Renormalization in the higgs triplet model
This presentation is the property of its rightful owner.
Sponsored Links
1 / 23

Renormalization in the Higgs triplet model PowerPoint PPT Presentation


  • 62 Views
  • Uploaded on
  • Presentation posted in: General

Renormalization in the Higgs triplet model . Mariko Kikuchi (Univ. of Toyama). Collaborators: Mayumi Aoki, Shinya Kanemura , Kei Y agyu. M . Aoki, S. Kanemura , M. Kikuchi, K. Yagyu , PLB 714, 279 ( 2012). Workshop on Multi-Higgs Models , 31. August, 2012, Lisbon. C ontents.

Download Presentation

Renormalization in the Higgs triplet model

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Renormalization in the higgs triplet model

Renormalization in the Higgs triplet model

Mariko Kikuchi (Univ. of Toyama)

Collaborators:

Mayumi Aoki, Shinya Kanemura, Kei Yagyu

M. Aoki, S. Kanemura, M. Kikuchi, K. Yagyu,PLB 714, 279(2012)

Workshop on Multi-Higgs Models , 31. August, 2012, Lisbon


C ontents

Contents

We focus on the Higgs triplet model.

The motivation is neutrino masses.

Higgs Triplet Model(HTM)

Renormalization in the EW parameters

One loop calculations in the Higgs potential

  • Type II seesaw scenario

  • EW ρ parameter, Mass Formula

mW2, ρ,

Γ(h→gg)

hWW coupling

Corrections to

Mass formula

hhh coupling

Corrections to


Neutrino mass

Neutrino Mass

Higgs triplet model (HTM) Type II seesaw model

Cheng, Li (PRD, 1980)

Mohapatra, Senjanovic (PRD, 1981)

Mass eigenstates

H±±, H±, A, H, h

Breaking L# two units

⇒ Majorana massesare produced.

×

If μ is small, masses of triplet fields can be at the TeV scale.

It is possible to test at the collider experiment.⇒MΔ~ O(100)GeV~ 1TeV!!!


Neutrino mass1

Neutrino Mass

Higgs triplet model (HTM) Type II seesaw model

Cheng, Li (PRD, 1980)

Mohapatra, Senjanovic (PRD, 1981)

Mass eigenstates

H±±, H±, A, H, h

Breaking L# two units

⇒ Majorana massesare produced.

×

  • ~ O(1)

    μ~ O(0.1-1)eV

If μ is small, masses of triplet fields can be at the TeV scale.

It is possible to test at the collider experiment.⇒MΔ~ O(100)GeV~ 1TeV !!!


Model

Model

  • Mass eigenstatesH±±, H±, A, H, h

  • Mass hierarchy

  • Mass spectrum

Mass difference arises due to λ5


Mass relation

Mass Relation

  • Constraint from ρ parameter

i = φ, Δ

HTM

(experiment)

vφ: VEV of φ

vΔ: VEV of Δ

vΔ2vφ2 ⇒ mixing between φ and Δis small.

(αis small.)

  • Mass formula

mH++2- mH+2≃ mH+2- mA2≃ -

This mass formula is useful to distinguish the model from the other models.

For future precision measurement,

we have to obtain the formula with radiative corrections.


Phenomenology

Phenomenology

If Δm≠0, decay processes of triplet-like scalar fields are different from the case with Δm=0.

  • Ex)) the decay process of H++

Δm≠ 0

Δm= 0

(Δm=30GeV)

the cascade decay of H++dominates.

H++→ H+W+→ H0W+W+→ bb W+W+

H++→ l+l+⇒

mH++>400GeV

LHCdata

In the case (Δm ≠ 0), mH++>400GeV

  • Mass identification

Aoki,

Kanemura,

Yagyu

(PRD85,

055007)

2012

All masses of triplet-like Higgs bosons may be measured at LHC

by evaluating the transverse mass distribution.


Renormalization for ew parameter

Renormalization for EW parameter

Model with ρ=1 at tree (SM, THDM, …)

3 inputs: GF, α, mZ2

+ -

Quadraticmass effects appear!

Parameters in Gauge Sector: v, vΔ, g, g’

HTM: ρ≠1 at tree

4 inputs: GF, α, mZ2, sin2θW

Renormalization

Condition for sin2θW

Blank, Hollik (NP,1998)

Kanemura, Yagyu (PRD, 2012)

Quadraticmass effectsare absorbed by the renormalization of sin2θW.


Renormalization in the higgs triplet model

Kanemura, Yagyu (PRD,2012)

Aoki, Kanemura, Kikuchi, Yagyu (in preparation)

mh=125GeV

mlightest=150 GeV

α = 0


Ew parameters

EW parameters

  • Input parameters

PDG(2010)

  • Tree level relations


M w 2

Kanemura, Yagyu (PRD,2012)

mW2, ρ

Aoki, Kanemura, Kikuchi, Yagyu (in preparation)

mh=125GeV

mlightest=150GeV, α = 0

Case I is favored !!!!!

Case II is constrained !!!


M w 21

mW2, ρ

Kanemura, Yagyu (PRD,2012)

Aoki, Kanemura, Kikuchi, Yagyu (in preparation)

mh=125GeV

mlightest=150GeV, α = 0

Δm= -400 GeV

Δm = -100 GeV

|Δm|=100~400GeV

Unitarity requires |Δm| < 300-400 GeV

|Δm|=mH++ - mH+


M w 22

mW2, ρ

Kanemura, Yagyu (PRD,2012)

mh=125GeV

mlightest=150GeV, α = 0

Aoki, Kanemura, Kikuchi, Yagyu (in preparation)

vΔis 3.5-8 GeV


Renormalization in the higgs triplet model

EW Data

|Δm|~ O(100-400) GeV

vΔ ~3.5-8 GeV

Unitarity Bound

|Δm| < 300-400 GeV

mH++~ 100-200GeV


Renormalization in the higgs triplet model

Rgg

2

t

W

H++

H+

Rggdepends on λ4

+

+

+

A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka, L. Rahili(arXiv:1112.5453 )

A. G. Akeroyd, S. Moretti (arXiv: 1206.0535 )

vΔ=5.69GeV

mlightest=300GeV

ICHEP(2012) Summary Talk

If λ4 is minus, Rgg can be larger than 1 !!

Unitarity Bound -3≦λ4≦4 (Δm=-100GeV)


Renormalization of the higgs potential

Renormalization of the Higgs potential

<Physical Parameters>

<Parameters in the Higgs potential>

μ , m , M , λ1 , λ2 , λ3 , λ4 , λ5

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

  • Counter-terms

δv, δvΔ,δmH++2 , δmH+2, δmA2, δmh2, δmH2 , δα

Tadpoles:δTφ,δTΔ ,

Renormalization of wave functions:δZh , δZH , δZA , δZG0 , δZH+ , δZG+ , δZH++ , δChH ,

δCAG0 , δCH+G+

  • We determine δv, δvΔby EW renormalization.

  • On-shellrenormalization scheme

Field strength

Mixing angle


Radiative correction to the mass formula

Radiative correction to the mass formula

In favored parameter sets by EW data

: mH++<mH+<mH,mA, vΔ=3.5-8 GeV,

Δm=100~300GeV, mlightest=100~150GeV

1

mA2(tree) have been an output parameter.

New Mass formula with the 1-loop correction

ΔR is large (O(10)% as a correction).

⇒ We have to take into account the radiative correction for comparing the precision data.


Hzz h ww

hZZ,hWW

hZZ

hWW

Δm= mH++-mH+

  • hZZ receives about -1.8~-2.5% correction.

  • hWW receives about -0.5~-1.8% correction.

  • ⇒ We expect to test hZZ and hWW coupling at ILC.


Renormalization in the higgs triplet model

hhh

  • hhh receives a large correction, about 25~100%

  • ⇒We expect to test hhh coupling at ILC.


Summary

Summary

  • The tree level

The precision measurement in the future

Theoretical calculations with radiative corrections

×

  • ρ≠ 1

mH++2- mH+2≃ mH+2- mA2

=

ID of a model

  • 1 loop correction

  • Renormalization scheme is different from the one of the SM.

Input parameters Gf, α, mZ2, + sin2θW

  • Results of radiative corrections

  • mW2 and ρ ⇒ Constraint to the parameters region

  • Rggcan be larger than 1.

  • ΔRcan be large. ~O(10)%

  • hZZ, hWW receives O(1)% corrections.

  • hhh can receive large corrections as non-decoupling effects.~10~30%

When we compare with the precision data,

we should consider the radiative correction !!!


Renormalization in the higgs triplet model

Thank you !!

Mariko


R in the case ii

ΔR in the case II


Renormalization for ew parameter1

Renormalization for EW parameter

Blank, Hollik (NP,1998)

Kanemura, Yagyu (PDR, 2012)

ρ deviates from unity at the tree level.

Parameters in the kinetic term:

v, vΔ, g, g’

Physical parameters:Gf, α, mZ2, sin2θW, mW2, v, (vΔ)

Input parameters Gf, α, mZ2, sin2θW

On-shellrenormalization

ρ≠1(HTM)

ρ=1(SM, THDM)

Δr

Δr

Quadraticmass effects in Δrare absorbed by renormal of sin2θW.

Quadraticmass effects appear!


  • Login