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Two Higgs doublets model in gauge-Higgs unification framework

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. Standard Model.

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Two Higgs doublets model in gauge-Higgs unification framework

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  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. Standard Model 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. Radial modes ~ Massive Jubin Park @ 2013 NRF WORKSHOP

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

  4. the Gauge Higgs unification model Jubin Park @ 2013 NRF WORKSHOP

  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 The pioneer works of GHU : ・N.S. Manton, Nucl. Phys. 58(’79)141. ・Y.Hosotani, Phys. Lett. B126 (‘83) 309 ``Hosotani mechanism” Higher dimensional Gauge Theory extra dimension 5D gauge field Higgs 4D gauge-field Zero mode 4D space-time Jubin Park @ 2013 NRF WORKSHOP

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

  7. Energy scales 10 TeV 1 TeV 200 MeV 5 GeV 80 GeV 172 GeV Weak scale B physics scale Theory cutoff scale Hadronization scale Compactification scale 10 ^19 GeV 10^15 ~ 10 ^17 GeV Planck scale- strong gravity Heavy right-handed Majorana for Seesaw Mechanism GUT- coupling unification 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 Jubin Park @ 2013 NRF WORKSHOP

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

  11. Kaluza-Klien mode expansion Remnant gauge symmetry 4D shift sym 4D gauge sym. 5D Gauge sym. 4D gauge sym. 4D shift sym Jubin Park @ 2013 NRF WORKSHOP

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

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

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

  15. 5D SU(3) example (with 2 scalar doublets) : Gell-Mann martices Lie algebra valued gauge field Boundary conditions (BCs) - Zero modes. Gauge sym. Breaking * Branching Rule Jubin Park @ 2013 NRF WORKSHOP

  16. We only focus on the zero modes, After we integrate out fifth dimension, Volume factor And rescale the gauge field, Relation between 4d and 5d gauge couplings Jubin Park @ 2013 NRF WORKSHOP

  17. Adding to brane kinetic terms SU(2) U(1) 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 Jubin Park @ 2013 NRF WORKSHOP

  18. Final 4D effective Lagrangian No mass term of the Higgs because of higher dimensional gauge symmetry Weak mixing angle 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. Jubin Park @ 2013 NRF WORKSHOP

  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 ? Jubin Park @ 2013 NRF WORKSHOP

  21. Possible answers for these problems Wrong weak mixing angle • Burdman and .~Nomura, Nucl. Phys. B656, 3. (2003) : arXiv:hep-ph/0210257]. - 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) • R. Coquereaux et.al, CNRSG.~ • I. Antoniadis, K. Benakli and M. Quiros, New J. Phys. 3, 20 (2001) [arXiv:hep-th/0108005]. Abandon the gauge coupling unification scheme . Jubin Park @ 2013 NRF WORKSHOP

  22. Higgs potential • - 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. • Y. Hosotani, PLB 126, 309, Ann. Phys. 190, 233 • N. Manton, Nucl. Phys. B 158, 141 Jubin Park @ 2013 NRF WORKSHOP

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

  24. Higgs potential, Radial modes ~ Massive Nambu-goldstone boson modes ~ Massless (flat direction) 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, Jubin Park @ 2013 NRF WORKSHOP

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

  28. Conventions for the GHU model with 2 Higgs doublets. Canonical commutation relations Structure constant Orthogonality Jubin Park @ 2013 NRF WORKSHOP

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

  30. General results of the commutators SU(2) Invariant ? One constraint Relations for the indices of structure constants Jubin Park @ 2013 NRF WORKSHOP

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

  32. Three conditions for the existence of the doublets First condition for the triangle : From ladder operation Root SPACE Second condition for the triangle : From SU(2) invariant So these three vectors should make anequilateral triangle in the root space Jubin Park @ 2013 NRF WORKSHOP

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

  34. Examples Right Triangle Regular Triangle Jubin Park @ 2013 NRF WORKSHOP

  35. Regular Triangle + Obtuse Triangle Right Triangle Jubin Park @ 2013 NRF WORKSHOP

  36. Dynkin diagrams of exceptional groups Jubin Park @ 2013 NRF WORKSHOP

  37. Gauge invariant and renormalizable The most general 2HD potential Jubin Park @ 2013 NRF WORKSHOP

  38. Typical form of the GHU potential 1-loop generated Higgs potential From commutator terms in 6d or higher dimensions (>6d). MSSM : with the identification 3g^2=g’^2 Jubin Park @ 2013 NRF WORKSHOP

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

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

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

  42. Modified mass relation between the W boson and the Higgs masses Brane Kinetic Terms Effect 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 . Jubin Park @ 2013 NRF WORKSHOP

  43. Decoupling limit Jubin Park @ 2013 NRF WORKSHOP

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

  45. 1. mass spectrum in the GHU model with N=1as a function of tan beta Jubin Park @ 2013 NRF WORKSHOP

  46. 2. mass spectrum in the GHU model with N=4as a function of tan beta Jubin Park @ 2013 NRF WORKSHOP

  47. 3. mass spectrum in the GHU model with N=7as a function of tan beta Jubin Park @ 2013 NRF WORKSHOP

  48. 4. Mass spectum in the GHU model with m12=1 TeVas a function of tan beta Jubin Park @ 2013 NRF WORKSHOP

  49. With the effects of the brane kinetic terms Jubin Park @ 2013 NRF WORKSHOP

  50. 5. Heavy U(1) prime scenario Heavy u(1) prime condition : Needed c2* number to go to the heavy U(1) prime scenario Jubin Park @ 2013 NRF WORKSHOP

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