Higgs Portal WS 14 MRM...symmetry-breaking in particle physics driven by a fundamental scalar likely...
Transcript of Higgs Portal WS 14 MRM...symmetry-breaking in particle physics driven by a fundamental scalar likely...
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Higgs Portal & Cosmology: Theory Overview
Higgs Portal WS May 2014!
M.J. Ramsey-Musolf U Mass Amherst
http://www.physics.umass.edu/acfi/
The Origin of Matter
Cosmic Energy Budget
Dark Matter
Dark Energy
68 %
27 %
5 %
Baryons Baryons
The Origin of Matter
Explaining the origin, identity, and relative fractions of the cosmic energy budget is one of the most compelling motivations for physics beyond the Standard Model
Cosmic Energy Budget
Dark Matter
Dark Energy
68 %
27 %
5 %
Baryons Baryons
Symmetries & Cosmic History
Symmetries & Cosmic History
Standard Model Universe
EW Symmetry Breaking: Higgs
QCD: n+p! nuclei
QCD: q+g! n,p…
Astro: stars, galaxies,..
Symmetries & Cosmic History
Standard Model Universe
EW Symmetry Breaking: Higgs
QCD: n+p! nuclei
QCD: q+g! n,p…
Astro: stars, galaxies,..
Symmetries & Cosmic History
Standard Model Universe
EW Symmetry Breaking: Higgs
QCD: n+p! nuclei
QCD: q+g! n,p…
Astro: stars, galaxies,..
What is the nature of the EW phase transition ?
Symmetries & Cosmic History
Standard Model Universe
EW Symmetry Breaking: Higgs
QCD: n+p! nuclei
QCD: q+g! n,p…
Astro: stars, galaxies,..
What is the nature of the EW phase transition ? ! Origin of matter ?
Symmetries & Cosmic History
Standard Model Universe
EW Symmetry Breaking: Higgs
New Forces ?
QCD: n+p! nuclei
QCD: q+g! n,p…
Astro: stars, galaxies,..
What is the Origin of Matter Baryogenesis: When? CPV? SUSY? Neutrinos?
What is the Origin of Matter
?
Baryogenesis: When? CPV? SUSY? Neutrinos?
What is the Origin of Matter
?
Baryogenesis: When? CPV? SUSY? Neutrinos?
EW Baryogenesis: testable w/ EDMs + colliders
Leptogenesis: less testable, look for ingredients w/ νs
What is the Origin of Matter
?
Baryogenesis: When? CPV? SUSY? Neutrinos?
EW Baryogenesis: testable w/ EDMs + colliders
Leptogenesis: less testable, look for ingredients w/ νs
Other Scenarios: • GUT baryogenesis • Affleck-Dine • Asymmetric DM • Post sphaleron…
What is the Origin of Matter
?
Baryogenesis: When? CPV? SUSY? Neutrinos?
EW Baryogenesis: testable w/ EDMs + colliders
Leptogenesis: less testable, look for ingredients w/ νs
Other Scenarios: • GUT baryogenesis • Affleck-Dine • Asymmetric DM • Post sphaleron…
Symmetries & the Origin of Matter
?
Baryogenesis: When? CPV? SUSY? Neutrinos?
EW Baryogenesis: testable w/ EDMs + colliders
Leptogenesis: less testable, look for ingredients w/ νs
Can new TeV scale physics explain the abundance of matter ?
If so, how will we know ?
Questions for This Workshop
• What happened ~ 10ps after the Big Bang?
Questions for This Workshop
• What happened ~ 10ps after the Big Bang?
• Single step (cross over) transition ?
• More d.o.f. with a richer pattern of EWSB?
• Single or multiple steps ? • First or second order ? • Coupled to origin of matter ?
Questions for This Workshop
• What happened ~ 10ps after the Big Bang?
• Single step (cross over) transition ?
• More d.o.f. with a richer pattern of EWSB?
• Single or multiple steps ? • First or second order ? • Coupled to origin of matter ?
• What are collider signatures that could provide clues?
• Modified Higgs properties (production, decays)
• New states
Recent Developments:
• Discovery of BEH-like boson ! Paradigm of symmetry-breaking in particle physics driven by a fundamental scalar likely correct
• Supersymmetry as an illustration
• Theoretical progress & challenges
• Our work
• Non-observation (so far) of physics beyond the Standard Model at the LHC
• BICEP2 CMB B-mode observation ! Evidence for primordial gravitational radiation associated with inflation
Recent Results
• Discovery of BEH-like scalar at the LHC
• Non-observation (so far) of sub-TeV particles at LHC
Recent Results
• Discovery of BEH-like scalar at the LHC
• Non-observation (so far) of sub-TeV particles at LHC
• Idea of φ-driven spontaneous EW symmetry breaking is likely correct
Recent Results
• Discovery of BEH-like scalar at the LHC
• Non-observation (so far) of sub-TeV particles at LHC • Sub-TeV BSM spectrum is compressed • Sub-TeV BSM is purely EW or Higgs portal • BSM physics lies at very different mass scale
• Idea of φ-driven spontaneous EW symmetry breaking is likely correct
Outline
• Portals & the Early Universe
• Why the Higgs Portal
• Scalar Fields in Particle Physics & Cosmology
• General Considerations
• Illustrative Higgs Portals: Simplest Extensions
I. Portals & Early Universe
Standard Model “Hidden Sector” : DM, early universe dynamics (EWPT)…
Portals Two approaches:
• Specific model (MSSM….)
• “Model independent”
Model Independent Portals
• Vector portal (“dark photons”…)
• Neutrino portal
• Axion portal
• Higgs portal
• Higher dimensional op’s portal
Model Independent Portals
• Vector portal (“dark photons”…)
• Neutrino portal
• Axion portal
• Higgs portal
• Higher dimensional op’s portal
Model Independent Portals
• Vector portal (“dark photons”…)
• Neutrino portal
• Axion portal
• Higgs portal
• Higher dimensional op’s portal
Higgs Portal: DM
• Renormalizable
• Z2 symmetric
• Dimensionless coupling
• φ (DM): singlet or charged under SU(2)L x U(1)Y
Higgs Portal: Phase Transitions
• Renormalizable ✔
• Z2 symmetric ✖
• Dimensionless coupling ✖
• φ (DM): singlet or charged under SU(2)L x U(1)Y
+…
Higgs Portal: Higher Dim Op’s
• Renormalizable ✖
• Z2 symmetric ✔
• Dimensionless coupling ✖
• χ (DM): singlet or charged under SU(2)L x U(1)Y
+…
II. Why the Higgs Portal ?
Stable EW Vacuum ? Preserving EW Min
top loops sets mH
VEFF
ϕ
top loops EW vacuum
Stable EW Vacuum ? Preserving EW Min “Funnel plot”
top loops sets mH
VEFF
ϕ
perturbativity top loops EW vacuum
Stable EW Vacuum ? Preserving EW Min “Funnel plot”
top loops sets mH
VEFF
ϕ
perturbativity top loops
naïve stability scale Λ
EW vacuum
SM stability & pert’vity
Stable EW Vacuum ? Preserving EW Min “Funnel plot”
top loops sets mH
VEFF
ϕ
perturbativity
mH
top loops
naïve stability scale Λ
EW vacuum
SM unstable above ~ 108 - 1015 TeV
SM stability & pert’vity
Stable EW Vacuum ? Preserving EW Min “Funnel plot”
top loops sets mH
VEFF
ϕ
perturbativity
mH
top loops
naïve stability scale Λ
EW vacuum
SM unstable above ~ 108 - 1013 TeV
SM stability & pert’vity
Higgs portal interactions ! more robust stability ?
What is the BSM Energy Scale Λ ?
~ 10-3 agreement with EWPO
EWPO: data favor a “light” SM-like Higgs scalar
BSM: OBSM = c / Λ2 !
Λ ~ 10 TeV
Barbieri & Strumia ‘99
LHC: so far no sub-TeV BSM physics
Higgs Portal: new low scale d.o.f. ?
III. Scalar Fields in Particle Physics & Cosmology
ϕ ?
Scalar Fields in Cosmology
What role do scalar fields play (if any) in the physics of the early universe ?
Scalar Fields in Cosmology
Problem Theory Exp’t
• Inflation
• Dark Energy
• Dark Matter
• Phase transitions
Scalar Fields in Cosmology
• Inflation
• Dark Energy
• Dark Matter
• Phase transitions
Problem Theory Exp’t
✔
✔
✔
✔
Scalar Fields in Cosmology
• Inflation
• Dark Energy
• Dark Matter
• Phase transitions
Problem Theory Exp’t
✔
✔
✔
✔
?
?
?
?
Scalar Fields in Cosmology
• Inflation
• Dark Energy
• Dark Matter
• Phase transitions
Problem Theory Exp’t
✔
✔
✔
✔
?
?
?
?
• Could experimental discovery of additional scalars point to early universe scalar field dynamics?
• Are there signatures in modified Higgs properties, new states, or EW precision tests ?
Scalar Fields in Cosmology
• Inflation
• Dark Energy
• Dark Matter
• Phase transitions
Problem Theory Exp’t
✔
✔
✔
✔
?
?
?
?
Focus of this talk, but perhaps part of larger role of scalar fields in early universe
IV. General Considerations
Thermal DM: ΩCDM & σSI
Thermal DM: WIMP
χ
χ SM
SM
Direct detection: Spin-indep DM-nucleus scattering
χ
χ A
A
LUX
1310.8214
XENON 100
Thermal DM: ΩCDM & σSI
Thermal DM: WIMP
χ
χ SM
SM
Direct detection: Spin-indep DM-nucleus scattering
χ
χ A
A
?
CDMS 2013
K McCarthy APS ‘13
EWPT & EW Baryogenesis
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB YB : CPV & EW sphalerons
€
Aλ
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB YB : CPV & EW sphalerons
€
Aλ
BSM
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB YB : diffuses into interiors
€
Aλ
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB YB : diffuses into interiors
Preserve YB
initial
Quench EW sph
EW Phase Transition: New Scalars & CPV
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB YB : diffuses into interiors
Preserve YB
initial
Quench EW sph
EW Phase Transition: New Scalars & CPV
EW Phase Transition: Gravity waves
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB
GW Spectra: ΔQ & ΔtEW F(φ)
Detonation & turbulence
nMSSM
ΔQ
ΔtEW
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Baryogenesis Gravity Waves Scalar DM LHC Searches
“Strong” 1st order EWPT
Bubble nucleation
EWSB YB : diffuses into interiors
Preserve YB
initial
Quench EW sph
EW Phase Transition: New Scalars & CPV
Electroweak Phase Transition
EW Phase Transition: St’d Model
v ?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
Lattice: Endpoint
S’td Model: 1st order EWPT requires light Higgs
EW Phase Transition: New Scalars
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars 1st order EWPT
Decreasing RH stop mass
CCB Vac
Lattice: Laine, Rummukainen
MSSM: Light RH stops
PT: Carena et al,…
EW Phase Transition: MSSM
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
MSSM: Light RH stops
CCB vac
Carena et al 2008: Higgs phase metastable
EW Phase Transition: MSSM
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
MSSM: Light RH stops
CCB vac
Carena et al 2008: Higgs phase metastable
EW Phase Transition: MSSM
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
MSSM: Light RH stops
CCB vac
Carena et al 2008: Higgs phase metastable
CMS PAS SUS-13-009
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
< φ >
+…
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
< φ >
+…
• Renormalizable
• φ : singlet or charged under SU(2)L x U(1)Y
• Generic features of full theory (NMSSM, GUTS…)
• More robust vacuum stability
• Novel patterns of SSB
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
< φ >
+…
• Renormalizable
• φ : singlet or charged under SU(2)L x U(1)Y
• Generic features of full theory (NMSSM, GUTS…)
• More robust vacuum stability
• Novel patterns of SSB
Higgs Portal: Simple Scalar Extensions
Extension EWPT DM DOF
May be low-energy remnants of UV complete theory & illustrative of generic features
Real singlet
Real singlet
Complex Singlet
Real Triplet
1
1
2
3
✔
✖
✔
✔
✖
✔
✔
✔
Higgs Portal: Simple Scalar Extensions
Extension EWPT DM DOF
May be low-energy remnants of UV complete theory & illustrative of generic features (NMSSM, GUTs, Hidden Valley….)
Real singlet
Real singlet
Complex Singlet
Real Triplet
1
1
2
3
✔
✖
✔
✔
✖
✔
✔
✔
Higgs Portal: Simple Scalar Extensions
Extension EWPT DM DOF
May be low-energy remnants of UV complete theory & illustrative of generic features (NMSSM, GUTs, Hidden Valley….)
Real singlet
Real singlet
Complex Singlet
Real Triplet
1
1
2
3
✔
✖
✔
✔
✖
✔
✔
✔
The Simplest Extension
Model
Independent Parameters:
v0, x0, λ0, a1, a2, b3, b4
H-S Mixing H1 ! H2H2
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M 2 =µh2 µhs
2 2µhs2 2 µs
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Mass matrix
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sinθ cosθcosθ −sinθ"
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Stable S (dark matter?) • Tree-level Z2 symmetry: a1=b3=0 to
prevent s-h mixing and one-loop s hh
• x0 =0 to prevent h-s mixing xSM EWPT: ✖
Signal Reduction Factor
Production Decay
Simplest extension of the SM scalar sector: add one real scalar S (SM singlet)
EWPT: a1,2 = 0 & <S> = 0
DM: a1 = 0 & <S> = 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, Cont’d
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Mass matrix
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The Simplest Extension, Cont’d
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Mass matrix
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x0 = <S>
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γ
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γ h1,2
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hk
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New topologies
The Simplest Extension, Cont’d
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Mass matrix
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Stable S (dark matter) • Tree-level Z2 symmetry: a1=0 to
prevent s-h mixing and one-loop s hh
• x0 =0 to prevent h-s mixing & s ! hh
x0 = <S>
€
γ
€
γ h1,2
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The Simplest Extension
Model H-S Mixing
H1 ! H2H2
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M 2 =µh2 µhs
2 2µhs2 2 µs
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# $
%
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Mass matrix
€
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# $
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sinθ cosθcosθ −sinθ"
# $
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# $ %
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Stable S (dark matter?) • Tree-level Z2 symmetry: a1=b3=0 to
prevent s-h mixing and one-loop s hh
• x0 =0 to prevent h-s mixing xSM EWPT: ✖
Signal Reduction Factor
Production Decay
DM Scenario
The Simplest Extension
Model
Independent Parameters:
v0, x0, λ0, a1, a2, b3, b4
H-S Mixing H1 ! H2H2
€
M 2 =µh2 µhs
2 2µhs2 2 µs
2
"
# $
%
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Mass matrix
€
h1h2
"
# $
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& ' =
sinθ cosθcosθ −sinθ"
# $
%
& ' hs"
# $ %
& '
Stable S (dark matter?) • Tree-level Z2 symmetry: a1=b3=0 to
prevent s-h mixing and one-loop s hh
• x0 =0 to prevent h-s mixing xSM EWPT: ✖
Signal Reduction Factor
Production Decay
DM Scenario
ΩDM & σSI
+ +…
DM Phenomenology Relic Density
He, Li, Li, Tandean, Tsai
Direct Detection
He, Li, Li, Tandean, Tsai
Barger, Langacker, McCaskey, R-M, Shaugnessy
New Scalars EW Vacuum Stability Preserving EW Min “Funnel plot”
VEFF
ϕ
perturbativity
mH
top loops
naïve stability scale Λ
EW vacuum
top loops
Gonderinger, Li, Patel, R-M; Gonderinger, Lim, R-M
SM stability & pert’vity
DM-H coupling
New Scalars EW Vacuum Stability Preserving EW Min “Funnel plot”
VEFF
ϕ
perturbativity
mH
top loops
naïve stability scale Λ
EW vacuum
top loops
Gonderinger, Li, Patel, R-M; Gonderinger, Lim, R-M
SM stability & pert’vity
SM + singlet: stable but non-pertur’tive
DM-H coupling
LHC & Higgs Phenomenology LHC discovery potential
Signal Reduction Factor
Production Decay
LHC & Higgs Phenomenology LHC discovery potential
Signal Reduction Factor
Production Decay
V1j < 1: mixed states hj New decays: h2 ! h1 h1
LHC & Higgs Phenomenology LHC discovery potential
Signal Reduction Factor
Production Decay
V1j < 1: mixed states hj New decays: h2 ! h1 h1
Dark matter: no mixing ! states are h,S
New decays h! SS (invisible!) possible
LHC & Higgs Phenomenology Invisible decays
He, Li, Li, Tandean, Tsai
Look for azimuthal shape change of primary jets (Eboli & Zeppenfeld ‘00)
Dijet azimuthal distribution
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A
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Γ (h!SS)=0 Invis search
LHC discovery potential
Signal Reduction Factor
Production Decay
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 j
€
A
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LHC discovery potential
Signal Reduction Factor
Production Decay
Jets + ET
LHC & Higgs Phenomenology Invisible decays
He, Li, Li, Tandean, Tsai
Look for azimuthal shape change of primary jets (Eboli & Zeppenfeld ‘00)
Dijet azimuthal distribution
€
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€
A
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A
LHC discovery potential
Signal Reduction Factor
Production Decay
ATLAS
Real Singlet: EWPT
Model H-S Mixing
H1 ! H2H2
€
M 2 =µh2 µhs
2 2µhs2 2 µs
2
"
# $
%
& '
Mass matrix
€
h1h2
"
# $
%
& ' =
sinθ cosθcosθ −sinθ"
# $
%
& ' hs"
# $ %
& '
Stable S (dark matter?) • Tree-level Z2 symmetry: a1=b3=0 to
prevent s-h mixing and one-loop s hh
• x0 =0 to prevent h-s mixing xSM EWPT: ✖
Signal Reduction Factor
Production Decay
Real Singlet: EWPT
Model H-S Mixing
H1 ! H2H2
€
M 2 =µh2 µhs
2 2µhs2 2 µs
2
"
# $
%
& '
Mass matrix
€
h1h2
"
# $
%
& ' =
sinθ cosθcosθ −sinθ"
# $
%
& ' hs"
# $ %
& '
Stable S (dark matter?) • Tree-level Z2 symmetry: a1=b3=0 to
prevent s-h mixing and one-loop s hh
• x0 =0 to prevent h-s mixing xSM EWPT: ✖
Signal Reduction Factor
Production Decay
Raise barrier Lower TC
Real Singlet: EWPT
Model
Independent Parameters:
v0, x0, λ0, a1, a2, b3, b4
H-S Mixing H1 ! H2H2
€
M 2 =µh2 µhs
2 2µhs2 2 µs
2
"
# $
%
& '
Mass matrix
€
h1h2
"
# $
%
& ' =
sinθ cosθcosθ −sinθ"
# $
%
& ' hs"
# $ %
& '
Stable S (dark matter?) • Tree-level Z2 symmetry: a1=b3=0 to
prevent s-h mixing and one-loop s hh
• x0 =0 to prevent h-s mixing xSM EWPT: ✖
Signal Reduction Factor
Production Decay
Low energy phenomenology
Mixing
Raise barrier Lower TC
Modified BRs
Two mixed (singlet-doublet) states w/ reduced SM branching ratios
EWPT & LHC Phenomenology Signatures m2 > 2 m1
m1 > 2 m2
Light: all models Black: LEP allowed
Profumo, R-M, Shaugnessy ‘07
Scan: EWPT-viable model parameters
EWPT & LHC Phenomenology Signatures m2 > 2 m1
m1 > 2 m2
Light: all models Black: LEP allowed
Scan: EWPT-viable model parameters
LHC exotic final states: 4b-jets, γγ + 2 b-jets…
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h1
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h2
Profumo, R-M, Shaugnessy ‘07
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Scan: EWPT-viable model parameters
LHC: reduced BR(h SM)
Mixed States: Precision $ ILC
EWPT & LHC Phenomenology Signatures m2 > 2 m1
m1 > 2 m2
Light: all models Black: LEP allowed
Scan: EWPT-viable model parameters
LHC exotic final states: 4b-jets, γγ + 2 b-jets…
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h2
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h1
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h2
Profumo, R-M, Shaugnessy ‘07
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Scan: EWPT-viable model parameters
LHC: reduced BR(h SM) Signal Reduction Factor
Production Decay
Mixed States: Precision $ ILC
EWPT: Resonant Di-Higgs Production Signatures m2 > 2 m1
m1 > 2 m2
Light: all models Black: LEP allowed
Scan: EWPT-viable model parameters
LHC exotic final states: 4b-jets, γγ + 2 b-jets…
R-M & No, arXiv:1310.6035
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h1
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h2
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h1€
b
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Scan: EWPT-viable model parameters Mixed States:
Precision $ ILC
τ+ τ-
bbτ+τ- : discovery with ~ 100 fb-1 in “τlep τhad” channel
m2 = 270 GeV “un-boosted” m2 = 370 GeV “boosted”
EWPT: Resonant Di-Higgs Production Signatures m2 > 2 m1
m1 > 2 m2
Light: all models Black: LEP allowed
Scan: EWPT-viable model parameters
LHC exotic final states: 4b-jets, γγ + 2 b-jets…
R-M & No, arXiv:1310.6035
€
h1
€
h2
€
h1€
b
€
b
Scan: EWPT-viable model parameters Mixed States:
Precision $ ILC
τ+ τ-
8
h2 → h1h1 tt̄ Z bb̄ Z jj
bb̄τlepτhad bb̄ℓτhad bb̄τlepτhad bb̄τlepτhad jjτlepτhadEvent selection (see section V.C) 19.17 5249 762 601 98∆Rbb > 2.1, PT,b1 > 45 GeV, PT,b2 > 30 GeV 11.45 2639 384 188 10.8h1-mass: 90 GeV < mbb < 140 GeV 8.00 531 80 69 3.68Collinear x1, x2 Cuts 4.81 209 36.4 41.6 2.41∆Rℓτ > 2 4.10 129 23.1 26.5 2.03mℓ
T < 30 GeV 3.44 30.9 11.1 24.4 1.90h1-mass: 110 GeV < mcoll
ττ < 150 GeV 1.56 4.97 2.05 4.92 0.38Emiss
T < 50 GeV 1.37 3.31 0.87 4.29 0.36h2-mass: 230 GeV < mcoll
bbττ < 300 GeV 1.29 0.39 0.17 1.21 0.13
TABLE IV: Event selection and background reduction for the bb̄τlepτhad channel in the un-boosted benchmark scenario. Weshow the NLO cross section (in fb) for the signal h2 → h1h1 → bb̄τlepτhad and the relevant backgrounds tt̄ → bb̄τlepτhad, bb̄ℓτhad,Z bb̄ → bb̄τlepτhad and Z jj → jjτlepτhad after successive cuts (same efficiency and face rate assumptions as in Table II).
h2 → h1h1 tt̄ Z bb̄ Z jj
bb̄τlepτhad bb̄ℓτhad bb̄τlepτhad bb̄τlepτhad jjτlepτhadEvent selection (see section V.C) 10.73 5249 762 601 98∆Rbb < 2.2, PT,b1 > 50 GeV, PT,b2 > 30 GeV 6.02 1576 223 85 2.46h1-mass: 90 GeV < mbb < 140 GeV 4.77 672 94 31.5 0.84|P⃗ bb
T | > 110 GeV 3.42 345 49 13.9 0.33Collinear x1, x2 Cuts 2.31 136 22.3 8.38 0.22∆Rℓτ < 2.3 1.71 68 11.1 4.31 0.055mℓ
T < 30 GeV 1.46 18.4 5.64 4.02 0.051h1-mass: 110 GeV < mcoll
ττ < 150 GeV 1.05 4.2 1.26 0.30 0.00325 GeV < Emiss
T < 90 GeV 0.76 2.93 0.75 0.23 0.002h2-mass: 330 GeV < mcoll
bbττ < 400 GeV 0.63 0.60 0.15 0.026 < 0.001
TABLE V: Event selection and background reduction for the bb̄τlepτhad channel in the boosted benchmark scenario (sameefficiency and face rate assumptions as in Table II).
(GeV)TmissE
0 20 40 60 80 100 120 140 160 180 200
mis
s/d
Eσ
) dσ
(1/
-210
-110
= 270 GeV)2
Signal (m
= 370 GeV)2
Signal (m
b Z b
t t Z jj
FIG. 7: Normalized EmissT distribution after event selection
(before cuts) for signal and background (“τlepτlep”)
events (largely dominated by tt̄ production), we cut onthe transverse mass of the lepton (see Fig. 8)
mℓT =
!
2pℓTEmissT (1 − cosφℓ,miss) < 30 GeV (13)
with φℓ,miss being the azimuthal angle between the di-rection of missing energy and the lepton transverse mo-mentum.
The corresponding impact of the cut-flow on signaland background cross sections are given in Tables IVand V for the unboosted and boosted scenarios. As forthe τlepτlep channel, the various cuts allow one to greatlysuppress the backgrounds and increase the signal signifi-cance. For the τlepτhad channel, since it is not possible toimpose a Z-peak veto through a cut in the invariant massof the lepton pair, we increase the lower end of the mcoll
ττ
invariant mass signal window (from 100 GeV to 110 GeV)in order to suppress Zbb̄ and Zjj backgrounds. The dis-tributions for mcoll
ττ and mcollbbττ in this channel are shown
in Figs. 9 and 10.
From the results from Tables IV and V, we find thatfor the semileptonic channel a S/
√S +B ∼ 5 for the
unboosted benchmark scenario can be obtained with ∼50 fb−1, while for the boosted benchmark scenario the re-quired integrated luminosity is slightly higher, ∼ 90 fb−1.This channel therefore appears to be promising both forthe boosted and unboosted regimes.
9
(GeV)Tlm
0 20 40 60 80 100 120
T/d
mσ
) dσ
(1/
-210
-110
= 270 GeV)2
Signal (m
= 370 GeV)2
Signal (m
b Z bτ t t~ -> l τ τ t t~ ->
Z jj
FIG. 8: Normalized mℓT distribution for signal and back-
ground (“τlepτhad”).
(GeV)ττcollm
50 100 150 200 250
/dm
σ) dσ
(1/
-210
-110
= 270 GeV)2
Signal (m
= 370 GeV)2
Signal (m
b Z b
t t Z jj
FIG. 9: Normalized mcollττ distribution for τ+τ− system in
signal and background (“τlepτhad”).
D. Hadronic (τhadτhad) final states.
The selection criteria for this channel are given by twohadronically-decaying τ -leptons (Nτh = 2), exactly zeroleptons ( Nℓ = 0), and a similar set of kinematic require-ments on the τ leptons and b-jets as in the other chan-nels: pτT > 10 GeV, |yb| < 2.5, ∆Rbb > 0.5, pbT > 10. Ascompared to the semileptonic and leptonic channels, thebackgrounds for the purely hadronic channel are smaller.The cut flows for the unboosted and boosted scenariosare given in Tables VI and VII, respectively.In light of the results from Tables VI and VII, we ob-
tain S/√S +B ∼ 5 with ∼ 100 fb−1 in the hadronic
channel for both the unboosted and boosted benchmark
(GeV)ττbbcollm
100 200 300 400 500 600
/dm
σ) d
σ(1
/
-210
-110
= 270 GeV)2
Signal (m
= 370 GeV)2
Signal (m
b Z b
t t Z jj
FIG. 10: Normalized mcollbbττ distribution for signal and back-
ground (“τlepτhad”).
scenarios. While this channel appears to be promisingboth for both scenarios, we caution that we have notconsidered other pure QCD backgrounds, such as multi-jet or bb̄jj production, where the jets fake a hadronicallydecaying τ lepton. The reason is the difficulty of reli-ably quantifying the jet fake rate for these events, whichwhile being under 5%, depends strongly on the character-istics of the jet [40]. While we do not expect this class ofbackground contamination to be an impediment to signalobservation in the τhadτhad channel, we are less confidentin our quantitative statements here than for the otherfinal states.
V. DISCUSSION AND OUTLOOK
Uncovering the full structure of the SM scalar sectorand its possible extensions will be a central task for theLHC in the coming years. The results will have impor-tant implications not only for our understanding of themechanism of electroweak symmetry-breaking but alsofor the origin of visible matter and the nature of darkmatter. Extensions of the SM scalar sector that addressone or both of these open questions may yield distinc-tive signatures at the LHC associated with either mod-ifications of the SM Higgs boson properties and/or theexistence of new states.In this study, we have considered one class of Higgs
portal scalar sector extensions containing a singlet scalarthat can mix with the neutral component of the SU(2)Ldoublet leading to two neutral states h1,2. This xSMscenario can give rise to a strong first order electroweakphase transition as needed for electroweak baryogenesis;it maps direction onto the NMSSM in the decouplinglimit; and it serves as a simple paradigm for mixed statesignatures in Higgs portal scenarios that contain other
9
(GeV)Tlm
0 20 40 60 80 100 120
T/d
mσ
) dσ
(1/
-210
-110
= 270 GeV)2
Signal (m
= 370 GeV)2
Signal (m
b Z bτ t t~ -> l τ τ t t~ ->
Z jj
FIG. 8: Normalized mℓT distribution for signal and back-
ground (“τlepτhad”).
(GeV)ττcollm
50 100 150 200 250
/dm
σ) dσ
(1/
-210
-110
= 270 GeV)2
Signal (m
= 370 GeV)2
Signal (m
b Z b
t t Z jj
FIG. 9: Normalized mcollττ distribution for τ+τ− system in
signal and background (“τlepτhad”).
D. Hadronic (τhadτhad) final states.
The selection criteria for this channel are given by twohadronically-decaying τ -leptons (Nτh = 2), exactly zeroleptons ( Nℓ = 0), and a similar set of kinematic require-ments on the τ leptons and b-jets as in the other chan-nels: pτT > 10 GeV, |yb| < 2.5, ∆Rbb > 0.5, pbT > 10. Ascompared to the semileptonic and leptonic channels, thebackgrounds for the purely hadronic channel are smaller.The cut flows for the unboosted and boosted scenariosare given in Tables VI and VII, respectively.In light of the results from Tables VI and VII, we ob-
tain S/√S +B ∼ 5 with ∼ 100 fb−1 in the hadronic
channel for both the unboosted and boosted benchmark
(GeV)ττbbcollm
100 200 300 400 500 600/d
mσ
) dσ
(1/
-210
-110
= 270 GeV)2
Signal (m
= 370 GeV)2
Signal (m
b Z b
t t Z jj
FIG. 10: Normalized mcollbbττ distribution for signal and back-
ground (“τlepτhad”).
scenarios. While this channel appears to be promisingboth for both scenarios, we caution that we have notconsidered other pure QCD backgrounds, such as multi-jet or bb̄jj production, where the jets fake a hadronicallydecaying τ lepton. The reason is the difficulty of reli-ably quantifying the jet fake rate for these events, whichwhile being under 5%, depends strongly on the character-istics of the jet [40]. While we do not expect this class ofbackground contamination to be an impediment to signalobservation in the τhadτhad channel, we are less confidentin our quantitative statements here than for the otherfinal states.
V. DISCUSSION AND OUTLOOK
Uncovering the full structure of the SM scalar sectorand its possible extensions will be a central task for theLHC in the coming years. The results will have impor-tant implications not only for our understanding of themechanism of electroweak symmetry-breaking but alsofor the origin of visible matter and the nature of darkmatter. Extensions of the SM scalar sector that addressone or both of these open questions may yield distinc-tive signatures at the LHC associated with either mod-ifications of the SM Higgs boson properties and/or theexistence of new states.In this study, we have considered one class of Higgs
portal scalar sector extensions containing a singlet scalarthat can mix with the neutral component of the SU(2)Ldoublet leading to two neutral states h1,2. This xSMscenario can give rise to a strong first order electroweakphase transition as needed for electroweak baryogenesis;it maps direction onto the NMSSM in the decouplinglimit; and it serves as a simple paradigm for mixed statesignatures in Higgs portal scenarios that contain other
bbτ+τ- : discovery with ~ 100 fb-1 in “τlep τhad” channel
m2 = 270 GeV “un-boosted” m2 = 370 GeV “boosted”
EWPT & LHC Phenomenology Signatures m2 > 2 m1
m1 > 2 m2
Light: all models Black: LEP allowed
Profumo, R-M, Shaugnessy ‘07
Scan: EWPT-viable model parameters Mixed States:
Precision $ ILC
Higgs Portal: Simple Scalar Extensions
Extension EWPT DM DOF
May be low-energy remnants of UV complete theory & illustrative of generic features
Real singlet
Real singlet
Complex Singlet
Real Triplet
1
1
2
3
✔
✖
✔
✔
✖
✔
✔
✔
Back up slides
Complex Singlet: EWB & DM? Barger, Langacker, McCaskey, R-M Shaugnessy
Spontaneously & softly broken global U(1)
Controls ΩCDM , TC , & H-S mixing
Gives non-zero MA
< S > = 0
Complex Singlet: EWB & DM? Barger, Langacker, McCaskey, R-M Shaugnessy
Consequences:
Three scalars: h1 , h2 : mixtures of h & S
A : dark matter
Phenomenology: • Produce h1 , h2 w/ reduced σ • Reduce BR (hj ! SM)
• Observation of BR (invis)
• Possible obs of σSI
Higgs Portal: Simple Scalar Extensions
Extension EWPT DM DOF
Simplest non-trivial EW multiplet
Real singlet
Real singlet
Complex Singlet
Real Triplet
1
1
2
3
✔
✖
✔
✔
✖
✔
✔
✔
Real Triplet
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 ) Fileviez-Perez, Patel, Wang, R-M: PRD 79: 055024 (2009); 0811.3957 [hep-ph]
EWPT: a1,2 = 0 & <Σ0> = 0
DM & EWPT: a1 = 0 & <Σ0> = 0
/ /
Real Triplet
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 ) Fileviez-Perez, Patel, Wang, R-M: PRD 79: 055024 (2009); 0811.3957 [hep-ph]
EWPT: a1,2 = 0 & <Σ0> = 0
DM & EWPT: a1 = 0 & <Σ0> = 0
/ /
Small: ρ-param
Real Triplet: DM
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 )
EWPT: a1,2 = 0 & <Σ0> = 0
DM & EWPT: a1 = 0 & <Σ0> = 0
/ /
Small: ρ-param
Fileviez-Perez, Patel, Wang, R-M: PRD 79: 055024 (2009); 0811.3957 [hep-ph]
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Real Triplet
Two-step EWPT & dark matter
Patel, R-M: arXiv 1212.5652 ; Fileviez-Perez, Patel, RM, Wang
<Σ0 >
Σ ~ (1,3,0)
Baryogenesis
Quench sphalerons
Small entropy dilution
Σ dark matter
Higgs Diphoton Decays • SM “background” well below new CPV expectations
• New expts: 102 to 103 more sensitive
• CPV needed for BAU?
LHC: H ! γγ
D
D
€
h j
€
h jD
D
€
h j γ
γ
Σ+
Post –Moriond 2013
Fileviez-Perez, Patel, Wang, R-M: PRD 79: 055024 (2009); 0811.3957 [hep-ph]
Real Triplet: EWPT
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 ) H. Patel & R-M, 1212.5652/hep-ph (2012)
Two-step EWSB
1. Break SU(2)L x U(1)Y w/ Σ vev
2. Transition to Higgs phase w/ small or zero Σ vev
EWB favorable
Real Triplet: EWPT
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 ) H. Patel & R-M, 1212.5652/hep-ph (2012)
Two-step EWSB
1. Break SU(2)L x U(1)Y w/ Σ vev
2. Transition to Higgs phase w/ small or zero Σ vev
EWB favorable
Real Triplet : DM Search
Mass splitting due to EW symmetry breaking: O5 =
��H
⇤
�̄� H†H (25)
M⌃± �M⌃0 ⇠ ↵
4⇡MW (26)
3
Σ+ ! Σ0 + π+ (soft)
Generalizes to higher dim EW multiplets
Real Triplet : DM Search
Basic signature: Charged track disappearing after ~ 5 cm
SM Background: QCD jZ and jW w/ Z !νν & W!lν
Trigger: Monojet (ISR) + large ET €
qq →W ±* → H ±H2
€
qq → Z*,γ * → H +H−
Fileviez-Perez, Patel, Wang, R-M: PRD 79: 055024 (2009); 0811.3957 [hep-ph]
Real Triplet : DM Search
Basic signature: Charged track disappearing after ~ 5 cm
SM Background: QCD jZ and jW w/ Z !νν & W!lν
Trigger: Monojet (ISR) + large ET €
qq →W ±* → H ±H2
€
qq → Z*,γ * → H +H−
Cuts: large ET
hard jet
One 5cm track
Fileviez-Perez, Patel, Wang, R-M: PRD 79: 055024 (2009); 0811.3957 [hep-ph]
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Patel, R-M, Wise: PRD 88 (2013) 015003
Do good symmetries today need to be good symmetries in the early Universe ?
Symmetry Breaking & Restoration
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Do good symmetries today need to be good symmetries in the early Universe ?
Increasing T !
Pie
zoel
ectri
city
Rochelle salt: KNaC4H4O6 4H20
J. Valasek
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Patel, R-M, Wise: PRD 88 (2013) 015003
Do good symmetries today need to be good symmetries in the early Universe ? No
• O(n) x O(n): Weinberg (1974)
• SU(5), CP…: Dvali, Mohapatra, Senjanovic (‘79, 80’s, 90’s)
• Cline, Moore, Servant et al (1999)
• EM: Langacker & Pi (1980)
• SU(3)C : Patel, R-M, Wise: PRD 88 (2013) 015003
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Colored Scalars
Color breaking & restoration
Patel, R-M, Wise: PRD 88 (2013) 015003
Do good symmetries today need to be good symmetries in the early Universe ? No
• O(n) x O(n): Weinberg (1974)
• SU(5), CP…: Dvali, Mohapatra, Senjanovic (‘79, 80’s, 90’s)
• Cline, Moore, Servant et al (1999)
• EM: Langacker & Pi (1980)
• SU(3)C : Patel, R-M, Wise: PRD 88 (2013) 015003
Color Breaking & Restoration
H. Patel, R-M, Wise 1303.1140 (2013) Two illustrative cases:
Extension EWPT DM DOF
Color triplet scalar
Color triplet + singlet
…..
6
7
✔
✔
✖
✖
Color Breaking & Restoration
H. Patel, R-M, Wise 1303.1140 (2013) Two illustrative cases:
Extension EWPT DM DOF
Color triplet scalar
Color triplet + singlet
…..
6
7
✔
✔
✖
✖
Spontaneous B violation
EW Phase Transition: Higgs Portal
?
φ
?
φ
?
F
?
F1st order 2nd order
Increasing mh
New scalars
Colored Scalars (triplet)
Color breaking & restoration
Patel, R-M, Wise: PRD 88 (2013) 015003
1. Break SU(3)C
2. Restore SU(3)C
1. Break SU(3)C
2. Restore SU(3)C
Summary: Workshop Questions
• What happened ~ 10ps after the Big Bang?
• Single step (cross over) transition ?
• More d.o.f. with a richer pattern of EWSB?
• Single or multiple steps ? • First or second order ? • Coupled to origin of matter ?
• What are collider signatures that could provide clues?
• Modified Higgs properties (production, decays)
• New states
Back Up Slides
Ingredients for Baryogenesis
• B violation (sphalerons)
• C & CP violation
• Out-of-equilibrium or CPT violation
Standard Model BSM
✔
✖
✖
✔
✔
✔
Ingredients for Baryogenesis
• B violation (sphalerons)
• C & CP violation
• Out-of-equilibrium or CPT violation
Standard Model BSM
✔
✖
✖
✔
✔
✔
Scenarios: leptogenesis, EW baryogenesis, Afflek-Dine, asymmetric DM, cold baryogenesis, post-sphaleron baryogenesis…
Ingredients for Baryogenesis
• B violation (sphalerons)
• C & CP violation
• Out-of-equilibrium or CPT violation
Standard Model BSM
✔
✖
✖
✔
✔
✔
Scenarios: leptogenesis, EW baryogenesis, Afflek-Dine, asymmetric DM, cold baryogenesis, post-sphaleron baryogenesis…
Testable
Baryon Number Preservation “Washout factor”
ζ = F(ϕ)
ln S ~ A(TC) e ζ
Two qtys of interest:
• TC from Veff
• Esph from Γeff
Daisy Resummation Convergence of PT: going beyond expansion
Patel & R-M ‘11 Light stop scenario
Increased ΔV ! Lowered TC
For given T, increasingly negative increases difference between two minima
Csikor ‘00
DM Phenomenology Relic Density
He, Li, Li, Tandean, Tsai
Direct Detection
He, Li, Li, Tandean, Tsai
Barger, Langacker, McCaskey, R-M, Shaugnessy
H S
S
f
f
-
Higgs pole
Real Triplet: EWPT
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 ) H. Patel & R-M, 1212.5652/hep-ph (2012)
Two-step EWSB
1. Break SU(2)L x U(1)Y w/ Σ vev
2. Transition to Higgs phase w/ small or zero Σ vev
Real Triplet: EWPT
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 ) H. Patel & R-M, 1212.5652/hep-ph (2012)
Two-step EWSB
Real Triplet: EWPT
Σ0 , Σ+, Σ- ~ ( 1, 3, 0 ) H. Patel & R-M, 1212.5652/hep-ph (2012)
Two-step EWSB
1. Break SU(2)L x U(1)Y w/ Σ vev
2. Transition to Higgs phase w/ small or zero Σ vev
Color Breaking & Restoration
H. Patel, R-M, Wise 1303.1140 (2013) Two illustrative cases:
Extension EWPT DM DOF
Color triplet scalar
Color triplet + singlet
…..
6
7
✔
✔
✖
✖
Spontaneous B violation “Light”: special flavor structure
Color Breaking & Restoration
H. Patel, R-M, Wise 1303.1140 (2013) Two illustrative cases:
Extension EWPT DM DOF
Color triplet scalar
Color triplet + singlet
…..
6
7
✔
✔
✖
✖
Spontaneous B violation heavy: generic flavor structure
SM + Color Triplet
H. Patel, R-M, Wise 1303.1140 (2013)
Decays: C ! <C> = υC : B violation
SM + Color Triplet
Upper bound on mC:
H. Patel, R-M, Wise 1303.1140 (2013)
SM + Color Triplet + Singlet
H. Patel, R-M, Wise 1303.1140 (2013)
Heavier colored scalar
Higgs Decays: All Channels
)µSignal strength ( -1 0 +1
Combined
4l→ (*) ZZ→H
γγ →H
νlν l→ (*) WW→H
ττ →H
bb→W,Z H
-1Ldt = 4.6 - 4.8 fb∫ = 7 TeV: s-1Ldt = 13 - 20.7 fb∫ = 8 TeV: s
-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 20.7 fb∫ = 8 TeV: s
-1Ldt = 4.8 fb∫ = 7 TeV: s-1Ldt = 20.7 fb∫ = 8 TeV: s
-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 20.7 fb∫ = 8 TeV: s
-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 13 fb∫ = 8 TeV: s
-1Ldt = 4.7 fb∫ = 7 TeV: s-1Ldt = 13 fb∫ = 8 TeV: s
= 125.5 GeVHm
0.20± = 1.30 µ
ATLAS Preliminary
Theoretical Issues
Gauge-dependence in VEFF (ϕ , T )
VEFF (ϕ , T ) ! VEFF (ϕ , T ; ξ )
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) 023521
• H. Gonderinger, H. Lim, & MRM, arXiv:1202.1316
Origin of Gauge Dependence Effective Action
Effective Potential
Source term:
Not GI
Nielsen Identities Identity:
Extremal configurations:
Effective potential:
Baryon Number Preservation “Washout factor”
ζ = F(ϕ)
ln S ~ A(TC) e ζ
Two qtys of interest:
• TC from Veff
• Esph from Γeff
Baryon Number Preservation: Pert Theory
~
ζ = F(ϕ)
Conventional treatments
Gauge Dep
H. Patel & MRM, JHEP 1107 (2011) 029 “Baryon number preservation criterion” (BNPC)
Baryon Number Preservation: Pert Theory
~
ζ = F(ϕ)
Conventional treatments
Gauge Dep
• GI TC from hbar exp, Veff (φ+φ), or Hamiltonian formulation
• Use GI scale in Esph computation
H. Patel & MRM, JHEP 1107 (2011) 029 “Baryon number preservation criterion” (BNPC)
Nielsen Identities: Application to TC Critical Temperature
Veff (ϕmin , TC) = Veff (0 , TC)
Apply consistently order-by-order in
Implement minimization order-by-order (defines φn )
Fukuda & Kugo ‘74: T=0 VEFF Laine ‘95 : 3D high-T Eff Theory Patel & R-M ‘11: Full high T Theory
Obtaining a GI TC 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 φ