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Page 1: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 2: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 3: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

‣ 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

Page 4: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  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

Page 5: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  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

H → ZZ and H→ WW modes are good agreement to the SM prediction.

Page 6: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  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

Obs. H → γγ signal seems to be large compared to the SM prediction.

Page 7: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  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

H → bb and H→ττ modes still have a large uncertainty.

Page 8: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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!

Page 9: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Extended Higgs sector

Page 10: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 11: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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?

Page 12: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 13: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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 !!

Page 14: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 15: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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)

Page 16: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 17: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 18: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 19: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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:

Page 20: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 21: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Phenomenology

Page 22: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 23: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Decay of the 3-plet Higgs bosons

Δm > 0

Δm < 0

mH3 = 150 GeV

Page 24: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 25: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 26: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 27: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 28: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 29: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 30: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 31: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Production cross sections

H5++ H5

+

H50

Page 32: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Production cross sections

H5++ H5

+

H50

VBF

Page 33: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Production cross sections

H5++ H5

+

H50

VBF

Associated

Page 34: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Production cross sections

H5++ H5

+

H50

Mixed DY

Page 35: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 36: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 37: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 38: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Δη distributionsDifference of the pseudo-rapidity:

Page 39: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Δη distributionsDifference of the pseudo-rapidity:

Δη > 3.5, (Δη > 4.0 for event)

Page 40: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

MT distributionsTransverse mass:

Page 41: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

MT distributionsTransverse mass:

50 GeV < MT < 150 GeV

Page 42: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Signal and background events(int. luminosity 100 fb-1)

b-jet tagging efficiency: 0.6

Page 43: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

3-plet Higgs reconstructions ★ We use the mixed DY production processes.

5-plet Higgs bosons → diboson decay, 3-plet Higgs bosons → dijet decay

Page 44: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Distributions in the mixed DY process

The Δη cut cannot be applied to the mixed DY process, while the MT cut can be used.

Page 45: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 46: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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:

Page 47: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Higgs decays into γγ and Zγ

Rγγ

RZγ

+

Page 48: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 49: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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.

Page 50: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Back up slides

Page 51: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

Constraint from Zbb vertex

Page 52: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 53: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

,

Page 54: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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

Page 55: Testing the custodial symmetry  in  the Higgs sector of the  Georgi-Machacek model  at  the  LHC

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).


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