1. 6D Gauge-Higgs unification with custodial symmetry Yutaka Sakamura (KEK) in collaboration with Yoshio Matsumoto (Sokendai) [arXiv:1407.0133] to appear in JHEP August 25, 2014Summer Institute 2014@Fuji Yoshida

2. Introduction August 25, 2014Summer Institute 2014@Fuji Yoshida Gauge-Higgs unification (GHU) Higher-dim. gauge sym. protects the Higgs mass against quantum correction. Higgs = [Manton, 1979; Fairlie, 1979; Hosotani, 1983; …] Simplest model 5D U(3) model on S /Z (flat spacetime) 5D SO(5)xU(1) model on S /Z (warped spacetime) 1 1 2 2 [Scrucca, Serone, Silvestrini, Wulzer, 2004; … ] [Agashe, Contino, Pomarol, 2005; … ] 1/13

3. August 25, 2014Summer Institute 2014@Fuji Yoshida Wilson line phase : The effective potential has quadratic terms (1 loop) quartic terms (tree) [Agashe, Contino, Pomarol, 2005; …] must be small, i.e., 2/13 In this work, we consider 6D gauge-Higgs unification. (determined at 1-loop level)

4. August 25, 2014Summer Institute 2014@Fuji Yoshida Gauge group : simple group The Weinberg angle is obtained by adjusting. (gauge couplings) In GHU, can deviate from 1 even at tree-level due to the mixing with the KK modes. 3/13 Extra dimensions : Introducing the custodial symmetry.

5. August 25, 2014Summer Institute 2014@Fuji Yoshida [Agashe, Contino, Da Rold, Pomarol, 2006] Rank 2 Rank 3 Custodial symmetry Find candidates for a setup of realistic 6D GHU by means of the group-theoretical analysis. Purpose 4/13

6. August 25, 2014Summer Institute 2014@Fuji Yoshida EW sym. is broken by a bidoublet Higgs: Symmetry breaking Rank 2 Rank 3 orbifold (at the fixed point) orbifold 5/13

7. August 25, 2014Summer Institute 2014@Fuji Yoshida SO(5) : G : 2 Rank 2 SU(4) : SO(7) : Sp(6) : Rank 3 Irreducible decomposition 6/13

8. where and. August 25, 2014Summer Institute 2014@Fuji Yoshida T /Z orbifold 2 N Orbifold conditions (N=2,3,4,6) Cartan generator Zero-mode conditions roots of G fixed points 7/13

9. August 25, 2014Summer Institute 2014@Fuji Yoshida 1 1 1 1 1 1 0 0 0 0 0 0 0 2 Number of Higgs bidoublets 8/13

10. We focus on the third generation quarks. August 25, 2014Summer Institute 2014@Fuji Yoshida Matter sector 6D fermion : 6D chirality 4D chirality This belongs to an irreducible rep. of G. 9/13 Possible ‘s are restricted by the condition for the VEV alignment of.

11. August 25, 2014Summer Institute 2014@Fuji Yoshida VEVs must be aligned as. Higgs bidoublet : VEV alignment The alignment can be achieved if 10/13

12. 2.The corresponding weights are related as 3. have zero-modes in, and have zero-modes in. August 25, 2014Summer Institute 2014@Fuji Yoshida Conditions for the VEV alignment Among the representations such that, only of SU(4) satisfies the above conditions. Top Yukawa 11/13

13. August 25, 2014Summer Institute 2014@Fuji Yoshida of SU(4) By orbifolding, Only on T /Z, there is a choice of the orbifold conditions that satisfy the condition 3. 2 3 12/13 Tree-level mass relations:

14. Summary We considered necessary conditions for Gauge-Higgs unification on T /Z with custodial symmetry. The requirements we demanded are August 25, 2014Summer Institute 2014@Fuji Yoshida  A Scalar bidoublet zero-mode exists. 2 N The best candidate is, and.  provides a right size group factor for the top Yukawa coupling.  The bosonic sector is symmetric under. 13/13  The top and bottom quarks are coupled to through.

15. August 25, 2014Summer Institute 2014@Fuji Yoshida If we obtain includes includes, If and only has zero-modes, we obtain After integrating out unnecessary modes, Yukawa couplings 14/13

16. August 25, 2014Summer Institute 2014@Fuji Yoshida Weight simple root Zero-mode conditions integer 15/13