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
‣ 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
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
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.
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.
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.
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
New physics modelsExtended Higgs sectorO(100) GeV higher than TeV scale
Predict
Determine
How can we know the true Higgs sector?
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.
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 !!
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.
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)
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.
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
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 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:
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
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
Decay of the 3-plet Higgs bosons
Δm > 0
Δm < 0
mH3 = 150 GeV
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
・ 3-plet Higgs decays
l
l H5
l
l
H3
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
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
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.
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
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
Production cross sections
H5++ H5
+
H50
Production cross sections
H5++ H5
+
H50
VBF
Production cross sections
H5++ H5
+
H50
VBF
Associated
Production cross sections
H5++ H5
+
H50
Mixed DY
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
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
Signal
Background
pp → W+W+jj, pp → W+Z jj, pp → W+W- / ZZ jj , tt
★ We use the VBF and associated production processes.
Δη distributionsDifference of the pseudo-rapidity:
Δη distributionsDifference of the pseudo-rapidity:
Δη > 3.5, (Δη > 4.0 for event)
MT distributionsTransverse mass:
MT distributionsTransverse 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 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:
Higgs decays into γγ and Zγ
Rγγ
RZγ
+
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
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
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
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
,
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
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).