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

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 2013 NRF WORKSHOP

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 2013 NRF WORKSHOP

the Gauge Higgs unification model

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 2013 NRF WORKSHOP Higher dimensional Gauge Theory

Jubin 2013 NRF WORKSHOP Kaluza-Klein gravity theory Gauge-Higgs unification

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 2013 NRF WORKSHOP

Simple examples in the Gauge Higgs unification (GHU) Jubin 2013 NRF WORKSHOP

5D pure Yang- Mill action

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

Jubin 2013 NRF WORKSHOP Kaluza-Klien mode expansion Remnant gauge symmetry

Jubin 2013 NRF WORKSHOP WHERE IS THE DOUBLET HIGGS ?

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

Jubin 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

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

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

Adding to brane kinetic terms Jubin 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

Final 4D effective Lagrangian Jubin 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.

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 2013 NRF WORKSHOP

HOW TO GENERATE THE HIGGS POTENTIAL ?

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 2013 NRF WORKSHOP  R. Coquereaux et.al, CNRSG.~  Burdman and.~Nomura, Nucl. Phys. B656, 3. (2003) : arXiv:hep-ph/ ].  I. Antoniadis, K. Benakli and M. Quiros, New J. Phys. 3, 20 (2001) [arXiv:hep-th/ ].

- 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 2013 NRF WORKSHOP  Y. Hosotani, PLB 126, 309, Ann. Phys. 190, 233  N. Manton, Nucl. Phys. B 158, 141

Jubin 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).

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

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 2013 NRF WORKSHOP

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

Jubin 2013 NRF WORKSHOP with the 2 Higgs doublets

Jubin 2013 NRF WORKSHOP Canonical commutation relations Orthogonality Structure constant

Jubin 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

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

Jubin 2013 NRF WORKSHOP Generators for the Stand model gauge groups

Jubin 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

Jubin 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

Jubin 2013 NRF WORKSHOP Examples

Jubin 2013 NRF WORKSHOP

Dynkin diagrams of exceptional groups

Jubin 2013 NRF WORKSHOP

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

Jubin 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

Jubin 2013 NRF WORKSHOP Characteristic of all Lie groups in the GHUm with 2HDs

Jubin 2013 NRF WORKSHOP Mass spectrum in the GHUm with the 2HDs

Jubin 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, GeV.

Jubin 2013 NRF WORKSHOP Decoupling limit

Jubin 2013 NRF WORKSHOP Numerical results in the GHU models with the 2HDs

Jubin 2013 NRF WORKSHOP

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

Jubin 2013 NRF WORKSHOP Higgs spectrum

Summary Jubin 2013 NRF WORKSHOP

Backup slides

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