Higgs mass in gauge-Higgs unification
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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.
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