Higgs effective potential in the warped Gauge-Higgs Unification
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2007/12/19 2007/12/19 @GUT07 @GUT07 Higgsless breaking of Grand Unification in preparation with N. Haba in preparation with N. Haba (Osaka Univ.) (Osaka Univ.) S. Matsumoto (Tohoku Univ.) S. Matsumoto (Tohoku Univ.) Higgs effective potential in the warped Gauge-Higgs Unification Toshifumi Yamashita (SISSA Osaka Univ.) in preparation with N. Haba in preparation with N. Haba (Osaka Univ.) (Osaka Univ.) Y. Sakamura Y. Sakamura (Osaka Univ.) (Osaka Univ.)
description
Higgsless breaking of Grand Unification. Higgs effective potential in the warped Gauge-Higgs Unification. Toshifumi Yamashita ( SISSA Osaka Univ. ). 2007/12/19 @GUT07. in preparation with N. Haba (Osaka Univ.) - PowerPoint PPT Presentation
Transcript of Higgs effective potential in the warped Gauge-Higgs Unification
2007/12/19 2007/12/19 @GUT07@GUT07
Higgsless breaking of Grand Unification
in preparation with N. Haba (Osaka Univ.)in preparation with N. Haba (Osaka Univ.) S. Matsumoto (Tohoku Univ.)S. Matsumoto (Tohoku Univ.) N. Okada (KEK)N. Okada (KEK)
Higgs effective potential in the warped Gauge-Higgs Unification
Toshifumi Yamashita (SISSA Osaka Univ.)
in preparation with N. Haba (Osaka Univ.)in preparation with N. Haba (Osaka Univ.) Y. Sakamura Y. Sakamura (Osaka Univ.)(Osaka Univ.)
Plan
• Introduction• Warped GHU• Gauge-Higgs Condition• Summary
Introduction
Gauge-Higgs Unification
5D theory
with KK modes gauge fieldHiggs
compactification
4D theory
gauge field
scalar field
5D gauge invariance protects the Higgs mass!!
D.B. Fairlie (1979)N.S. Manton (1979)
H.Hatanaka, T.Inami and C.S.Lim (1998)
ex)
Introduction
Orbifold
Fields may not be invariant !
ex)
Symm. transformation
ex)
Introduction
Orbifold breaking
Doublet Higgs!
flat directionsIt is important to calculate effective potential.
Y.Kawamura (2000)
M.Kubo, C.S.Lim and H.Yamashita (2002) N.Haba and T.Y. (2004)
Introduction
finite!!
1-loop effective potential
We need .
When , we get .
tuning
too small !!
Introduction
Higgs mass
The quartic coupling is zero at the tree level.
The Higgs mass tends to be too small.
Top YukawaTop 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• Gauge-Higgs Condition• Summary
Warped Gauge-Higgs Unification
Randall-Sundrum
natural scale : TeV
Randall & Sundrum (1999)
Warped Gauge-Higgs Unification
Weak scale vs. KK & top massA parameter of fermions
gauge
flat case
N.Haba, S.Matsumoto,N.Okada and T.Y.in preparation
In the warped GHU scenario, the gauge coupling is rather suppressed.
Warped Gauge-Higgs Unification
Effective Potential + : periodic
- : anti-periodic
N.Haba, S.Matsumoto,N.Okada and T.Y.in preparation
Warped Gauge-Higgs Unification
Effective Potential
w/ 2 anti-periodic fundamental fermions 1 periodic adjoint fermion
N.Haba, S.Matsumoto,N.Okada and T.Y.in preparation
N. Haba and T.Y. (2004)
Warped Gauge-Higgs Unification
Effective Potential
w/ 2 anti-periodic fundamental fermions 1 periodic adjoint fermion
A large Higgs mass
N.Haba, S.Matsumoto,N.Okada and T.Y.in preparation
Plan
• Introduction• Warped GHU• Gauge-Higgs Condition• Summary
Gauge-Higgs Condition
4D effective theory
Theory of zero-modes.renormalization condition
: Gauge-Higgs condition
= SM + GH condition
S.Coleman and E.Weinberg
Gauge-Higgs Condition
4D effective theory
Theory of zero-modes.
• 5D theory appears from .
renormalization condition
: Gauge-Higgs condition
= SM + GH condition
In 5D theory, higgs is unified with gauge.
Vanishing potential.
little corrections by anti-periodic modes
Gauge-Higgs Condition
4D effective theory
Theory of zero-modes.
• We can calculate everything more easily.
renormalization condition
: Gauge-Higgs condition
= SM + GH condition
• complicated models• RG improved analysis• Higher loop corrections
warped GHU?
Gauge-Higgs Condition
4D effective theory
Theory of zero-modes.renormalization condition
: Gauge-Higgs condition
= SM + GH condition
S.Coleman and E.Weinberg
w/ IR log. divergence.
Gauge-Higgs Condition
In warped GHU
flat case
weaker divergence
Gauge-Higgs Condition
In warped GHU
weaker divergence
• larger
• threshold at
not easy to evaluate…
sizable corrections by anti-periodic modes
Summary
warped Gauge-Higgs unification
• large KK scale, top & Higgs mass
Effective potential is calculated
• Non-orbifold like fermions
Vanishing contributions
N.Haba, S.Matsumoto,N.Okada and T.Y.in preparation
• Gauge-Higgs condition is studied.
not goes well.
Plan
IntroductionWarped GHUGauge-Higgs ConditionInterval v.s. orbifoldSummary
ex)
Interval v.s. orbifold
Orbifold
= interval (?)
Fields may not be invariant !
ex)
Symm. transformation
ex)
Interval v.s. orbifold
Orbifold
= interval (?)
wider class of BCs • In the orbifold picture
• In the interval picture
+ : Neumann
- : Dirichlet
Periodic Anti-Periodic
All vanishing !!
Preliminary
C. Csaki et al (2004)N. Sakai and N. Uekusa (2007)
N.Haba, S.Matsumoto,N.Okada and T.Y.in preparation
