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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.)

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Higgs effective potential in the warped Gauge-Higgs Unification

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  1. 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)

  2. Plan • Introduction • Warped GHU • Interval v.s. orbifold • Summary

  3. 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)

  4. Introduction • Orbifold ex) Fields may notbe invariant ! ex) Symm. transformation

  5. Introduction • Orbifold breaking Y.Kawamura (2000) ex) Doublet Higgs! It is important to calculate effective potential. flat directions

  6. 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 .

  7. 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.

  8. 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.

  9. Plan • Introduction • Warped GHU • Interval v.s. orbifold • Summary

  10. Warped Gauge-Higgs Unification • Randall-Sundrum Randall & Sundrum (1999) natural scale : TeV

  11. 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

  12. Warped Gauge-Higgs Unification + : periodic -: anti-periodic • Effective Potential N.Haba, S.Matsumoto, N.Okada and T.Y. in preparation

  13. 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)

  14. 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

  15. Plan • Introduction • Warped GHU • Interval v.s. orbifold • Summary

  16. Interval v.s. orbifold • Orbifold ex) = interval (?) Fields may notbe invariant! ex) Gauge transformation

  17. 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 !!

  18. 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

  19. Back-up Slides

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