Renormalization of the Higgs Triplet

ModelMariko Kikuchi （ Univ. of Toyama ）

CollaboratorsM. Aoki （ Kanazawa Univ. ） , S. Kanemura （ Univ. of Toyama ） ,

K. Yagyu （ National Central University ）

　　 2012. 06. 09 　Aoki, Kanemura, Kikuchi, Yagyu arXiv:1204.1951 [hep-ph]

Introduction Higgs sector is unknown.• The Higgs sector of the SM(minimal) is just assumption.• There are many possibilities for the Higgs sector.

Several phenomena which can not be explained in the SM• Tiny neutrino masses • Existence of dark matter • Baryon asymmetry of

the Universe→ 　 New physics beyond the SM is required !!!

New physics 　⇔　 the Higgs sector 　 ?

• Some new physics models contain each characteristic extended Higgs sector.Determination of the Higgs sector

New physics

Our studying is determining the Higgs sector by the result of the accelerator experiment.

THDs (Φ1 ＋ Φ2)

MSSM

Φ1 ＋ Φ2(inart)

New physics model(DM)

Contents

１． We constructed the renormalization scheme for the one-loop calculation of the observables in HTM with Y=1.　　　 ρ≠1 at the tree level, renormalization of mixing angles, lepton number breaking 　　　　　　　　　２． We calculate the radiative correction to the characteristic mass formula at the tree level .Mass formula () is given a large contribution of radiative corrections.３． We calculate radiative corrections to hhh coupling.　　 It can devite from the SM prediction due to the non-decoupling property.

SM-likeTriplet-like

The precision measurement expected in the future × Theoretical calculations

with radiative corrections= ID of a model

• Type II seesaw scenario is a mechanism which generates tiny neutrino masses.

• The Higgs sector of the Type II seesaw model is Φ ＋ Δ.

• We focus on the HTM this time.

Type II seesaw model = Higgs triplet model

Neutrino mass （ Seesaw mechanism ）

There is a dimension-five operator relevant for neutrino masses.

Type seesawⅠ 　　　　　　　　　　Type seesawⅡ Radiative seesaw （ Zee

model ）×

A complex triplet scalar field

・ A charged singlet scalar field・ Perturbative effect

Right hand neutrinos

There are many mechanisms which predict this operator .

The Higgs boson obtains the vacuum

expectation values(VEV).

Neutrinos cannot have masses in the SM. (Dirac mass, Majorana mass )

ℒ=𝐶Λ 𝑙𝑐 𝑙 𝜙𝜙 𝐶

Λ 𝜈𝑐𝜈𝜙0𝜙0 𝐶Λ

⟨𝜙0 ⟩ ⟨𝜙0 ⟩𝜈𝑐𝜈

TypeⅡseesaw mechanism

must be very large (GeV) in an ordinary way, with O(1) couplings, in order to give tiny neutrino masses. But…

×

SU(2)L U(1)Y U(1)LΦ 2 1/2 0Δ 3 1 -2

Majorana type neutrino masses are produced because μ term breaks L# two units.

TypeⅡseesaw mechanism

must be very large (GeV) in an ordinary way, in order to give tiny neutrino masses. But…

×

SU(2)L U(1)Y U(1)LΦ 2 1/2 0Δ 3 1 -2

Majorana type neutrino masses are produced because μ term breaks L# two units.

h and μ are small → EW scale In this case this model can be tested by LHC or Linear Colliders.

Recently, a mechanism which have very small μ was proposed by perturbative effects. 　　Kanemura, Sugiyama （ arXiv:1202.5231 (2011))

LagrangianSU(2)L U(1)Y U(1)L

Φ 2 1/2 0Δ 3 1 -2New Yukawa interaction terms

A Higgs potential

Mass structure Constraint from the experimental result of ρ parameter 　

Constraint from ρ parametervΔ

2<<vφ2 　

→Mixing between φ and Δ is very small.

（ an experimental value ）

SM-like scalar field : 　 hTriplet-like scalar field ：　 H±±, H±, H, A

vφ 　：　 VEV of the doublet fieldvΔ 　：　 VEV of the triplet fieldMass eigenstates

Extended Higgs with (Ti, Yi)

Mass structureMass spectrum

　 Constraint from

ρ parametervΔ

2<<vΦ2

We focus on the interesting relation among masses

mΦ2 － mΦ’

2

　mH++2 － mH+

2 m≃ H+2 － mA

2

This model has a characteristic mass formula at the tree level.

mH++2 － mH+

2 m≃ H+2 － mA

2 　≃ －This mass formula is useful to distinguish the model from the other models when all mass of the triplet-like Higgs bosons.

Phenomenology • Phenomenology of the HTM without the mass difference often has

been studied. • Phenomenology of the HTM with the mass difference is very

different from it without the mass difference.

Case (Δm=30GeV)ⅡNO the mass difference The mass difference exists

H++ のBR

Han et.al (2008)

Aoki, Kanemura, Yagyu (2011)Akeroyd, Sugiyama (2011)

• The parameter corresponding to the mass difference is λ5.

• λ5 is a free parameter. 　→　 We take λ5≠0, and consider the case which there is

the mass difference.

mH++2 － mH+

2 m≃ H+2 － mA

2 　≃ －

Phenomenology

𝑚𝐻++¿¿

Aoki, Kanemura, Yagyu, (Phys.Rev. D85 (2012))

Production and decay processes of H++

　 in the Case II 　

H++ → 　 H+W+ → 　 H0W+W+ → 　 bb W+W+

The case of Δm2≠0Cascade decays of triplet fields dominate.

All masses of triplet-like Higgs bosons can be measured in LHC by observing the Yacobian peak in the transverse mass distribution.

Radiative correction of the HTMRenormalization of the gauge

sector （ g,g’,v,vΔ ）• In the HTM(Y=1), ρ parameter deviates from unity at the tree level.

• Renormalization scheme of the HTM is different from it of the SM.

There is more one independently measured parameters of the HTM than them of the SM.

Renormalization of V(φ, Δ) This talk

• Mass spectrum Radiative corrections to the mass formula

• hhh coupling We calculate radiative corrections and evaluate the ratio of them of the HTM to them of the SM.

Kanemura, Yagyu (arXiv:1201.6287 (2011))

Radiative correction of the HTMRenormalization of the gauge

sector （ g,g’,v,vΔ ）• In the HTM(Y=1), ρ parameter deviates from unity at the tree level.

• Renormalization scheme of the HTM is different from it of the SM.

There is more one independently measured parameters of the HTM than them of the SM.

Renormalization of V(φ, Δ) This talk

• Mass spectrum Radiative corrections to the mass formula

• hhh coupling We calculate radiative corrections and evaluate the ratio of them of the HTM to them of the SM.

Kanemura, Yagyu (arXiv:1201.6287 (2011))

Renormalization of the Higgs sector

Tadpole ：　 δTφ , δTΔ ,

δv , δvΔ , δmH++2 , δmH+

2 , δmA2, δmh

2 , δmH2 , δα

Wave function renormalization ：δZh , δZH , δZA , δZG0 , δZH+ , δZG+ , δZH++ , δChH , δCAG0 , δCH+G+

Parameters of potential （ 8 ）Physical parameters (8)

Counter-terms (20)

v , vΔ , mH++ , mH+ , mA , mh , mH , α

μ , m , M , λ1 , λ2 , λ3 , λ4 , λ5

Renormalization of the Higgs sector

δv , δvΔ

Vacuum conditions

On-shell conditions

Diagonalizationat the one-loop level

• By renormalization conditions of electroweak parameters (GF , sin2θW , αEM, mZ) 　

• The others are determined by renormalization conditions of the Higgs sector.

Tadpoles

Two point functions

δTφ , δTΔ

δα , δChH , δCAG0 , δCH+G+, …..

δmH++2 , δmH+

2 , δmA2, δmh

2 , δmH2

Determining counter-terms

Kanemura, Yagyu (arXiv:1201.6287), 2011

P2=mφ2 ， mφ’

2

P2=mφ2

Radiative corrections to the mass spectrum

mh=125GeV , α=0Δm = mH++ - mH+

ΔR

1

In favored parameter sets by EW precision date:mH++ ～ O(100)GeV, 　 |Δm| ～100GeV 　R is given a large correction as large as O(10)%.

Case Ⅰ

Modification of R = 1 by the one-loop correction : ΔR

The pole mass of A is a predicted value

(mA2)tree is determined by mH++

2 and mH+2 　　

Ratio of the mass difference R

One-loop corrected hhh coupling

By measuring the hhh coupling in ILC, the HTM can be tested ！

α=0, 　 vΔ2 << vφ

2

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 EW parameters suggest mH++ ～ O(100)GeV, |Δm| ～ 100GeV.In this parameter region, Deviation in hhh is predected more than 25% ！

Case Ⅰ(%)

Unitarity is broken

on-shell renormalization of the hhh coupling

Summary• Type II seesaw model (the HTM) has a mechanism which can simply produce tiny

neutrino masses .

• In the HTM, there is a characteristic mass formula at the tree level from a constraint from ρ parameter.　　→ It’s very useful to test the model.

• It is important to calculate the observables at one-loop level to compare them from the precision measurement expected in future. So we have constructed the renormalization of the Higgs sector in the HTM and calculated some observables at the one-loop level.

• We find that the radiative correction to the mass formula which depends on triplet like Higgs masses and the mass difference is large. 　　　　　　　→ we may be able to identify the model by precisely measuring the mass spectrum

at the LHC and the ILC.

• We find that the radiative correction to the hhh coupling is large in the allowed region under the EW precision data. 　　　　　　　　　　→ We may be able to identify the model at the ILC.

mH++2 － mH+

2 m≃ H+2 － mA

2 　

hhh coupling in the THDMKanemura, Okada, Senaha, Yuan (2004)

Widths of Δ-like Higgs bosons

Production cross section

ΔR in the case II

hhh coupling in the case II

LHC ILC