Electroweak Phase Transition, Scalar Dark Matter, & the LHC M.J. Ramsey-Musolf Wisconsin-Madison NPAC Theoretical Nuclear, Particle, Astrophysics & Cosmology TNT Colloquium, November 2012

Recent Work M. Gonderinger, Y. Li, H. Patel, & MRM, arXiv: M. Buckley & MRM JHEP 1109 (2011) 094 H. Patel & MRM, JHEP 1107 (2011) 029 C. Wainwright, S. Profumo, MRM Phys Rev. D84 (2011) M. Gonderinger, H. Lim, & MRM, Phys. Rev. D86 (2012) W. Chao, M. Gonderinger, & MRM, arXiv: Earlier Work D. O’Connell, MRM, & M.B. Wise, PR D75 (2007) S. Profumo, MRM, & G. Shaugnessy, JHEP 0708 (2007) 010 V. Barger, P. Langacker, M. McCaskey, MRM, & G. Shaugnessy, PR D77 (2008) , D79 (2009) P. Fileviez-Perez, H. Patel, MRM & K. Wang, PR D79 (2009)

Stuart J. Freedman

Outline I. Intro & Motivation II.EWPT & General Features III. Three minimal extensions of the Standard Model scalar sector IV.( How will we know it’s a scalar ? ) V.( Theoretical issues )

I. Intro & Motivation

Scalar Fields in Cosmology What role do scalar fields play (if any) in the physics of the early universe ?

Dark Matter Portals Standard ModelHidden Sector (DM)

Scalar Fields & the Higgs Portal

Scalar Fields in Particle Physics Scalar fields are a simple Has a fundamental scalar finally been discovered ? Scalar fields are theoretically problematic  m 2 ~  2 If so, is it telling us anything about  ?

What is the BSM Energy Scale  ? Remarkable agreement with EWPO EWPO: data favor a “light” SM-like Higgs scalar Tension: EWPO + Direct Searches

What is the BSM Energy Scale  ? Remarkable agreement with EWPO Agreement w/ SM at ~ level: O NP = c /  2  ~ 10 TeV generically Barbieri & Strumia ‘99

Scalar Fields in Particle Physics Scalar fields are a simple Must  BSM ~ TeV to maintain a weak scale scalar ? Scalar fields are theoretically problematic  m 2 ~  2 EWPO: for new interactions coupling to gauge bosons or fermions,  BSM >> TeV

Scalar Fields in Particle Physics Scalar fields are a simple Must  BSM ~ TeV to maintain a weak scale scalar ? Scalar fields are theoretically problematic  m 2 ~  2 Perhaps new weak scale physics couples only to scalar sector: “Higgs portal”

Scalar Fields in Cosmology ProblemTheoryExp’t Inflation Dark Energy Dark Matter Phase transitions

Scalar Fields & Cosmic History Standard Model Universe EW Symmetry Breaking: Higgs ? New Scalars ? QCD: n+p! nuclei QCD: q+g! n,p… Astro: stars, galaxies,..

Scalar Fields & Inflation Standard Model Universe EW Symmetry Breaking: Higgs ? New Scalars ? QCD: n+p! nuclei QCD: q+g! n,p… Astro: stars, galaxies,.. Flatness Isotropy Homogeneity Scalar Field: Inflaton “Slow roll” Reheat

Scalar Fields & Dark Energy ?  CDM Supernovae BAO > 0 Cosmological constant ? Scalar Field: Quintessence ?

Scalar Fields & the Origin of Matter ? Baryogenesis: When? CPV? SUSY? Neutrinos? Non-equilibrium dynamics or CPT violation? BBN ( t ~ 100 s ) CMB ( t ~ 10 5 y )

Scalar Fields & the Origin of Matter ? Baryogenesis: When? CPV? SUSY? Neutrinos? Non-equilibrium dynamics or CPT violation? BBN ( t ~ 100 s ) CMB ( t ~ 10 5 y ) Electroweak Phase Transition ? New Scalars

Scalar Fields & the Origin of Matter ? ? Darkogenesis: When? SUSY? Neutrinos? Axions ? Y B related ? Baryogenesis: When? CPV? SUSY? Neutrinos? Non-equilibrium dynamics or CPT violation? Rotation curves Lensing Bullet clusters Electroweak Phase Transition ? New Scalars

Scalar Fields & the Origin of Matter ? ? Darkogenesis: When? SUSY? Neutrinos? Axions ? Y B related ? Baryogenesis: When? CPV? SUSY? Neutrinos? Non-equilibrium dynamics or CPT violation? Rotation curves Lensing Bullet clusters Electroweak Phase Transition ? New Scalars: CDM ?

Scalar Fields in Cosmology Inflation Dark Energy Dark Matter Phase transitions ProblemTheoryExp’t     ? ? ? ?

Scalar Fields in Cosmology Inflation Dark Energy Dark Matter Phase transitions ProblemTheoryExp’t     ? ? ? ? Could experimental discovery of a fundamental scalar point to early universe scalar field dynamics?

Scalar Fields in Cosmology Inflation Dark Energy Dark Matter Phase transitions ProblemTheoryExp’t     ? ? ? ? Focus of this talk, but perhaps part of larger role of scalar fields in early universe

Questions for this Talk: Was there a cosmic phase transition at T ~ 100 GeV ? Did it have the characteristics needed for successful electroweak baryogenesis and/or production of gravity waves? Are its dynamics coupled to dark matter ? What are the experimental signatures ? How robust is the underlying theory ?

II. General Features

Effective Potential L = (D   y  D   - V(  ) Tree level V(  ) ) V EFF ( ,T) Quantum corrections * Many applications: Effective action * T=0 : Coleman-Weinberg (RG improved) T>0 : Finite-T effective potential

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSB

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSBY B : CPV & EW sphalerons

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSBY B : diffuses into interiors

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSBY B : diffuses into interiors Preserve Y B initial Quench EW sph

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSBY B : diffuses into interiors Preserve Y B initial Quench EW sph T C, E sph, S tunnel F(  )

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSB Detonation & turbulence

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSB GW Spectra:  Q &  t EW F(  ) Detonation & turbulence

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM LHC Searches “Strong” 1 st order EWPT Bubble nucleation EWSB GW Spectra:  Q &  t EW F(  ) Detonation & turbulence nMSSM QQ  t EW

EW Phase Transition: New Scalars 1st order2nd order Increasing m h New scalars Baryogenesis Gravity Waves Scalar DM ? LHC Searches ? “Strong” 1 st order EWPT Bubble nucleation EWSB T C, E sph, S tunnel  Q &  t EW F(  ) Y B preservation, detonation & turbulence

Higgs Boson Searches

SM Higgs? SM “background” well below new CPV expectations New expts: 10 2 to 10 3 more sensitive CPV needed for BAU? LEP, Tevatron, & ATLAS Exclusion Non-SM Higgs(es) ? LHC Observation Precision Tests LHC Exclusion SM Higgs properties ?

Dark Matter:   &  SI Thermal DM: WIMP   SM Direct detection: Spin-indep DM-nucleus scattering   A A

III. Simplest Scalar Extensions ExtensionEWPTDMDOF May be low-energy remnants of UV complete theory & illustrative of generic features Real singlet Complex Singlet Real Triplet    ?    

Higgs Portal: Simple Scalar Extensions ExtensionEWPTDMDOF May be low-energy remnants of UV complete theory & illustrative of generic features Real singlet Complex Singlet Real Triplet    ?    

The Simplest Extension Model Independent Parameters: v 0, x 0, 0, a 1, a 2, b 3, b 4 H-S Mixing H 1 ! H 2 H 2 Mass matrix Stable S (dark matter?) Tree-level Z 2 symmetry: a 1 =b 3 =0 to prevent s-h mixing and one-loop s hh x 0 =0 to prevent h-s mixing xSM EWPT:  Signal Reduction Factor ProductionDecay Simplest extension of the SM scalar sector: add one real scalar S (SM singlet) EWPT: a 1,2 = 0 & = 0 DM: a 1 = 0 & = 0 // O’Connel, R-M, Wise; Profumo, R-M, Shaugnessy; Barger, Langacker, McCaskey, R-M Shaugnessy; He, Li, Li, Tandean, Tsai; Petraki & Kusenko; Gonderinger, Li, Patel, R-M; Cline, Laporte, Yamashita; Ham, Jeong, Oh; Espinosa, Quiros; Konstandin & Ashoorioon…

The Simplest Extension Model Independent Parameters: v 0, x 0, 0, a 1, a 2, b 3, b 4 H-S Mixing H 1 ! H 2 H 2 Mass matrix Stable S (dark matter?) Tree-level Z 2 symmetry: a 1 =b 3 =0 to prevent s-h mixing and one-loop s hh x 0 =0 to prevent h-s mixing xSM EWPT:  Signal Reduction Factor ProductionDecay EWPT Scenario Raise barrierLower T C : a 2 < 0

Finite Temperature Potential Multiple fields & new interactions: novel patters of symmetry breaking, lower T C, greater super-cooling, “stronger 1 st order EWPT”

The Simplest Extension Model Independent Parameters: v 0, x 0, 0, a 1, a 2, b 3, b 4 H-S Mixing H 1 ! H 2 H 2 Mass matrix Stable S (dark matter?) Tree-level Z 2 symmetry: a 1 =b 3 =0 to prevent s-h mixing and one-loop s hh x 0 =0 to prevent h-s mixing xSM EWPT:  Signal Reduction Factor ProductionDecay Low energy phenomenology Raise barrierLower T C MixingModified BRs Two mixed (singlet-doublet) states w/ reduced SM branching ratios

Mixed States h 1 = cos  h + sin  s h 2 = -sin  h + cos  s

EWPT & LHC Phenomenology Signatures m 2 > 2 m 1 m 1 > 2 m 2 LHC: reduced BR(h SM) Signal Reduction Factor ProductionDecay Light: all models Black: LEP allowed Scan: EWPT-viable model parameters LHC exotic final states: 4b-jets,  + 2 b-jets… Profumo, R-M, Shaugnessy

EWPT & LHC Phenomenology Signatures EWPO compatible m 2 > 2 m 1 m 1 > 2 m 2 LHC: reduced BR(h SM) Scan: EWPT-viable model parameters LHC exotic final states: 4b-jets,  + 2 b-jets… Profumo, R-M, Shaugnessy Signal Reduction Factor ProductionDecay Scan: EWPT-viable model parameters Light: all models Black: LEP allowed

EWPT & LHC Phenomenology Signatures EWPO compatible m 2 > 2 m 1 m 1 > 2 m 2 LHC: reduced BR(h SM) Signal Reduction Factor ProductionDecay Light: all models Black: LEP allowed Scan: EWPT-viable model parameters LHC exotic final states: 4b-jets,  + 2 b-jets… EWPO comp w/ a 1 =0=b 3 LHC: reduced BR(h SM) Profumo, R-M, Shaugnessy

EWPT & LHC Phenomenology Signatures EWPO compatible m 2 > 2 m 1 m 1 > 2 m 2 LHC: reduced BR(h SM) Signal Reduction Factor ProductionDecay Light: all models Black: LEP allowed Scan: EWPT-viable model parameters LHC exotic final states: 4b-jets,  + 2 b-jets… EWPO comp w/ a 1 =0=b 3 LHC: reduced BR(h SM) CMS 30 fb -1  SM-like Singlet-like SM-like SM-like w/ H 2 ->H 1 H 1 or Singlet-like Barger, Langacker, McCaskey, R-M, Shaugnessy

The Simplest Extension Model Independent Parameters: v 0, x 0, 0, a 1, a 2, b 3, b 4 H-S Mixing H 1 ! H 2 H 2 Mass matrix Stable S (dark matter?) Tree-level Z 2 symmetry: a 1 =b 3 =0 to prevent s-h mixing and one-loop s hh x 0 =0 to prevent h-s mixing xSM EWPT:  Signal Reduction Factor ProductionDecay DM Scenario  DM &  SI ++…

DM Phenomenology Relic Density He, Li, Li, Tandean, Tsai Direct Detection He, Li, Li, Tandean, Tsai Barger, Langacker, McCaskey, R-M, Shaugnessy

New Scalars &  BSM Preserving EW Min“Funnel plot” V EFF  perturbativity m H top loops naïve stability scale  EW vacuum Gonderinger, Li, Patel, R-M SM stability & pert’vity SM unstable above ~ 10 8 TeV top loops sets m H

New Scalars &  BSM Preserving EW Min“Funnel plot” V EFF  perturbativity m H top loops naïve stability scale  EW vacuum top loops Gonderinger, Li, Patel, R-M SM stability & pert’vity SM + singlet: stable but non-pertur’tive DM-H coupling

Dark Matter Stability Preserving EW Min“Funnel plot” Gonderinger, Li, Patel, R-M V EFF  perturbativity m H ?  s Z 2 -breaking vacuum Z 2 -preserving EW vacuum No DM: Z 2 -breaking vac top loops naïve stability scale  EW vacuum m S 2 = b 2 + a 2 v 2

LHC & Higgs Phenomenology Invisible decays He, Li, Li, Tandean, Tsai Look for azimuthal shape change of primary jets (Eboli & Zeppenfeld ‘00) Dijet azimuthal distribution LHC discovery potential Signal Reduction Factor ProductionDecay ATLAS

LHC & Higgs Phenomenology Giardino et al: arXiv 1207:1347

Higgs Portal: Simple Scalar Extensions ExtensionEWPTDMDOF May be low-energy remnants of UV complete theory & illustrative of generic features Real singlet Complex Singlet Real Triplet    ?    

Complex Singlet: EWB & DM? Barger, Langacker, McCaskey, R-M Shaugnessy Spontaneously & softly broken global U(1) Controls  CDM, T C, & H-S mixing Gives non-zero M A

Complex Singlet: EWB & DM Barger, Langacker, McCaskey, R-M, Shaugnessy  2 controls  CDM & EWPT M H1 = 120 GeV, M H2 =250 GeV, x 0 =100 GeV decreasing T C

Complex Singlet: EWB & DM? Barger, Langacker, McCaskey, R-M Shaugnessy Consequences: Three scalars: h 1, h 2 : mixtures of h & S A : dark matter Phenomenology: Produce h 1, h 2 w/ reduced   Reduce BR (h j ! SM) Observation of BR (invis) Possible obs of  SI

Complex Singlet: Direct Detection Barger, Langacker, McCaskey, R-M, Shaugnessy Two component case (x 0 =0) Little sensitivity of scaled  SI to  

SM Higgs? Three scalars: h 1,2 (Higgs-like) D (dark matter) LHC: WBF “Invisible decay” search D D D D SM Branching Ratios ? He et al Barger, Langacker, McCaskey, RM, Shaugnessy EWPT WIMP-Nucleus Scattering Viable Dark Matter ? Gonderinger, Lim, R-M 2 nd light state  TH <  WMAP  Xenon Br(inv) > 0.6  = 1 TeV

Higgs Portal: Simple Scalar Extensions ExtensionEWPTDMDOF May be low-energy remnants of UV complete theory & illustrative of generic features Real singlet Complex Singlet Real Triplet    ?    

      ~ ( 1, 3, 0 ) EWPT: a 1,2 = 0 & = 0 DM & EWPT: a 1 = 0 & = 0 // Small:  -param Fileviez-Perez, Patel, Wang, R-M: PRD 79: (2009); [hep-ph]

Finite Temperature Potential Multi-step EWSB transition: Step 1: quench sphalerons Step 2: move to EW/DM vac H. Patel & MRM in progress

Real Triplet       ~ ( 1, 3, 0 ) Fileviez-Perez, Patel, Wang, R-M: [hep-ph] New feature: gauge interactions & direct detection Y = 2 ( Q - I 3 ) g  Z / 2 I Q sin 2  W Want Y = 0

Real Triplet       ~ ( 1, 3, 0 ) Fileviez-Perez, Patel, Wang, R-M: [hep-ph] New feature: gauge interactions & LHC production q q     W + q q     Z 0 EW cross sections w/ charged states + E T

Real Triplet : DM Search Basic signature: Charged track disappearing after ~ 5 cm SM Background: QCD jZ and jW w/ Z !  & W!l Trigger: Monojet (ISR) + large E T Cuts: large E T hard jet One 5cm track Cirelli et al: M  = 500 GeV:    CDM ~ 0.1

SM Higgs? SM “background” well below new CPV expectations New expts: 10 2 to 10 3 more sensitive CPV needed for BAU? SM Branching Ratios ? Four scalars: h 1 (Higgs-like)   (dark matter)     (new states) D D D D Fileviez-Perez, Patel, R-M, Wang   

SM Higgs? SM “background” well below new CPV expectations New expts: 10 2 to 10 3 more sensitive CPV needed for BAU? LHC: H !  D D D D   

IV. Is it a Scalar ? Real singlet Complex Singlet Real Triplet ExtensionEWPTDM    ?     DOF

IV. Is it a Scalar ? Real singlet Complex Singlet Real Triplet ExtensionEWPTDM    ?     DOF Mixed Higgs-like states and/or modified BRs: signal reduction  invisible search…

IV. Is it a Scalar ? Real singlet Complex Singlet Real Triplet ExtensionEWPTDM    ?     DOF Could be fermionic triplet [e.g., Buckley, Randall, Shuve, JHEP 1105 (2011) 97]. How to distinguish?

Di-Jet Correlations J1J1 J2J2 V V p1p1 p2p2 Buckley, R-M JHEP 1109 (2011) 094 R-hadrons from gg fusion Scalars Fermions

Di-Jet Correlations J1J1 J2J2 V V p1p1 p2p2 Buckley, R-M JHEP 1109 (2011) 094 M2M2 M1M1 M pair A 3 / | M pair | 2 > 0 Scalars: Abelian Non-ableian for large  Fermions:A 3 < 0

V. Theoretical Issues Gauge-dependence in V EFF ( , T ) V EFF ( , T ) ! V EFF ( , T ;  ) Ongoing research: approaches for carrying out tractable, GI computations H. Patel & MRM, JHEP 1107 (2011) 029 C. Wainwright, S. Profumo, MRM Phys Rev. D84 (2011) H. Gonderinger, H. Lim, & MRM, arXiv:

Origin of Gauge Dependence Effective Action Effective Potential Source term: Not GI

Nielsen Identities Identity: Extremal configurations: Effective potential:

Baryon Number Preservation “Washout factor”  F(  ) ln S ~ A(T C ) e  Two qtys of interest: T C from V eff E sph from  eff

Baryon Number Preservation: Pert Theory ~  F(  ) Conventional treatments Gauge Dep GI T C from hbar exp, V eff (    ), or Hamiltonian formulation Use GI scale in E sph computation H. Patel & MRM, JHEP 1107 (2011) 029 “Baryon number preservation criterion” (BNPC)

Nielsen Identities: Application to T C Critical Temperature V eff (  min, T C ) = V eff ( , T C ) Apply consistently order-by-order in Implement minimization order-by-order (defines  n ) Fukuda & Kugo ‘74: T=0 V EFF Laine ‘95 : 3D high-T Eff Theory Patel & R-M ‘11: Full high T Theory

Obtaining a GI T C Track evolution of minima with T using expansion Track evolution of different minima with T using n=1 n=2 n=3 Patel & R-M ‘11 Illustrative results in SM: Full 

Gravity Waves from EWPT: Pert Theory Abelian Higgs Model C. Wainwright, S. Profumo, R-M Phys Rev. D84 (2011) arXiv: [hep-ph]

Vacuum Stability & Gauge Dependence Complex Singlet Model M. Gonderinger, H. Lim, M. R-M arXiv: [hep-ph] Possible runaway direction for  2 < 0 (EWPT) Tree-level stability Full V EFF (1-loop):  -dependence GI Stability Condition Use  -fns

Conclusions Cosmology loves scalar fields (inflation): given observation of a fundamental scalar, perhaps scalar fields can address a number of questions about the early universe Simple extensions of the SM scalar sector and lead to observable (  SI, LHC) particle dark matter and/or EWPT with interesting implications: baryogenesis, GW, new Higgs states/modified Higgs properties…. Perhaps observation of these scalars will point to a richer structure for scalar fields in the early universe involving both visible and dark physics

Back Up Slides

LHC & Higgs Phenomenology Invisible decays He, Li, Li, Tandean, Tsai Look for azimuthal shape change of primary jets (Eboli & Zeppenfeld ‘00) Dijet azimuthal distribution  (h!SS)=0 Invis search LHC discovery potential Signal Reduction Factor ProductionDecay

LHC & Higgs Phenomenology Invisible decays He, Li, Li, Tandean, Tsai Look for azimuthal shape change of primary jets (Eboli & Zeppenfeld ‘00) Dijet azimuthal distribution LHC discovery potential Signal Reduction Factor ProductionDecay

Complex Singlet: LHC Discovery Barger, Langacker, McCaskey, R-M, Shaugnessy Traditional search: CMSInvisible search: ATLAS Single component case (x 0 = 0) EWPT

Baryon Number Preservation: Pert Theory ~  F(  ) Conventional treatments “Baryon number preservation criterion” (BNPC)

DM & Higgs Phenomenology Relic DensityVac stability He, Li, Li, Tandean, Tsai Gonderinger, Li, Patel, R-M

Nielsen Identities: Example General SU(N) theory: Scalars: physical & WB GB T & L gauge bosons Scalar gauge bosons FP Ghosts Use  0 : m A 2 (  0 ) ij & M ij 2 (  0 ) simultaneously diagonalizable & eigenvalues in distinct subspaces !  -dependent WB GB, scalar gauge, & FPG terms cancel Patel & R-M ‘11

Scalar Fields in Cosmology Inflation Dark Energy Dark Matter Phase transitions ProblemTheoryExp’t

Scalar Fields & Cosmic History Standard Model Universe EW Symmetry Breaking: Higgs ? New Forces ? QCD: n+p! nuclei QCD: q+g! n,p… Astro: stars, galaxies,..

BBN and Y B

CMB and Y B

Cosmic Baryon Asymmetry ? Baryogenesis: When? CPV? SUSY? Neutrinos? Big Bang Nucleosynthesis: Light element abundances depend on Y B

Cosmic Baryon Asymmetry ? Baryogenesis: When? CPV? SUSY? Neutrinos? Cosmic Microwave Bcknd: Shape of anisotropies depends on Y B

VBF: Invisible Search I Central Jet Veto H ! W + W - !  jj : ideally only W decay products in central region (Chehime & Zeppenfeld ‘93)  H ! W + W - ! l + l -  : central region minijet from SM bcknd,  separation from dilepton pair (Barger, Phillips, Zeppenfeld ‘94)

VBF: Invisible Search II p T (H) distribution  Large p T (invisible decay) Look for azimuthal shape change of primary jets (Eboli & Zeppenfeld ‘00) Dijet azimuthal distribution  Cahn et al ‘87

Complex Singlet: EWB & DM? Barger, Langacker, McCaskey, R-M Shaugnessy Key features for EWPT & DM: (1)Softly broken global U(1) (2)Closes under renormalization (3)SSB leading to two fields: S that mixes w/ h and A is stable (DM)

Complex Singlet: EWB & DM? Barger, Langacker, McCaskey, R-M Shaugnessy Key features for EWPT & DM: (1)Softly broken global U(1) (2)Closes under renormalization (3)SSB leading to two fields: S that mixes w/ h and A is stable (DM) Controls  CDM & EWPT

Normalized Latent Heat Peak amplitude: GW Spectra (detonations): Peak frequency: See, eg, Caprini, Durrer, Servant ‘08; Huber & Konstandin ‘08; Caprini et al ‘09; Chung & Zhou ‘10