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Higgs effective potential in the warped Gauge-Higgs Unification

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.)

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Higgs effective potential in the warped Gauge-Higgs Unification

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  1. 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.) S. Matsumoto (Tohoku Univ.) N. Okada (KEK) in preparation with N. Haba (Osaka Univ.) Y. Sakamura (Osaka Univ.)

  2. Plan • Introduction • Warped GHU • Gauge-Higgs Condition • 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 • Gauge-Higgs Condition • 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 • Gauge-Higgs Condition • Summary

  16. Gauge-Higgs Condition • 4D effective theory = SM + GH condition Theory of zero-modes. renormalization condition : Gauge-Higgs condition S.Coleman and E.Weinberg

  17. Gauge-Higgs Condition • 4D effective theory = SM + GH condition Theory of zero-modes. little corrections by anti-periodic modes renormalization condition : Gauge-Higgs condition 5D theory appears from . In 5D theory, higgs is unified with gauge. Vanishing potential.

  18. Gauge-Higgs Condition • 4D effective theory = SM + GH condition Theory of zero-modes. renormalization condition : Gauge-Higgs condition We can calculate everything more easily. warped GHU? complicated models RG improved analysis Higher loop corrections

  19. Gauge-Higgs Condition • 4D effective theory = SM + GH condition Theory of zero-modes. renormalization condition : Gauge-Higgs condition S.Coleman and E.Weinberg w/ IR log. divergence.

  20. Gauge-Higgs Condition • In warped GHU weaker divergence flat case

  21. larger • threshold at Gauge-Higgs Condition • In warped GHU weaker divergence sizable corrections by anti-periodic modes not easy to evaluate…

  22. Summary • warped Gauge-Higgs unification large KK scale, top & Higgs mass N.Haba, S.Matsumoto, N.Okada and T.Y. in preparation • Effective potential is calculated Gauge-Higgs condition is studied. not goes well. Non-orbifold like fermions Vanishing contributions

  23. Plan • Introduction • Warped GHU • Gauge-Higgs Condition • Interval v.s. orbifold • Summary

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

  25. 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 !!

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