1. Higgs effective potential in the warped Gauge-Higgs Unification
Toshifumi Yamashita　
(SISSA Osaka Univ.)
2007/12/13
@KEK Theory Meeting
in preparation with N.Haba (Osaka Univ.)
S.Matsumoto (Tohoku Univ.)
N.Okada (KEK)

2. Plan
Introduction
Warped GHU
Interval v.s. orbifold
Summary

3. Introduction Gauge-Higgs Unification 5D theory gauge field 4D theory
D.B. Fairlie　 (1979)
N.S. Manton　(1979)
Gauge-Higgs Unification
5D theory
gauge field
compactification
4D theory
gauge field
scalar field
with KK modes
Higgs
5D gauge invariance protects the Higgs mass!!
H.Hatanaka, T.Inami and C.S.Lim (1998)

4. Introduction Orbifold ex) Fields may not be invariant ! ex)
Symm. transformation

5. Introduction Orbifold breaking ex) Doublet Higgs!
Y.Kawamura (2000)
ex)
Doublet Higgs!
It is important to calculate effective potential.
flat directions

6. Introduction 1-loop effective potential finite!! too small !!
M.Kubo, C.S.Lim and
H.Yamashita (2002)
N.Haba and T.Y. (2004)
1-loop effective potential
finite!!
too small !!
When , we get
We need
tuning

7. Introduction Higgs mass Top Yukawa
The quartic coupling is zero at the tree level.
The Higgs mass tends to be too small.
Top Yukawa
Top Yukawa is larger than the gauge coupling.
In the flat GHU scenario, typically
too small KK scale, Higgs mass & top mass.

8. Introduction warped GHU
The problems are solved (almost) automatically.
A lot of studies have been made.
R. Contino, Y. Nomura and A. Pomarol (2003)
K. Oda and A. Weiler (2005)
K. Agashe, R. Contino and A. Pomarol (2005)
Y. Hosotani and M. Mabe (2005)
Y. Hosotani, S. Noda, Y. Sakamura and S. Shimasaki (2006)
Y. Sakamura and Y. Hosotani (2007) …
The eff. potential is studied less exhaustively.
We investigate it.

9. Plan
Introduction
Warped GHU
Interval v.s. orbifold
Summary

10. Warped Gauge-Higgs Unification
Randall-Sundrum
Randall & Sundrum (1999)
natural scale : TeV

11. Warped Gauge-Higgs Unification
Weak scale vs. KK & top mass
A parameter
of fermions
flat case
In the warped GHU scenario,
the gauge coupling is rather suppressed.
gauge
N.Haba, S.Matsumoto,
N.Okada and T.Y.
in preparation

12. Warped Gauge-Higgs Unification
+ : periodic
- : anti-periodic
Effective Potential
N.Haba, S.Matsumoto,
N.Okada and T.Y.
in preparation

13. Warped Gauge-Higgs Unification
N.Haba, S.Matsumoto,
N.Okada and T.Y.
in preparation
Effective Potential w/
2 anti-periodic fundamental fermions
1 periodic adjoint fermion
N. Haba and T.Y. (2004)

14. Warped Gauge-Higgs Unification
N.Haba, S.Matsumoto,
N.Okada and T.Y.
in preparation
Effective Potential w/
2 anti-periodic fundamental fermions
1 periodic adjoint fermion
A large Higgs mass

15. Plan
Introduction
Warped GHU
Interval v.s. orbifold
Summary

16. Interval v.s. orbifold Orbifold ex) = interval (?)
Fields may not be invariant!
ex)
Gauge transformation

17. Interval v.s. orbifold Preliminary Orbifold - : Dirichlet ex)
N.Haba, S.Matsumoto,
N.Okada and T.Y.
in preparation
Orbifold
+ : Neumann
- : Dirichlet
ex)
= interval (?)
wider class of BCs
C. Csaki et al (2004)
N. Sakai and N. Uekusa (2007)
In the orbifold picture
Periodic
Anti-Periodic
In the interval picture
Preliminary
All vanishing !!

18. Summary warped Gauge-Higgs unification
large KK scale
large top mass
large Higgs mass
N.Haba, S.Matsumoto,
N.Okada and T.Y.
in preparation
Effective potential is calculated
Non-orbifold like fermions
Vanishing contributions
The low energy effective theory
is also analyzed in the coming paper

19. Back-up Slides