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.)

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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)


Plan

  • Introduction

  • Warped GHU

  • Interval v.s. orbifold

  • Summary


Introduction

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

  • Orbifold

ex)

Fields may notbe invariant !

ex)

Symm. transformation


Introduction

  • Orbifold breaking

Y.Kawamura (2000)

ex)

Doublet Higgs!

It is important to calculate effective potential.

flat directions


Introduction

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

  • 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

  • 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

  • Introduction

  • Warped GHU

  • Interval v.s. orbifold

  • Summary


Warped Gauge-Higgs Unification

  • Randall-Sundrum

Randall & Sundrum (1999)

natural scale : TeV


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


Warped Gauge-Higgs Unification

+ : periodic

-: anti-periodic

  • Effective Potential

N.Haba, S.Matsumoto,

N.Okada and T.Y.

in preparation


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)


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


Plan

  • Introduction

  • Warped GHU

  • Interval v.s. orbifold

  • Summary


Interval v.s. orbifold

  • Orbifold

ex)

= interval (?)

Fields may notbe invariant!

ex)

Gauge transformation


wider class of BCs

Periodic

Anti-Periodic

Interval v.s. orbifold

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 !!


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


Back-up Slides


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