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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

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Higgs effective potential in the warped Gauge-Higgs Unification

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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)

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

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)

- Orbifold

ex)

Fields may notbe invariant !

ex)

Symm. transformation

- Orbifold breaking

Y.Kawamura (2000)

ex)

Doublet Higgs!

It is important to calculate effective potential.

flat directions

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 .

- 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.

- 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.

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

- Randall-Sundrum

Randall & Sundrum (1999)

natural scale : TeV

- 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

+ : periodic

-: anti-periodic

- Effective Potential

N.Haba, S.Matsumoto,

N.Okada and T.Y.

in preparation

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)

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

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

- Orbifold

ex)

= interval (?)

Fields may notbe invariant!

ex)

Gauge transformation

wider class of BCs

Periodic

Anti-Periodic

N.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 !!

- 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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