Renormalization of the Higgs Triplet Model

Kei Yagyu (National Central U)

S. Kanemura, KY, arXiv: 1201.6287 [hep-ph], acceptedM. Aoki, S. Kanemura, M. Kikuchi. KY, arXiv: 1204.1951 [hep-ph]

National Taiwan University, 14th May 20121/35

Phenomenology of the Higgs Triplet Model at the LHC

Kei YAGYU 　 (Univ. of Toyama)　　　　　　　　　柳生　慶　　　　　富山大学

M. Aoki, S. Kanemura, KY, arXiv: 1110.4625 [hep-ph]

2nd Jan. 2012 National Taiwan University

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Plan of the talk• Introduction - The Higgs triplet model

• Renormalization of the Higgs Triplet Model - Radiative corrections to the EW parameters - Radiative corrections to the Higgs potential

• Phenomenology - Higgs → 2 photon decay - LHC physics

• Summary3/35

Introduction・ The Higgs sector has not been confirmed. - Minimal? or Non-minimal? - The Higgs boson search is underway at the LHC. The Higgs boson mass is constrained to be 115 GeV < mh < 127 GeV or mh > 600 GeV at 95% CL. - There is a “SM-like” Higgs boson at around 125 GeV.

・ There are phenomena which cannot be explained in the SM. - Tiny neutrino masses, dark matter and Baryon asymmetry of the Universe

・ New physics may explain these phenomena above the TeV scale. 100 GeV TeV or 100 TeV or GUT scale or …

SM New physics model, where mν, DM, BAU are explained. Energy scale

Energy scale100 GeV

SM with extended Higgs sectors, where mν, DM, BAU are explained.

TeV

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Explanation by extended Higgs sectors• Tiny neutrino masses - The type II seesaw model - Radiative seesaw models (e.g. Zee model)

• Dark matter

- Higgs sector with an unbroken discrete symmetry • Baryon asymmetry of the Universe - Electroweak baryogenesis

Introduced extended Higgs sectors

SU(2) doublet Higgs + Singlet [U(1)B-L model] + Doublet [Inert doublet model] + Triplet [Type II seesaw model], etc…

Studying extended Higgs sectors is important to understand the phenomena beyond the SM. 5/35

How we can constrain various Higgs sectors?

Higgs Potential・ Higgs boson mass・ Higgs self coupling

Yukawa Interaction・ Flavor changing neutral current

EW Parameters・ Rho parameter ・ Gauge boson masses

Experimental DataLEP, LHC, ILC, …

It is necessary to prepare precise calculations of observables in order to compare the experimental data and to distinguish various Higgs sectors.

An Extended Higgs Sector

Affects

Compare

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How we can constrain various Higgs sectors?

Yukawa Interaction・ Flavor changing neutral current

Experimental DataLEP, LHC, ILC, …

Affects

Compare

In this talk, we focus on the Higgs Triplet Model (HTM) and its renormalization of electroweak parameters and the Higgs potential.

An Extended Higgs Sector

Higgs Potential・ Higgs boson mass・ Higgs self coupling

EW Parameters・ Rho parameter ・ Gauge boson masses

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The 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

When the lepton number breaking parameter μ is taken to be of O(eV) scale, we can take MΔ ~ O(100-1000) GeV. In this case, the HTM can be tested at colliders. 8/35

Important predictions (Tree-Level)

How these predictions are modified by the radiative corrections?

2. Characteristic relations among the masses of the Δ-like Higgs bosons are predicted.

1. Rho parameter deviates from unity.

A, H

H+

H++A, H

H+

H++

Case I Case II Mass2 Mass2

Under vΔ << vΦ (Required by ρexp ~ 1)

mH++2 － mH+

2 m≃ H+2 －

mA2

mA2 m≃ H

2

Renormalization of the electroweak parameters

Renormalization of the Higgs potential

These relations are useful to test the model.

・ Mass eigenstates: (SM-like) h, (Triplet-like) H±±, H±, H, A

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StrategyRenormalization of the EW parameters. We search allowed parameter regions by the EW precision data.

Renormalization of the Higgs potential By using the constrained parameter space, we calculate one-loop corrected predictions of observables in the Higgs potential (e.g., the mass spectrum, hhh coupling).

Phenomenology at the LHC

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Renormalization of the EW parameters

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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

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.

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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

,

Models with ρ = 1 at the tree level

The electroweak observables are described by the 3 input parameters.

There are 3 parameters: g, g’ and v in the kinetic term of Higgs fields.

We can choose αem, GF and mZ as the 3 input parameters.

αem(mz) = 128.903 ± 0.0015, GF = 1.16637 ± 0.00001 GeV-2,

mz = 91.1876 ± 0.0021 GeV

The weak angle sin2θW = sW2 and mW can be written in terms of the above 3 inputs.

The counter term of δsW2 is derived as ~ δρ = ρ-1 = αem T

The quantity δρ (or T) measures the violation of the custodial symmetry. 14/35

Scalar boson and fermion loop contributions to δρ

Peskin, Wells (2001);Grimus, Lavoura, Ogreid, Osland (2008);Kanemura, Okada, Taniguchi, Tsumura (2011).

Dependence of the quadratic mass splitting among particles in the same isospin multiplet appears in the T (rho) parameter.

The two Higgs doublet model case

Custodial sym. breaking in the top-bottom sector

Custodial sym. breaking in the scalar sector

mh = 117 GeV

500 GeV

15/35mH+ = 300 GeVmA = 200 – 300 GeV

αem T =

Models without ρ = 1 at the tree level

e

e

ZsW2 is defined by the effective Zee vertex: ^

sW2 = 0.23146 ± 0.00012^

There are 4 parameters (instead of 3 in the SM): g, g’, v and ρ0 in the kinetic term of Higgs fields.

The electroweak observables are described by the 4 input parameters.

We can choose αem, GF, mZ and sW2 as the input parameters.^

Blank, Hollik (1997)

In order to calculate the EW parameters at one-loop order, we shift the bare parameters and impose reno. conditions.

This parameter causes ρtree ≠ 1 at the tree level. Ex. the VEV of the triplet Higgs in the HTM.

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On-shell renormalization scheme

IPI diagram Counter term Counter termIPI diagram

On-shell renormalization conditions

From these 5 conditions, 5 counter terms (δg, δg’, δv, δZW and δZB) are determined.

2-pointfunction

3-pointfunction= =

++

Parameters shift: g → g + δg, g’ → g’ + δg’, v → v + δv, sW2 → sW

2 + δ sW2,

Wμ → ZW1/2 Wμ , Bμ → ZB

1/2 Bμ

^ ^ ^

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On-shell renormalization scheme

IPI diagram Counter term Counter termIPI diagram

On-shell renormalization conditions

2-pointfunction

3-pointfunction= =

++

Parameters shift: g → g + δg, g’ → g’ + δg’, v → v + δv, sW2 → sW

2 + δ sW2,

Wμ → ZW1/2 Wμ , Bμ → ZB

1/2 Bμ

How we can determine the counter term δ sW2 ?

^ ^ ^

^18/35

Radiative corrections to ρ in models w/o ρ = 1 at the tree level sW

2 　 is an independent parameter. → Additional renormalization condition is necessary. Blank, Hollik (1997)

By the renormalization of δsW2, quadratic dependence of mass splitting disappear.

Model w/ ρtree = 1

Model w/o ρtree = 1

Effect of the custodial symmetry breaking

= 0

1PI diagram Counter term

^

^

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In models without ρ = 1 at the tree level, one-loop contribution toρ dose not measure the violation of the custodial symmetry.

Radiative corrections to ρ in models w/o ρ = 1 at the tree level sW

2 　 is an independent parameter. → Additional renormalization condition is necessary. Blank, Hollik (1997)

By the renormalization of δsW2, quadratic dependence of mass splitting disappear.

We apply this renormalization scheme to the HTM.

Model w/ ρtree = 1

Model w/o ρtree = 1

Effect of the custodial symmetry breaking

= 0

1PI diagram Counter term

^

^

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Renormalized ρ and mW in model w/o ρtree = 1

,

One-loop corrected ρ and mW are given by:

Renormalization conditions

+ Vertex corrections and box diagram corrections

=X Y

p

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Prediction of the W boson mass at the 1-loop level

In Case I, by the effect of the mass splitting, there are allowed regions . Case II is highly constrained by the data.

A, H

H+

H++

Case I mH++ = 150 GeV mH++ = 300 GeV

Kanemura, KY, arXiv: 1201.6287 [hep-ph]

Δm = mH++ - mH+

A, H

H+

H++

Case II

mA = 150 GeV mA = 300 GeV

We fixed mh=125 GeV andmt=173 GeV.

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One-loop corrected rho parameter in the HTM

A, H

H+

H++

Case I

A, H

H+

H++

Case II

In Case I, mH++ = 150 GeV, 100 GeV <|Δm| < 400 GeV , 3 GeV < vΔ < 8 GeV is favored, whileCase II is highly constrained by the data.

vΔ is calculated by the tree level formula:

Kanemura, KY, arXiv: 1201.6287 [hep-ph]

Δm = mH++ - mH+

mH++ = 150 GeV, mh = 125 GeV mA= 150 GeV, mh = 125 GeV

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Heavy mass limit

When we take heavy mass limit, loop effects of the triplet-like scalar bosons disappear. Even in such a case, the prediction does not coincide with the SM prediction.

ξ = mH++2 – mH+

2

SM prediction

Case I

Case II

Kanemura, KY, arXiv: 1201.6287 [hep-ph]

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Decoupling property of the HTM

HTM with L# (μ ≠ 0)

・　 ρ ≠ 1 at the tree level (vΔ ≠ 0)・　 4 input parameters (αem, GF, mZ and sW

2)

HTM with L# (μ = 0)

・　 ρ = 1 at the tree level (vΔ = 0)・　 3 input parameters (αem, GF and mZ ) with sW

2 = 1-mW2/mZ

2

SM・　 L# is conserved.・　 ρ = 1 at the tree level・　 3 input parameters (αem, GF and mZ ) with sW

2 = 1-mW2/mZ

2

Heavy Δ-like fields limitHeavy Δ-like fields limit

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Renormalization of the Higgs potential

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Higgs Potential

Non-minimalHiggs sectors

Discovery of extra Higgs bosons; i.e., Charged Higgs bosons H±, …

Deviation of (SM-like) Higgs couplings (hVV, hff, hhh) from those predicted values in the SM.

Precise calculation of these physics quantities is very important to discriminate various Higgs sectors.

★ Once “SM-like” Higgs boson (h) is discovered, precise measurements for the Higgs mass and the triple Higgs coupling turns to be very important.

Direct evidence

Indirect signature

★Measuring the mass spectrum, decay branching ratios of these extra Higgs bosons.

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・ The most general form under the SU(2)×U(1) gauge sym.

10 scalar states can be translated to 3 NG bosons, 1 SM-like scalar boson and 6 Δ-like scalar bosons. . 6 Δ-like scalar bosons → H±±, H±, A and H 　　　

Doubly-charged Singly-charged CP-odd CP-even

There are 10 degrees of freedom of scalar states.

The Higgs potential in the HTM

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・ The most general form under the SU(2)×U(1) gauge sym.

8 parameters in the potential 8 physical parametersv , vΔ , mH++ , mH+ , mA , mH , mh , α μ , m , M , λ1 , λ2 , λ3 , λ4 , λ5

If the U(1) lepton number sym. is approximately restored (μ → 0, vΔ → 0 ),

5 parameters contribute to the masses 5 physical parametersv , M , mh , + 2 triplet Higgs massesm , M , λ1 , λ4 , λ5

The Higgs potential in the HTM

2 of 4 triplet-like Higgs masses are not independent. → There must be 2 relations:

mH++2 － mH+

2 = mH+2 － mA

2 = -v2λ5 /428/35

Renormalization of the Higgs potential8 parameters in the potential 8 physical parameters

v , vΔ , mH++ , mH+ , mA , mh , mH , α μ , m , M , λ1 , λ2 , λ3 , λ4 , λ5

Vanishing 1-point function δTφ , δTΔ

Tadpole ：　 δTφ , δTΔ ,Wave function renormalization ： δZH++, δZH+, δZA, δZH, δZh

Counter termsδv , δvΔ , δmH++

2 , δmH+2 , δmA

2, δmh2 , δmH

2 , δα

On-shell condition δmH++2 , δmH+

2 , δmA2, δmh

2 , δmH2

δZH++, δZH+, δZA, δZH, δZh

No-mixing condition δα

where 2-point function is defined by

Aoki, Kanemura, Kikuchi, KY, arXiv: 1204.1951

Renormalization of GF and sw2 δv , δvΔ ^

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Radiative corrections to the mass spectrum

In favored parameter sets by EW precision data: mH++ = O(100)GeV, |Δm| ～ 100GeV, 　 ΔR can be as large as O(10)%.

Case I

(mA2)treeis determined by mH++

2 and mH+2 :

Ratio of the squared mass difference R

Tree level:

Less than 10-3

Loop level: Loop correction

Aoki, Kanemura, Kikuchi, KY, arXiv: 1204.1951

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One-loop corrected hhh couplingOn-shell renormalization of the hhh coupling:

By measuring the mass spectrum as well as the hhh coupling, the HTM can be tested.

For α = 0 and vΔ2 << v2

Quartic mass dependence of Δ-like Higgs bosons appears to the hhh coupling ⇒Non-decoupling property of the Higgs sector.

Results for the renormalization of the EW parameter suggests mH++ = O(100)GeV, |Δm| ～ 100GeV. In this set, deviation of hhh is predicted more than 25%

Case I

Unitarity is broken

Aoki, Kanemura, Kikuchi, KY, arXiv: 1204.1951

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Phenomenology

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Higgs → two photon decay

A, H

H+

H++

Case I

SM contribution 　　　　　　 ＋ Triplet-like scalar loop contribution

The decay rate of h → γγ is around half in the HTM compared with that in the SM.

+

Kanemura, KY, arXiv: 1201.6287 [hep-ph]

mH++ = 150 GeV, mh = 125 GeV mH++ = 300 GeV, mh = 125 GeV

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Phenomenology at the LHC★From the results of the renormalization of the EW parameters

Favored scenario by the precision data: 1. Case I (mH++ > mH+ > mA, mH) 2. Δm (=mH++ - mH+ ) = O(100) GeV 3. mH++ < 300-400 GeV 4. vΔ = O(1) GeV

★From the results of the renormalization of the Higgs potentialΔR ~ - 10% 　→　 (mH++

2 - mH+ 2)/(mH+

2 – mA 2) ~ 0.9

★ Decays of triplet-like Higgs bosons (Multi-W boson event may be expected):

H++ → W+W+

H+ → W-H++

H, A → W±H∓ → W±W±H ∓ ∓

C.-W. Chiang, T. Nomura, K. Tsumura (2012) → Studied multi-W signature assuming Δm = 0.

M. Aoki, S. Kanemura, KY (2011) → Studied the pheno. of the HTM with Δm ≠ 0. Cascade decay

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Summary• Precise calculations of EW parameters as well as Higgs couplings (hhh, hVV, hff)

are important to discriminate various Higgs sectors. • The important predictions in the Higgs Triplet Model:

• Renormalization of the EW parameters - 4 input parameters (not 3 as the SM) are necessary in to describe the EW parameters. ⇒ mA > mH+ > mH++ with Δm=O(100) GeV is favored. • Renormalization of the Higgs potential - One-loop corrected mass spectrum: ΔR = O(10)% - One-loop corrected hhh coupling : deviation from the SM prediction can be as large as O(100) %• The decay rate of h→γγ is half compared to that of the SM prediction. At the LHC, multi-W signatures can be expected.

mH++2 － mH+

2 m≃ H+2 － mA

2

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Back up slides

Transverse mass distribution Ex.) Measurement for W boson mass 　　　　　 Definition of the transverse mass　　　　　　　　　　　　　　　　　　　　　　　　　　　　

𝑚𝑊

pp →𝑊+𝑊− →(𝑙+𝜈)(𝑗𝑗) ≃

Smith,Neerven,Vermaseren,PRL(1983)

Counter terms δv and δvΔ

Measurements of hhh coupling at colliders

LHC gg → hh → W+W-W+W- → l+l+4j

ILC

Baur, Plehn, Rainwater, PRL89 (2002)

e+e- → hhνν

- mh < 140 GeV : It is difficult to detect the hhh

coupling at the LHC. Yasui, Kanemura, Kiyoura, Odagiri, Okada, Senaha, Yamashita, hep-ph/0211047

mh (GeV)

e+e- → Zhh

It can be expected around 10-30% accuracy. Detector level simulation is underway.

Mass reconstructionqq’ → H++H- → (l+l+ννbb)(jjbb) qq’ → H+H → (l+νbb)(bb) qq → HA → (bb)(bb)

8.0 fb (14 TeV) 2.8 fb (7 TeV)

33 fb 12 fb

130 fb 42 fb

All the masses of the Δ-like scalar bosons may be reconstructed.

vΔ = 10-2 GeV

MT

MT

MT, Minv

mH++ mH+ mH, mA

Signal only

hH, A

H+

H++

114 GeV119 GeV130 GeV

140 GeV

Large mh and mH++ case (Case I)mh = 125 GeV and mH++ = 150 GeV mh = 125 GeV and mH++ = 300 GeV

mh = 700 GeV and mH++ = 150 GeV mh = 700 GeV and mH++ = 300 GeV

Approximately formulae of Δr

Case I:

Case II:

mA > mH+ > mH++

mH++ > mH+ > mA

By using

Case I:

Case II:

with mlightest = mH++

with mlightest = mA

Y=1 Higgs Triplet Model:Kinetic term

CovariantDerivative

VEVs

Masses for Gauge bosons

ρ parameter

Branching ratio of H++

Δm = 0 Δm = 10 GeV

vΔ = 0.1 MeV, mH++ = 200 GeV

mH++ = 150 GeV

mH++ = 300 GeVmH++ = 500 GeV

Phenomenology of Δm ≠ 0 is drastically different from that of Δm = 0.

mH++ = 150 GeV

mH++ = 300 GeV

mH++ = 500 GeV

Chakrabarti, Choudhury, Godbole, Mukhopadhyaya, (1998);Chun, Lee, Park, (2003); Perez, Han, Huang, Li, Wang, (2008); Melfo, Nemevsek, Nesti, Senjanovic, (2011)

Branching ratios of H+, H and A

★ The H+ → f0 W+ mode can be dominant in the case of Δm ≠ 0.

★ The f0 → bb mode can be dominant when vΔ > MeV.

Renormalized hhh coupling in the 2HDMKanemura, Okada, Senaha, Yuan (2004)