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

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 Unification

  • Introduction

  • Warped GHU

  • Interval v.s. orbifold

  • Summary


Introduction
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)


Introduction1
Introduction Unification

  • Orbifold

ex)

Fields may notbe invariant !

ex)

Symm. transformation


Introduction2
Introduction Unification

  • Orbifold breaking

Y.Kawamura (2000)

ex)

Doublet Higgs!

It is important to calculate effective potential.

flat directions


Introduction3
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 .


Introduction4
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.


Introduction5
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
Warped Gauge-Higgs Unification Unification

  • Randall-Sundrum

Randall & Sundrum (1999)

natural scale : TeV


Warped gauge higgs unification1
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 unification2
Warped Gauge-Higgs Unification Unification

+ : periodic

-: anti-periodic

  • Effective Potential

N.Haba, S.Matsumoto,

N.Okada and T.Y.

in preparation


Warped gauge higgs unification3
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 unification4
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
Interval v.s. orbifold Unification

  • Orbifold

ex)

= interval (?)

Fields may notbe invariant!

ex)

Gauge transformation


Interval v s orbifold1

wider class of BCs Unification

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
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


Back up slides

Back-up Slides Unification


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