1. Two Higgs doublets model in gauge-Higgs unification framework 2013. 6. 8 @ Yonsei University Jubin Park (SNUT)  Collaboration with Prof. We-Fu Chang, Prof. Sin Kyu Kang

2. A fundamental scalar field (Higgs) is introduced to explain spontaneous symmetry breaking of gauge group of electroweak symmetry. The same field is also responsible for masses of all matter fields through Yukawa interactions. Standard Model Jubin Park @ 2013 NRF WORKSHOP

3. The Higgs potential is written by HAND. So the Higgs sector is very sensitive to the UV scale of the theory Without symmetry protection, Moreover, Unknown origin Hierarchy Problem Jubin Park @ 2013 NRF WORKSHOP

4. the Gauge Higgs unification model

5. Unification of gravity (s=2) & electromagnetic (s=1) Kaluza-Klein gravity theory Unified theory of gauge (s=1) & Higgs (s=0) Gauge-Higgs unification 4D space-time 4D gauge-field Higgs 5D gauge field extra dimension The pioneer works of GHU : ・ N.S. Manton, Nucl. Phys. 58(’79)141. ・ Y. Hosotani, Phys. Lett. B126 (‘83) 309 ``Hosotani mechanism” Jubin Park @ 2013 NRF WORKSHOP Higher dimensional Gauge Theory

6. Jubin Park @ 2013 NRF WORKSHOP Kaluza-Klein gravity theory Gauge-Higgs unification

7. Weak scale Hadronization scale B physics scale 200 MeV5 GeV80 GeV172 GeV 10 TeV Energy scales 1 TeV Compactification scale Theory cutoff scale 10 ^19 GeV 10^15 ~ 10 ^17 GeV Planck scale- strong gravity GUT- coupling unification Heavy right-handed Majorana for Seesaw Mechanism Jubin Park @ 2013 NRF WORKSHOP

8. Simple examples in the Gauge Higgs unification (GHU) Jubin Park @ 2013 NRF WORKSHOP

9. 5D pure Yang- Mill action

10. Jubin Park @ 2013 NRF WORKSHOP 5D quantum electrodynamics(QED) on S1/Z2 Model setup Boundary conditions (BCs)

11. Jubin Park @ 2013 NRF WORKSHOP Kaluza-Klien mode expansion Remnant gauge symmetry

12. Jubin Park @ 2013 NRF WORKSHOP WHERE IS THE DOUBLET HIGGS ?

13. Jubin Park @ 2013 NRF WORKSHOP Integrating out fifth dimension Using a ‘t Hooft gauge.

14. Jubin Park @ 2013 NRF WORKSHOP 5D SU(2) example (Non-Abelian case) Lie algebra valued gauge field Boundary conditions (BCs) Only diagonal components can have “Zero modes” due to Neumann boundary conditions at two fixed points

15. Jubin Park @ 2013 NRF WORKSHOP 5D SU(3) example (with 2 scalar doublets) Lie algebra valued gauge field Boundary conditions (BCs)

16. We only focus on the zero modes, After we integrate out fifth dimension, And rescale the gauge field, Jubin Park @ 2013 NRF WORKSHOP

17. Adding to brane kinetic terms Jubin Park @ 2013 NRF WORKSHOP We can easily understand that these terms can give a modification to the gauge couplings without any change of given models. From the effective Lagrangian, we can expect this relation Similarly, for the U(1) coupling

18. Final 4D effective Lagrangian Jubin Park @ 2013 NRF WORKSHOP This number is completely fixed by the analysis of structure constants of given Lie group (or Lie algebra) regardless of volume factor Z if there are no brane kinetic terms in given models.

19. Well-known problems Wrong weak mixing angle (,, ) No Higgs potential (to trigger the EWSB). - may generate too low Higgs mass (or top quark) even if we use quantum corrections to make its potential. Realistic construction of Yukawa couplings Jubin Park @ 2013 NRF WORKSHOP

20. HOW TO GENERATE THE HIGGS POTENTIAL ?

21. Possible answers for these problems - Brane kinetic terms - Violation of Lorentz symmetry ( SO(1,4) -> SO(1,3) ) - Graded Lie algebra (ex. ) - Using a non-simple group. an anomalous additional U(1) (or U(1)s) Jubin Park @ 2013 NRF WORKSHOP  R. Coquereaux et.al, CNRSG.~  Burdman and.~Nomura, Nucl. Phys. B656, 3. (2003) : arXiv:hep-ph/0210257].  I. Antoniadis, K. Benakli and M. Quiros, New J. Phys. 3, 20 (2001) [arXiv:hep-th/0108005].

22. - Using a non-simply connected extra- dimension ( the fluctuation of the AB type phase – loop quantum correction) - Using a 6D (or more) pure gauge theory. - Using a background field like a monopole in extra dimensional space. Jubin Park @ 2013 NRF WORKSHOP  Y. Hosotani, PLB 126, 309, Ann. Phys. 190, 233  N. Manton, Nucl. Phys. B 158, 141

23. Jubin Park @ 2013 NRF WORKSHOP 1-loop generated Higgs potential Cosmological Constant for more generalized GHU model means KK states are ~ 200 GeV OR Monopole-like background -Forbidden by higher dimensional gauge symmetry From commutator terms in 6d or higher dimensions (>6d).

24. Finally, we can get this relation ( with brane Kinetic terms ), We can rewrite the equation with previous relation, Jubin Park @ 2013 NRF WORKSHOP

25. So our goals are Stability of the electroweak scale (from the quadratic divergences – Gauge hierarchy problem) Higgs potential - to trigger the electroweak symmetry breaking Correct weak mixing Jubin Park @ 2013 NRF WORKSHOP

26. We focus on the GHU models in 6D with Brane kinetic terms Therefore,

27. Jubin Park @ 2013 NRF WORKSHOP with the 2 Higgs doublets

28. Jubin Park @ 2013 NRF WORKSHOP Canonical commutation relations Orthogonality Structure constant

29. Jubin Park @ 2013 NRF WORKSHOP The Lie algebra valued function in complex coordinate (5D + 6D) Field assignments in terms of the Higgs doublets Higgs doublet The GHU models in 6D

30. Jubin Park @ 2013 NRF WORKSHOP General results of the commutators Relations for the indices of structure constants One constraint

31. Jubin Park @ 2013 NRF WORKSHOP Generators for the Stand model gauge groups

32. Jubin Park @ 2013 NRF WORKSHOP Three conditions for the existence of the doublets First condition for the triangle : Second condition for the triangle : So these three vectors should make an equilateral triangle in the root space

33. Jubin Park @ 2013 NRF WORKSHOP Allowed angle between beta and gamma vectors and corresponding possible groups and triangles through Lie algebra Third condition for the triangle : Not allowed ratios between lengths of two root vectors by the Lie algebra

34. Jubin Park @ 2013 NRF WORKSHOP Examples

35. Jubin Park @ 2013 NRF WORKSHOP

36. Dynkin diagrams of exceptional groups

37. Jubin Park @ 2013 NRF WORKSHOP

38. Typical form of the GHU potential From commutator terms in 6d or higher dimensions (>6d). 1-loop generated Higgs potential with the identification 3g^2=g’^2

39. Jubin Park @ 2013 NRF WORKSHOP 1-loop generated Higgs potential Cosmological Constant for more generalized GHU model means KK states are ~ 200 GeV OR Monopole-like background -Forbidden by higher dimensional gauge symmetry From commutator terms in 6d or higher dimensions (>6d). Again, structure of the Higgs potential in the GHUm

40. Jubin Park @ 2013 NRF WORKSHOP Characteristic of all Lie groups in the GHUm with 2HDs

41. Jubin Park @ 2013 NRF WORKSHOP Mass spectrum in the GHUm with the 2HDs

42. Jubin Park @ 2013 NRF WORKSHOP Modified mass relation between the W boson and the Higgs masses This factor reduces the proportional constant number. So almost GHU models (except exceptional groups) in the decoupling limit can not easily escape the Well-known LEP bound, 114.4 GeV.

43. Jubin Park @ 2013 NRF WORKSHOP Decoupling limit

44. Jubin Park @ 2013 NRF WORKSHOP Numerical results in the GHU models with the 2HDs

45. Jubin Park @ 2013 NRF WORKSHOP

50. Heavy u(1) prime condition : Needed c2* number to go to the heavy U(1) prime scenario

51. Jubin Park @ 2013 NRF WORKSHOP Higgs spectrum

52. Summary Jubin Park @ 2013 NRF WORKSHOP

53. Backup slides

54. Jubin Park @ 2013 NRF WORKSHOP

55. Numerical results for the light Higgs particle in the decoupling limit. All masses are smaller than 114.4 GeV. Jubin Park @ 2013 NRF WORKSHOP