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Tree-level unitarity in Gauge-Higgs Unification

Tree-level unitarity in Gauge-Higgs Unification. Yutaka Sakamura (RIKEN) with Naoyuki Haba (Osaka Univ.) and Toshifumi Yamashita (Nagoya Univ.) December 5, 2009 @ RIKEN seminars. arXiv:0908.1042. Plan of talk. Introduction Set up Weak boson scattering Unitarity violation Summary.

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Tree-level unitarity in Gauge-Higgs Unification

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  1. Tree-level unitarity in Gauge-Higgs Unification Yutaka Sakamura (RIKEN) with Naoyuki Haba (Osaka Univ.)and Toshifumi Yamashita (Nagoya Univ.)December 5, 2009 @ RIKEN seminars arXiv:0908.1042

  2. Plan of talk • Introduction • Set up • Weak boson scattering • Unitarity violation • Summary

  3. Introduction

  4. Standard model Electroweak sym. breaking,(perturbative) unitarity Higgs boson e.g.) + +

  5. Amplitude w/o Higgs unitaritybound w/ Higgs 1 TeV If the WWH coupling vanishes, the Higgs boson cannot contribute to the unitarization. This occurs in the Gauge-Higgs Unification modelsin the warped spacetime.

  6. Models with extra dimension Boundary conditionsalong the extra dimension EW breaking Higgsless model [Csaki, et.al, 2003] Unitarity is recovered by KK gauge bosons Gauge-Higgs Unification [Fairlie; Manton, 1979; Hosotani, 1983,…] Higgs Unitarity is recovered by KK gauge bosonsand zero-mode of

  7. 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. Extra-dimensional model is non-renormalizable.

  8. Gauge-Higgs Unification Wilson line phase: Contribution to the saturation of amplitudes Higgs KK modes main less less main [Falkowski, Pokorski, Roberts, 2007]

  9. Set up

  10. tuning q w suppressing T-parameter SO(5)xU(1) model on S /Z 1 2 [Agashe, Contino, Pomarol, 2005]

  11. = Higgs doublet Gauge symmetry : SO(4) zero-modes Wilson line phase:

  12. WWH, ZZH couplings Flat case These are the same as the SM values. Warped case [Hosotani & Y.S., 2006-2007]

  13. Weak boson scattering

  14. KK equivalence theorem [Chivukula, Dicus & He, 2002, …] Equivalence Theorem [Cornwall, Levin & Tiktopoulos, 1974; Lee, Quigg & Thacker, 1977] longitudinal mode would-be NG boson

  15. As an example, we consider . Equivalence theorem

  16. Scattering amplitude Metric

  17. For , each coupling deviates from the SM value. [Hosotani & Y.S., 2007] Flat case Warped case

  18. In the unit of the KK scale , The amplitude stops growing when the KK modes start to propagate.

  19. Unitarity violation

  20. Unitarity condition elastic scattering involving KK modes where (S-wave amplitude)

  21. Unitarity violation scale L uni

  22. unitarity cond.

  23. c.f.

  24. e.g.) 5D 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

  25. In the conventional KK expansion, where where

  26. Summary • Weak boson scattering in GHU model • Equivalence theorem holds well. • Amplitudes have large -dependencein the warped spacetime. • Tree-level unitarity is violated at

  27. For the 2 →2 channel, Then we obtain Unitarity condition

  28. If we assume that the S-wave component is dominant, we obtain

  29. translated into a cut-off for f Comment on Thus, the S-wave amplitude diverges. Taking into account the width of the W boson, the divergence at is smeared out.

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