0 2 0 2 4 6 8 − κ PH, A. Joglekar, B. Li, and C. Wagner. 2015 λ Enough room for new physics 7
Electroweak Phase Transitions V(Φ) h h h • First Order Phase Transition • v is discontinuous ) • V eff has a barrier, bubbles nucleated • Possibly interesting cosmological relics! h Φ New physics to generate a barrier 8
Generating a barrier SM + Scalar Espinosa & Quiros, 1993; Benson, 1993; Choi & Volkas, 1993; McDonald, 1994; Vergara, 1996; Branco, Delepine, Emmanuel-Costa, & Gonzalez,1998; Ham, Jeong, & Oh, 2004; Ahriche, 2007; Espinosa & Singlet Quiros,2007; Profumo, Ramsey-Musolf, & Shaughnessy, 2007; Noble &Perelstein, 2007; Espinosa, Konstandin, No, & Quiros, 2008; Ashoorioon & Konstandin, 2009; Das, Fox, Kumar, & Weiner, 2009; Espinosa, Konstandin, & Riva, 2011; Chung & Long, 2011; Wainwright,Profumo, & Ramsey-Musolf, 2012; Barger, Chung, Long, & Wang, 2012; Huang, Shu, Zhang, 2012; Jiang, Bian, Huang, Shu, 2015; PH,Joglekar, Li, ,Wagner, 2015; Chen, Kozaczuk, & Lewis (2017) SM + Scalar Turok, Zadrozny 92, Davies, Froggatt, Jenkins, Moorhouse 94, Cline, Lemieux 97, Huber 06, Froome, Huber, Seniuch 06, Cline, Kainulainen, Trott 11, Dorsch, Huber, No 13, Dorsch, Huber, Mimasu, No 14, Basler, Doublet Krause, Muhlleitner, Wittbrodt, Wlotzka 16, Dorsch, Huber, Mimasu, No 17, Bernon, Bian, Jiang 17... SM + Scalar Patel, Ramsey-Musolf 12... Triplet MSSM Carena, Quiros, Wagner 96, Delepine, Gerard, Gonzalez Felipe, Weyers 96, Cline, Kainulainen 96, Laine, Rummukainen 98, Carena, Nardini, Quiros, Wagner 09, Cohen, Morrissey, Pierce 12, Curtin, Jaiswal, Meade 12, Carena, Nardini, Quiros, Wagner 13, Katz, Perelstein, Ramsey-Musolf, Winslow 14... NMSSM Pietroni 93, Davies, Froggatt, Moorhouse 95, Huber, Schmidt 01, Ham, Oh, Kim, Yoo, Son 04, Menon, Morrissey, Wagner 04, Funakubo, Tao, Yokoda 05, Huber, Konstandin, Prokopec, Schmidt 07, Chung, Long 9 10, Kozaczuk, Profumo, Stephenson Haskins, Wainwright 15...
Generating a barrier • Scalars V ( φ h , φ s , T ) = m 2 0 + a 0 T 2 h + t s φ s + m 2 h + λ h h + λ hs s + λ s s + a s φ 2 4 φ 4 h + a hs φ s φ 2 2 φ 2 s φ 2 2 φ 2 s 3 φ 3 4 φ 4 s 2 Integrate out the singlet, ✓ 8 z 2 � 4 yz λ h + 3 yz λ hs V eff ( H, T ) = m 2 0 + a 0 T 2 2 y � 2 m 2 z ✓ λ h ◆ ◆ 4 � z H 2 + H 4 + H 6 . 3 v 2 6 v 2 y 2 V(Φ) ( H † H ) 2 ( H † H ) ( ( H † H ) 3 Φ 10
Generating a barrier • Scalars • Integrating out , ( H † H ) 3 expansion) • Thermal effect (high T expansion), negative cubic term • Fermions • Low T, scalars and fermions contribute equally − T 2 m 2 ( φ ) T 2 m ( φ ) 2 e − 2 m ( φ ) /T � � � � K 2 m ( φ ) /T + O 2 π 2 Consider the possibility of generating a barrier through fermions in this talk – leaving no stones unturned! 11
Outline • Consider a Vector-Like Lepton (VLL) model. • A non-trivial thermal history of the universe. • Signatures • Gravitational Wave signatures • Collider signatures 12
A Minimal Vector-Like Lepton (VLL) Model • Fermion models for strong first order phase transitions? • Strong couplings to the Higgs! • To avoid large mixing between the VLLs and SM leptons, and large contributions to the T parameter, we add ✓ ◆ N N 0 E 0 L L,R = ∼ (1 , 2) � 1 / 2 , L,R ∼ (1 , 1) 0 , L,R ∼ (1 , 1) � 1 E L,R • The most general Lagrangian is, × × − L V LL = y N R L L ˜ 0 L ˜ 0 H † L R + y E R L L HE 0 L H † L R HN 0 R + y N L N R + y E L E 0 0 + m L L L L R + m N N L N 0 R + m E E L E 0 R + h . c . , 13
A Minimal Vector-Like Lepton (VLL) Model × × − L V LL = y N R L L ˜ L ˜ 0 0 H † L R + y E R L L HE 0 L H † L R HN 0 R + y N L N R + y E L E 0 0 L N 0 L E 0 + m L L L L R + m N N R + m E E R + h . c . , • 2 neutral and 2 charged VLLs • Ranges of the parameters considered, √ m L , m N , m E ∈ [500 , 1500] GeV , y N L,R , y E L,R ∈ [2 , 4 π ] . • Constraints: • S & T parameters • Diphoton signal strength, 0 . 71 < µ γγ < 1 . 29 ATLAS, 1802.04146 eigenstates, m > • Masses of the lighter states, es, m E 1 > 100 GeV and m N 1 > 90 GeV LEP2, Phys Rept 427(2006)257-454 14
Thermal Evolution of the Effective Potential • For each surviving point, calculate the phase transition strength, ξ = φ c /T c V ( φ , T ) = V SM tree ( φ ) + V SM 1 − loop ( φ , T ) + V V LL 1 − loop ( φ , T ) + V Daisy ( φ , T ) ( + + + + · · · • Benchmark A, y N L ' 3 . 40 , y N R ' 3 . 49 , y E L ' 3 . 34 , y E R ' 3 . 46 , m L ' 1 . 06 TeV , m N ' 0 . 94 TeV , m E ' 1 . 34 TeV . µ γγ = 1 . 28 , ∆ χ 2 ( S, T ) = 1 . 33 , m N 1 = 400 GeV , m E 1 = 592 GeV . 15
Thermal Evolution of the Effective Potential Cross over Early universe, symmetric EWSB 16
Thermal Evolution of the Effective Potential • The broken minimum becomes less and less deep • A potential barrier starts developing between the symmetric phase and the broken phase • At T c2 , a strong first order phase transition • The universe tunnels back to the symmetric phase EW symmetry restored 17
Thermal Evolution of the Effective Potential EWSB again through a strongly first order phase transition, at T c1 18
Thermal Evolution of the Effective Potential Responsible for the BAU 19
Outline • Consider a Vector-Like Lepton (VLL) model. × × − L V LL = y N R L L ˜ 0 L ˜ 0 H † L R + y E R L L HE 0 L H † L R HN 0 R + y N L N R + y E L E 0 0 L N 0 L E 0 + m L L L L R + m N N R + m E E R + h . c . , • A non-trivial thermal history of the universe. • Signatures • Gravitational wave signatures • Collider signatures 20
Signatures – Gravitational Waves • When the bubbles collider, some of their energy is transferred to gravitational radiation, and persists today as stochastic GW background. • Multi-peak gravitational waves from a single scalar field! • GW spectrum is (mostly) determined by two parameters, − − latent heat Larger 𝛽 , stronger signal α = radiation energy Larger 𝛾 , weaker signal, higher frequencies β = PT rate • Typically, for the later phase transition, β /H PT ∼ 10 3 − 10 4 . α ∼ 0 . 01 − 0 . 1 , • For the earlier one, g α 2 < α 1 and ( β /H PT ) 2 > ( β /H PT ) 1 . 21 are listed in Table. 2. We show in Fig.
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