Download - Testing the custodial symmetry in the Higgs sector of the Georgi-Machacek model at the LHC
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Testing the custodial symmetry in the Higgs sector of the
Georgi-Machacek model at the LHC
Kei Yagyu (National Central U)
C.-W. Chiang, KY, arXiv: 1211.2658 [hep-ph], to be published in JHEP
National Taiwan University, 17th December 2012
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Plan of the talk• Introduction - Current status of the Higgs boson search at the LHC
• Extended Higgs sectors - Motivation - The Georgi-Machacek model
• Phenomenology - Higgs decays - Higgs productions - Simulation study at the LHC - Higgs to γγ and Zγ decay
• Summary
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‣ The Higgs-like particle has been found at around 126 GeV at the LHC with 5σ.
Historic Milestone but only the Beginning.
h → ZZ* → 4 leptonh → γγ
R. Heuer, July 4th, CERN
Current states of the Higgs search at the LHC
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Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012, ATLAS
Hadron Collider Physics Symposium 2012, CMS
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Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012, ATLAS
Hadron Collider Physics Symposium 2012, CMS
H → ZZ and H→ WW modes are good agreement to the SM prediction.
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Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012, ATLAS
Hadron Collider Physics Symposium 2012, CMS
Obs. H → γγ signal seems to be large compared to the SM prediction.
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Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012, ATLAS
Hadron Collider Physics Symposium 2012, CMS
H → bb and H→ττ modes still have a large uncertainty.
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The SM-like Higgs boson?
• At present, observed new resonance at 126 GeV looks like the SM-like Higgs boson.
(-Consistent with the precision measurements at LEP, - Observed from expected events γγ and ZZ → H is spin 0 or 2)
• Large deviation from the SM prediction in H→γγ mode• The central value for the H → ττ mode exceeds 0.
We need to collect more data in order to clarify the property of the new particle w/126 GeV.
Still there are possibilities to consider non-minimal Higgs sectors!
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Extended Higgs sector
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Why extended Higgs sector?• No principle in the Higgs sector - Negative μ2 term → Just an assumption - Higgs boson as an elementary scalar. → Cause for the quadratic div. in the Higgs mass correction.
• Phenomena which cannot be explained in the SM - Neutrino masses - Dark matter - Baryon asymmetry of the Universe
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Why extended Higgs sector?• No principle in the Higgs sector → Supersymmetry, Dynamical symmetry breaking, Little Higgs models, …
• Phenomena which cannot be explained in the SM - Neutrino masses → Rad. seesaw models, type-II seesaw mechanism - Dark matter → Discrete sym. in the Higgs sector e.g. Inert doublet - Baryon asymmetry of the Universe → Electroweak baryogenesis
New physics modelsExtended Higgs sectorO(100) GeV higher than TeV scale
Predict
Determine
How can we know the true Higgs sector?
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Basic two constraints from experimentsThere are hints to determine the structure of the Higgs sector.
1. Electroweak rho parameter ρexp = 1.0008
Additional doublets or singlets Additional triplets or higher isospin Reps.→ ρtree = 1 → In general, ρtree ≠ 1
-0.0007+0.0017
2. Flavor Changing Neutral Current (FCNC)Tree level FCNC processes should be suppressed.
Models with multi-doublet structure → There appear tree level FCNCs.
★Additional doublet(s) → FCNC, ★Additional triplet(s) → Rho parameter
In this talk, we focus on the possibility that the Higgs sector has triplets.
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The minimal Higgs Triplet Model
The Higgs triplet field Δ is added to the SM.
MΔ : Mass of triplet scalar boson. vΔ : VEV of the triplet Higgs
Cheng, Li (1980); Schechter, Valle, (1980); Magg, Wetterich, (1980);Mohapatra, Senjanovic, (1981).
・ Important new interaction terms:
SU(2)I U(1)Y U(1)L
Φ 2 1/2 0
Δ 3 1 -2
Lepton number breaking parameter
・ Neutrino mass matrix
O(1)
O(0.1) eVO(0.1) eV
246 GeV
O(100) GeV
The HTM can be tested at colliders !!
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The minimal Higgs Triplet Model
The Higgs triplet field Δ is added to the SM.
MΔ : Mass of triplet scalar boson. vΔ : VEV of the triplet Higgs
Cheng, Li (1980); Schechter, Valle, (1980); Magg, Wetterich, (1980);Mohapatra, Senjanovic, (1981).
・ Important new interaction terms:
SU(2)I U(1)Y U(1)L
Φ 2 1/2 0
Δ 3 1 -2
Lepton number breaking parameter
・ Neutrino mass matrix
Non-zero vΔ breaks the custodial symmetry → ρ deviates from unity at the tree level.We discuss the extension of the HTM to keep the custodial symmetry.
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The Georgi-Machacek (GM) Model
★ Two isospin triplet Higgs fields are introduced to the SM.
SU(2)I U(1)Y U(1)L
Φ 2 1/2 0
χ 3 1 -2
ξ 2 0 0 ★ The doublet field and the triplet fields can
be expressed as SU(2)L×SU(2)R form:
★ If we take two triplet VEVs are the same: <χ0> = <ξ0>
★ The minimal extension of the HTM.
HTM
GM
SU(2)L ×SU(2)R → SU(2)V (Custodial Symmetry)
SU(2)R
SU(2)L
Georgi, Machacek (1985)
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Decomposition Φ : 2 × 2 Δ : 3 × 3
Irreducible decomposition
5 + 3 + 1 3 + 1
5-plet Higgs
h, H1
Mixing (angle α) : SM-like Higgs + Singlet Higgs
Mixing (angle β): Goldston bosons + 3-plet Higgs
The Higgs bosons belonging to the same multiplet are degenerate in mass because of the custodial symmetry.
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Interactions
(Usual) Yukawa interaction
Gauge interaction
f
f
H3
∝tanβ ∝cosα/cosβ, sinα/cosβ
∝ sinβ h, H1
∝ cosβ*cosα, cosβ*sinα
(Neutrino) Yukawa interaction
f
fh, H1
H5
V
V
V
V
l
lH3
l
l H5
l
lh, H1
∝1/sinβ ∝cosβ/sinβ ∝cosβ/sinβ
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Higgs potential ★ The most general SU(2)L×SU(2)R invariant potential:
★ There are 9 parameters in the potential: [m1, m2, μ1, μ2 : dimension full, λ1 – λ5 : dimension less]
2 VEVs : v, vΔ, 4 masses : mH5, mH3, mH1, mh, 1 mixing angle : α and reminding 2 parameters: μ1, μ2.
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Decoupling limitThe mass formulae (α = 0)
In the limit of vΔ →0 (β → 0, M22 → 0)
★ Triplet-like Higgs bosons are decoupled when M1
2 is taken to be large values.
★There is a relationship among the masses:
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Consequences of the custodial sym.
1. Electroweak rho parameter is unity at the tree level → Triplet VEV can be taken to be O(10) GeV.
2. Mass degeneracies among 5- and 3-plet Higgs bosons; mH5++ = mH5+ = mH50 = mH5, mH3+ = mH30 = mH3
3. Specific interactions; 5-plet Higgs can couple to gauge boson pairs. 3-plet Higgs can couple to fermion pairs .
We focus on the features 2 and 3 in order to identify the custodial symmetric GM model at the LHC.
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Phenomenology
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Decay of the 5-plet Higgs bosons
H5++ H5
+ H50
Δm = mH3 – mH5
The case of Δm > 0 is the same as the case of Δm=0.
mH3 = 150 GeV, Δm > 0
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Decay of the 3-plet Higgs bosons
Δm > 0
Δm < 0
mH3 = 150 GeV
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4 regions on the vΔ – mΔ plane★Decays of the triplet-like Higgs bosons can be classified into 4 distinctive regions depending on the vΔ and Δm.
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4 regions on the vΔ – mΔ plane★Region I: small vΔ and small mΔ
・ 5-plet Higgs decays
・ 3-plet Higgs decays
l
l H5
l
l
H3
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4 regions on the vΔ – mΔ plane★Region III: small vΔ and large mΔ
l
l H5
・ 5-plet Higgs decays
VH5
H3
・ 3-plet Higgs decays
V
H3
H5
V
H3
H1
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4 regions on the vΔ – mΔ plane★Region IV: large vΔ and large mΔ
・ 5-plet Higgs decays
VH5
H3
・ 3-plet Higgs decays
H5
V
V
V
H3
H5
V
H3
H1
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4 regions on the vΔ – mΔ plane★Region II: large vΔ and small mΔ
H5
V
V
・ 5-plet Higgs decays
・ 3-plet Higgs decays
f
f
H3
We discuss the phenomenology for Region II.
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Production modes for 5- and 3-plet Higgs
1. Drell-Yan Process:
2. Mixed Drell-Yan Process:
3. Vector boson fusion Process
4. Gauge boson associate Process
5. Yukawa Process
H5
H3
H5’ , H3
’
H5, H3
V
H5
H5
Both 5-plet 3-plet
H3+
H30, H3
+
, t
H30
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Production modes for 5- and 3-plet Higgs
1. Drell-Yan Process:
2. Mixed Drell-Yan Process:
3. Vector boson fusion Process
4. Gauge boson associate Process
5. Yukawa Process
H5
H3
H5’ , H3
’
V
H5
H5
H3+
H30, H3
+
, t
Both 5-plet 3-plet
H30
H5, H3
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Production cross sections
H5++ H5
+
H50
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Production cross sections
H5++ H5
+
H50
VBF
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Production cross sections
H5++ H5
+
H50
VBF
Associated
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Production cross sections
H5++ H5
+
H50
Mixed DY
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StrategyThe VBF and associated processes
H5
H5
V2 forward jets tagging
The mass degeneracy of the 5-plet may be tested.
H5+ and H5
0 may be detected.
Transverse mass cut + b-jet veto
H5++ may be detected.
Transverse mass cut
The mass degeneracy of the 3-plet may be tested.
The mixed DY processH5
H3
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Scenario• mH3 = 150 GeV, mH5 = 140 GeV, vΔ = 20 GeV, α = 0
→ Concrete example for Region II
• Branching fractions: BR(H5→VV) ~ 100 %,
BR(H3+ → cs) ~ 30%, BR(H3
+ → τν) ~ 70%,
BR(H30 → bb) ~ 90%
• We perform the signal & background analysis by using MadGraph5 with the parton level.
We consider the hadronic decay of the 3-plet Higgs bosons
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5-plet Higgs reconstructions
Signal
Background
pp → W+W+jj, pp → W+Z jj, pp → W+W- / ZZ jj , tt
★ We use the VBF and associated production processes.
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Δη distributionsDifference of the pseudo-rapidity:
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Δη distributionsDifference of the pseudo-rapidity:
Δη > 3.5, (Δη > 4.0 for event)
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MT distributionsTransverse mass:
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MT distributionsTransverse mass:
50 GeV < MT < 150 GeV
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Signal and background events(int. luminosity 100 fb-1)
b-jet tagging efficiency: 0.6
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3-plet Higgs reconstructions ★ We use the mixed DY production processes.
5-plet Higgs bosons → diboson decay, 3-plet Higgs bosons → dijet decay
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Distributions in the mixed DY process
The Δη cut cannot be applied to the mixed DY process, while the MT cut can be used.
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Signal and background events(int. luminosity 100 fb-1)
After taking the same MT cut, the signal significance can exceed 5 in both the events.
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Mjj distributions
The masses of H3+ and H3
0 may be measured by the peak in the dijet invariant mass distribution.
★The dijet invariant mass distribution after taking the MT cut:
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Higgs decays into γγ and Zγ
Rγγ
RZγ
+
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Higgs to γγ and Zγ decay
★ Current LHC data of h→γγ mode can be explained when mH5 <~ 150 GeV and mH3 = 150 GeV.
★ Measuring the h→Zγ channel is also important to test the structure of the Higgs sector. (Chiang, KY, arXiv: 1207: 1065[hep-ph]) When Rγγ ~ 1.6, RZγ ~ 1.2.
Rγγ
RZγ
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Summary• The Georgi-Machacek (GM) model is the minimal model included Higgs
triplet fields whose Higgs sector is custodial symmetric.
• In the GM model, there are the 5-plet, 3-plet and singlet Higgs bosons under the custodial SU(2)V symmetry.
• The masses of the Higgs bosons belonging to the same SU(2)V multiplet are the same.
• Testing mass degeneracy among the 5-plet Higgs bosons: → The VBF and weak boson associated processes are useful. • Testing mass degeneracy among the 3-plet Higgs bosons: → The mixied DY process is useful after the detection of the 5-plet.
The custodial symmetry in the GM model may be tested by above the two steps at the LHC.
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Back up slides
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Constraint from Zbb vertex
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Higgs Potential
The electroweak rho parameter ★ The experimental value of the rho parameter is quite close to unity.
There is the custodial SU(2) sym. in the kinetic term
ρexp ~ 1
Tree-level expression for the rho parameter ( Kinetic term of Higgs fields)
・ Models with Higgs fields whose isospin is larger than ½ e.g., the HTM.
ρtree = 1 ρtree ≠ 1
・ Standard Model
・ Multi-doublet (with singlets) model
The custodial SU(2) sym. is broken in the kinetic term.
Yukawa interaction
These sector affects the rho parameter by the loop effects. 12/35
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Custodial SymmetryThe SM Lagrangian can be written by the 2×2 matrix form of the Higgs doublet:
★ Kinetic term
★ Higgs potential
★ Yukawa interaction (top-bottom sector)
SU(2)V breaking by g’ is included in the definition of the rho parameter, while that by yA is not. There is a significant contribution to the deviation of rho = 1 from the top-bottom sector by the loop effect.
13/35
After the Higgs field gets the VEV:
this symmetry is reduced to SU(2)L= SU(2)R =SU(2)V (custodial symmetry).
When we take g’ and yA → 0, Lagrangian is invariant under SU(2)L×SU(2)R
,
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Testing an extended Higgs sector at colliders
• Direct way: Discovery of extra Higgs bosons Ex. Charged Higgs boson, CP-odd Higgs boson, …
• Indirect way: Precise measurement for the Higgs couplings Ex. hhh, hff, hVV
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InteractionsYukawa interaction
Gauge interaction
f
f
H3 ∝tanβ
f
f
h, H1 ∝ cosα/cosβ, sinα/cosβ
H5
V
V
∝ sinβ h, H
V
V
∝ cosβ*cosα, cosβ*sinα
5-plet Higgs can (cannot) couple to the gauge boson (fermons). 3-plet Higgs can (cannot) couple to the fermions (gauge bosons).