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Higgs effective potential in the warped Gauge-Higgs UnificationPowerPoint Presentation

Higgs effective potential in the warped Gauge-Higgs Unification

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### Higgs effective potential in the warped Gauge-Higgs Unification

### Back-up Slides 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)

Plan Unification

- Introduction
- Warped GHU
- Interval v.s. orbifold
- Summary

Introduction Unification

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)

Introduction Unification

- Orbifold breaking

Y.Kawamura (2000)

ex)

Doublet Higgs!

It is important to calculate effective potential.

flat directions

Introduction Unification

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 .

tuning

We need .

Introduction Unification

- Higgs mass

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.

Introduction Unification

- 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.

Plan Unification

- Introduction
- Warped GHU
- Interval v.s. orbifold
- Summary

Warped Gauge-Higgs Unification Unification

- Randall-Sundrum

Randall & Sundrum (1999)

natural scale : TeV

Warped Gauge-Higgs Unification 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

Warped Gauge-Higgs Unification Unification

+ : periodic

-: anti-periodic

- Effective Potential

N.Haba, S.Matsumoto,

N.Okada and T.Y.

in preparation

Warped Gauge-Higgs Unification 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)

Warped Gauge-Higgs Unification 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

Plan Unification

- Introduction
- Warped GHU
- Interval v.s. orbifold
- Summary

Interval v.s. orbifold Unification

- Orbifold

ex)

= interval (?)

Fields may notbe invariant!

ex)

Gauge transformation

wider class of BCs Unification

Periodic

Anti-Periodic

Interval v.s. orbifoldN.Haba, S.Matsumoto,

N.Okada and T.Y.

in preparation

- Orbifold

+ : Neumann

-: Dirichlet

ex)

= interval (?)

In the orbifold picture

C. Csaki et al (2004)

N. Sakai and N. Uekusa (2007)

In the interval picture

Preliminary

All vanishing !!

Summary Unification

- 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

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