Treelevel unitarity in GaugeHiggs Unification Yutaka Sakamura RIKEN
- Slides: 29
Tree-level unitarity in Gauge-Higgs Unification Yutaka Sakamura (RIKEN) with Naoyuki Haba (Osaka Univ. ) and Toshifumi Yamashita (Nagoya Univ. ) ar. Xiv: 0908. 1042 December 5, 2009 @ RIKEN seminars
Plan of talk 1. Introduction 2. Set up 3. Weak boson scattering 4. Unitarity violation 5. Summary 1
Introduction 2
Standard model Higgs boson Electroweak sym. breaking, (perturbative) unitarity e. g. ) + + 3
Amplitude w/o Higgs unitarity bound w/ Higgs 1 Te. V If the WWH coupling vanishes, the Higgs boson cannot contribute to the unitarization. This occurs in the Gauge-Higgs Unification models in the warped spacetime. 4
Models with extra dimension EW breaking Higgsless model Boundary conditions along the extra dimension [Csaki, et. al, 2003] Unitarity is recovered by KK gauge bosons Gauge-Higgs Unification [Fairlie; Manton, 1979; Hosotani, 1983, …] Unitarity is recovered by KK gauge bosons and zero-mode of Higgs 5
Extra-dimensional model is non-renormalizable. Tree-level unitarity will be violated at some scale. Purpose We numerically estimate • scattering amplitudes for W, Z bosons • a scale at which the tree-level unitarity is violated in the Gauge-Higgs Unification. 6
Gauge-Higgs Unification Wilson line phase: Contribution to the saturation of amplitudes Higgs KK modes main less main [Falkowski, Pokorski, Roberts, 2007] 7
Set up 8
SO(5)x. U(1) model on S 1/Z 2 [Agashe, Contino, Pomarol, 2005] tuning qw suppressing T-parameter 9
Gauge symmetry : zero-modes = SO(4) Higgs doublet Wilson line phase: 10
WWH, ZZH couplings Flat case These are the same as the SM values. Warped case [Hosotani & Y. S. , 2006 -2007] 11
Weak boson scattering 12
Equivalence Theorem [Cornwall, Levin & Tiktopoulos, 1974; Lee, Quigg & Thacker, 1977] longitudinal mode would-be NG boson KK equivalence theorem [Chivukula, Dicus & He, 2002, …] 13
As an example, we consider . Equivalence theorem 14
Scattering amplitude Metric 15
For , each coupling deviates from the SM value. [Hosotani & Y. S. , 2007] Flat case Warped case 16
In the unit of the KK scale , The amplitude stops growing when the KK modes start to propagate. 17
Unitarity violation 18
Unitarity condition elastic scattering involving KK modes where (S-wave amplitude) 19
Unitarity violation scale Luni 20
unitarity cond. 21
c. f. 22
5 D propagator [Gherghetta & Pomarol, 2001] (written by Bessel functions) Advantages We can calculate the amplitudes without • the knowledge of the KK mass eigenvalues • summation over infinite KK modes e. g. ) 23
where In the conventional KK expansion, where 24
Summary • Weak boson scattering in GHU model • Equivalence theorem holds well. • Amplitudes have large -dependence in the warped spacetime. • Tree-level unitarity is violated at 25
Unitarity condition For the 2 → 2 channel, Then we obtain 26
If we assume that the S-wave component is dominant, we obtain 27
Comment on Thus, the S-wave amplitude diverges. Taking into account the width of the W boson, the divergence at is smeared out. translated into a cut-off for f 28
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