IntroductionIntroductionOrbifolding & Hosotani breakingOrbifolding & Hosotani breakingHiggs mass in GHUHiggs mass in GHUSummarySummary hep-ph/0411250 with N.Haba (Tokushima)hep-ph/0411250 with N.Haba (Tokushima)

K.Takenaga(Osaka) K.Takenaga(Osaka)

Higgs mass in gauge-Higgs unification

Toshifumi Yamashita　(KEK)

2005/6/10 2005/6/10 @Taipei Summer @Taipei Summer InstituteInstitute

Introduction

Gauge-Higgs Unification

5D theory

with KK modes gauge field

Higgs

compactification

4D theory

gauge field

scalar field

5D gauge invariance protect the Higgs mass!!

Introduction

To do

Higgs sector

•To yield doublet Higgs scalar(s)•To reproduce a correct EWSB•To get a sufficiently heavy Higgs

Quark/Lepton sector

•To yield the matter content of SM•To reproduce appropriate Yukawa

hierarchy, mixing, large

To get a sufficiently heavy Higgs

orbifolding

NPB 669 (2003) Scrucca, Serone, and Silvestrini

ex)

Orbifolding & Hosotani breaking

Orbifold

Fields may not be invariant!

ex)

ex)

Orbifolding & Hosotani breaking

Orbifold breaking

Doublet Higgs!

flat directionsIt is important to calculate effective potential.

Y.Kawamura

Orbifolding & Hosotani breaking

Effective potential•induced through quantum effect •1-loop effective potential :

M.Kubo, C.S.Lim and H.Yamashita

Orbifolding & Hosotani breaking

Effective potential•induced through quantum effect •1-loop effective potential :

M.Kubo, C.S.Lim and H.Yamashita

We need , because .

finite!!

Orbifolding & Hosotani breaking

Effective potential

•appropriate bulk fields

correct EWSB

PRD 70, 1015010 (2004) N.Haba, Y.Hosotani, Y.Kawamura and T.Y.

Higgs mass?

Higgs mass in GHU

Higgs mass

The quartic coupling is zero at the tree level.

The Higgs mass tends to be small.

We found appropriate bulk fields can also yield a large Higgs mass.

goal When?

PRD 70, 1015010 (2004) N.Haba, Y.Hosotani, Y.Kawamura and T.Y.

Other contributions are also written by a linear combination of w/o .

Higgs mass in GHU

Effective potentialgauge sectorex)

hep-ph/0411250 N.haba, K.Takenaga and T.Y.

Higgs mass in GHU

Approximation formulae

<0

<0>0

>0

• is dominated by , w/ . Bulk fields w/ are required.

•When , a large number of bulk fields w/ are required to yield .

•When , a large Higgs mass is realized.

hep-ph/0411250 N.haba, K.Takenaga and T.Y.

Higgs mass in GHU

Conclusion

When , a large Higgs mass may be realized, w/o so many bulk fields.

Numerical study

hep-ph/0411250 N.haba, K.Takenaga and T.Y.

Summary

Summary

•We investigated the Higgs mass in GHU analytically.

•A numerical analysis confirmed the result.

•A large Higgs mass can be obtained w/ a few bulk fields, when .

This analysis can be applied for many models.