two higgs doublets model in gauge-higgs unification framework 2013. 6. 8 @ yonsei university jubin...

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

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

The Higgs potential is written by HAND.

2 2 2(| | )HiggsV v

So the Higgs sector is very sensitive to the UV scale of the theory

Without symmetry protection,

2 2Higgsm

Moreover,

Unknown origin

Hierarchy Problem



• 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”


Higher dimensional Gauge Theory


00 01 02 03 0

10 11 12 13 1

20 21 22 23 2

30 3231 31 3

0 31 2

MN

g g g g A

g g g g A

G g g g g A

g gg g A

A AA A

Kaluza-Klein gravity theory

Gauge-Higgs unification

0

1

2

3

M

A

A

A A

A

WMbmL QCD Weak scale

Hadronization scale

B physics scale

tm

200 MeV 5 GeV 80 GeV 172 GeV 10 TeV

Energy scales

P lM

1 TeV

Compactification scale

1 / CR

?

LTheory cutoff scale

GUTMMajoranaM

10 ^19 GeV10^15 ~ 10 ^17 GeVPlanck scale-

strong gravity

GUT- coupling

unification

Heavy right-handed

Majorana for Seesaw

Mechanism


• Simple examples in the Gauge Higgs unification (GHU)



5D pure Yang- Mill action


5D quantum electrodynamics(QED) on S1/Z2

Model setup

Boundary conditions (BCs)


Kaluza-Klien mode expansion

Remnant gauge symmetry


WHERE IS THE DOUBLET HIGGS ?


Integrating out fifth dimension

Using a ‘t Hooft gauge.


5D SU(2) example (Non-Abelian case)

Lie algebra valued gauge field


Only diagonal components can have “Zero modes” due to Neumann boundary conditions at two fixed points


5D SU(3) example (with 2 scalar doublets)

Lie algebra valued gauge field


We only focus on the zero modes,

After we integrate out fifth dimension,

0 0 0 00

5( )a abc b cDgZ Z ZF A A fZ

A Z A

And rescale the gauge field,


Adding to brane kinetic terms


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


g g

1 2

* Note that the value of tangent angle

for weak mixing angle is 3 0.whenc c

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


exp

1tan

3


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)


55

1( )

4 4

aL a F F F F

(2 |1)SU

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].

• - 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.


256( )L tr F

25~ [ , ]BL A A

Y. Hosotani, PLB 126, 309, Ann. Phys. 190, 233

N. Manton, Nucl. Phys. B 158, 141


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

22 2 4

0 5 52eff tree

gV V V A g A

R

22 2

5 2 2

1/ 1/

gA R

R g

From commutator terms in 6d or higher dimensions (>6d).

| | ,After the Higgs obtains H v 42 2 ,2D

H W

g vM v M

24,2Dg

Finally, we can get this relation ( with brane Kinetic terms ),

We can rewrite the equation with previous relation,


4H DM g v 4

1

DW

g vM

Z

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



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

Therefore,


with

the 2 Higgs doublets


Canonical commutation relations

Orthogonality

Structure constant


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


General results of the commutators

Relations for the indices of structure constants

One constraint


Generators for the Stand model gauge groups


Three conditions for the existence of the doubletsFirst condition for the triangle :

Second condition for the triangle :

VVVVVVVVVVVVVV

So these three vectors should make

an equilateral triangle in the root space


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


Examples


Dynkin diagrams of exceptional groups


Typical form of the GHU potential



with the identification 3g^2=g’^2



Cosmological Constant for more generalized GHU model

means KK states are ~ 200 GeV

OR

Monopole-like background

-Forbidden by higher dimensional gauge symmetry

22 2 4

0 5 52eff tree

gV V V A g A

R

22 2

5 2 2

1/ 1/

gA R

R g


Again, structure of the Higgs potential

in the GHUm


Characteristic of all Lie groups

in the GHUm with 2HDs

exp

1tan

3 2

expsin 0.22292


Mass spectrum in the GHUm with the 2HDs


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 .


Decoupling limit


Numerical results in the GHU models

with the 2HDs


Heavy u(1) prime condition :

Needed c2* number to go to the heavy U(1) prime scenario


Higgs spectrum

Summary


Backup slides

Numerical results for the light Higgs particle in the decoupling limit.

All masses are smaller than 114.4 GeV.


two higgs doublets model in gauge-higgs unification framework 2013. 6. 8 @ yonsei university jubin...

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