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Report
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
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
Current states of the Higgs search at the LHC
‣ The Higgs-like particle has been found at around 126 GeV
at the LHC with 5σ.
h → γγ
h → ZZ* → 4 lepton
Historic Milestone but only the Beginning.
R. Heuer, July 4th, CERN
Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012,
CMS
Hadron Collider Physics Symposium 2012,
ATLAS
Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012,
CMS
Hadron Collider Physics Symposium 2012,
ATLAS
H → ZZ and H→ WW modes are good agreement to the SM prediction.
Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012,
CMS
Hadron Collider Physics Symposium 2012,
ATLAS
Obs. H → γγ signal seems to be large compared to the SM prediction.
Current states of the Higgs search at the LHC
Signal strength (σobs/σSM) in each mode
Hadron Collider Physics Symposium 2012,
CMS
Hadron Collider Physics Symposium 2012,
ATLAS
H → bb and H→ττ modes still have a large uncertainty.
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!
Extended Higgs sector
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
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
Predict
Extended
sector
How Higgs
can we
know the true New
Higgs
sector?
physics
models
O(100) GeV
Determine
higher than TeV scale
Basic two constraints from experiments
There are hints to determine the structure of the Higgs sector.
1. Electroweak rho parameter
Additional doublets or singlets
→ ρtree = 1
+0.0017
ρexp = 1.0008 -0.0007
Additional triplets or higher isospin Reps.
→ In general, ρtree ≠ 1
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.
The minimal Higgs Triplet Model
The Higgs triplet field Δ is added to the SM.
・Important new interaction terms:
Cheng, Li (1980);
Schechter, Valle, (1980);
Magg, Wetterich, (1980);
Mohapatra, Senjanovic, (1981).
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
MΔ : Mass of triplet scalar boson.
vΔ : VEV of the triplet Higgs
O(0.1) eV
O(0.1) eV
O(1)
246 GeV
O(100) GeV
The HTM can be
tested at colliders !!
The minimal Higgs Triplet Model
The Higgs triplet field Δ is added to the SM.
・Important new interaction terms:
Cheng, Li (1980);
Schechter, Valle, (1980);
Magg, Wetterich, (1980);
Mohapatra, Senjanovic, (1981).
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
MΔ : Mass of triplet scalar boson.
vΔ : VEV of the triplet Higgs
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.
Georgi, Machacek (1985)
The Georgi-Machacek (GM) Model
★ The minimal extension of the HTM.
★ Two isospin triplet Higgs fields
are introduced to the SM.
HTM
GM
★ The doublet field and the triplet fields can
be expressed as SU(2)L×SU(2)R form:
SU(2)I
U(1)Y
U(1)L
Φ
2
1/2
0
χ
3
1
-2
ξ
2
0
0
SU(2)R
SU(2)L
★ If we take two triplet VEVs are the same: <χ0> = <ξ0>
SU(2)L ×SU(2)R → SU(2)V (Custodial Symmetry)
Decomposition
Δ:3×3
Φ:2×2
Irreducible decomposition
5 +3 +1
5-plet Higgs
3 +1
Mixing (angle β):
Goldston bosons
+ 3-plet Higgs
Mixing (angle α) :
SM-like Higgs
+ Singlet Higgs
h, H1
The Higgs bosons belonging to the same multiplet are degenerate
in mass because of the custodial symmetry.
Interactions
(Neutrino) Yukawa interaction
l
H5
h, H1
H3
∝1/sinβ
l
l
l
∝cosβ/sinβ
l
∝cosβ/sinβ
l
(Usual) Yukawa interaction
f
h, H1
H3
∝tanβ
Gauge interaction
f
f
f
∝cosα/cosβ, sinα/cosβ
V
V
∝ sinβ
H5
V
h, H1
∝ cosβ*cosα, cosβ*sinα
V
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.
Decoupling limit
The mass formulae (α = 0)
In the limit of vΔ →0 (β → 0, M22 → 0)
★ Triplet-like Higgs bosons are decoupled
when M12 is taken to be large values.
★There is a relationship among the masses:
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.
Phenomenology
Decay of the 5-plet Higgs bosons
Δm = mH3 – mH5
mH3 = 150 GeV, Δm > 0
H5++
H5+
The case of Δm > 0 is the same as the case of Δm=0.
H50
Decay of the 3-plet Higgs bosons
mH3 = 150 GeV
Δm > 0
Δm < 0
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.
4 regions on the vΔ – mΔ plane
★Region I: small vΔ and small mΔ
・5-plet Higgs decays
l
H5
l
・3-plet Higgs decays
l
H3
l
4 regions on the vΔ – mΔ plane
★Region III: small vΔ and large mΔ
・5-plet Higgs decays
H3
l
H5
H5
l
V
・3-plet Higgs decays
H5
H3
H3
H1
V
V
4 regions on the vΔ – mΔ plane
★Region IV: large vΔ and large mΔ
・5-plet Higgs decays
V
H5
H3
H5
V
・3-plet Higgs decays
H5
H3
H3
V
V
H1
V
4 regions on the vΔ – mΔ plane
★Region II: large vΔ and small mΔ
・5-plet Higgs decays
V
H5
V
・3-plet Higgs decays
f
H3
f
We discuss the phenomenology for Region II.
Production modes for 5- and 3-plet Higgs
5-plet
Both
1. Drell-Yan Process:
H5, H3
3-plet
3. Vector boson fusion Process
5. Yukawa Process
H3+
H5
H5’ , H3’
2. Mixed Drell-Yan Process:
H5
4. Gauge boson associate Process
H30
H5
H3
H30, H3+
V
,t
Production modes for 5- and 3-plet Higgs
5-plet
Both
1. Drell-Yan Process:
H5, H3
3-plet
3. Vector boson fusion Process
5. Yukawa Process
H3+
H5
H5’ , H3’
2. Mixed Drell-Yan Process:
H5
4. Gauge boson associate Process
H30
H5
H3
H30, H3+
V
,t
Production cross sections
H5++
H5+
H50
Production cross sections
H5++
H5+
VBF
H50
Production cross sections
H5++
H5+
VBF
Associated
H50
Production cross sections
H5++
H5+
Mixed DY
H50
Strategy
The VBF and associated processes
H5
H5
2 forward jets tagging
H5++ may be detected.
Transverse mass cut + b-jet veto
H5+ and H50 may be detected.
The mass degeneracy of the 5-plet may be tested.
H5
H3
The mixed DY process
Transverse mass cut
The mass degeneracy of the 3-plet may be tested.
V
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
5-plet Higgs reconstructions
★ We use the VBF and associated production processes.
Signal
Background
pp → W+W+jj,
pp → W+Z jj,
pp → W+W- / ZZ jj , tt
Δη distributions
Difference of the pseudo-rapidity:
Δη distributions
Difference of the pseudo-rapidity:
Δη > 3.5, (Δη > 4.0 for
event)
MT distributions
Transverse mass:
MT distributions
Transverse mass:
50 GeV < MT < 150 GeV
Signal and background events
(int. luminosity 100 fb-1)
b-jet tagging efficiency: 0.6
3-plet Higgs reconstructions
★ We use the mixed DY production processes.
5-plet Higgs bosons → diboson decay, 3-plet Higgs bosons → dijet decay
Distributions in the mixed DY process
The Δη cut cannot be applied to the mixed DY process,
while the MT cut can be used.
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.
Mjj distributions
★The dijet invariant mass distribution after taking the MT cut:
The masses of H3+ and H30 may be measured by the peak
in the dijet invariant mass distribution.
Higgs decays into γγ and Zγ
+
RZγ
Rγγ
Higgs to γγ and Zγ decay
RZγ
Rγγ
★ 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.
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.
Back up slides
Constraint from Zbb vertex
The electroweak rho parameter
★ The experimental value of the rho parameter is quite close to unity.
ρexp ~ 1
Tree-level expression for the rho parameter (Kinetic term of Higgs fields)
ρtree = 1
・ Standard Model
・Multi-doublet
(with singlets) model
There is the custodial SU(2) sym.
in the kinetic term
Higgs Potential
ρtree ≠ 1
・ Models with Higgs fields
whose isospin is larger than ½
e.g., the HTM.
The custodial SU(2) sym. is
broken in the kinetic term.
These sector affects
the rho parameter by the
loop effects.
Yukawa interaction
12/35
Custodial Symmetry
The SM Lagrangian can be written by the 2×2 matrix form of the Higgs doublet:
When we take g’ and yA → 0,
Lagrangian is invariant under SU(2)L×SU(2)R
★ Kinetic term
,
After the Higgs field gets the VEV:
★ Higgs potential
this symmetry is reduced to
SU(2)L=SU(2)R =SU(2)V (custodial symmetry).
★ 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
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
Interactions
Yukawa interaction
f
H3
∝tanβ
f
h, H1
∝ cosα/cosβ, sinα/cosβ
f
f
V
V
Gauge interaction
H5
∝ sinβ
V
h, H
∝ cosβ*cosα, cosβ*sinα
V
5-plet Higgs can (cannot) couple to the gauge boson (fermons).
3-plet Higgs can (cannot) couple to the fermions (gauge bosons).

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