Weak Mixing Angle and Higgs Mass in Gauge-Higgs Unification Models with Brane Kinetic Terms

Weak Mixing Angle andHiggs Mass

in Gauge-Higgs Unification Models

with Brane Kinetic Terms 2012. 2. 21 @YongPyong2012

Jubin Park Collaboration with

Prof. Sin Kyu Kang and Prof. We-Fu Chang arXiv:1111.5422 [hep-ph] submitted to JHEP

Jubin Park @YongPyong2012

ContentsThe Standard Model(SM) and Hierarchy problem – Higgs massSolutions about the Hierarchy problemBrief introduction to Gauge Higgs unification(GHU)A toy example – 5D SU(3) GHU model on S1/Z2.Problems in the toy modelGoalsPossible answers for these problemsPhenomenologically viable GHU modelsHiggs potential in 6DNumerical results.Summary


A fundamental scalar field (Higgs) is introduced to explain spontaneous symmetry breaking of gauge group of elec-troweak symmetry.

The same field is also responsible for masses of all matter fields through Yukawa interactions.

Standard Model

RADIAL MODES ~MASSIVE


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 2

Higgsm

Moreover,

Unknown origin

Hierarchy Problem


h h

W,Zh

h

h

h

2 2 22 2

3 34 8

tt

mv

2 22

116

g

h

top

22

116

2t

tv m

For example : Significant Higgs loop corrections in the standard Model


‘Little’(low mass) Higgs and Fine Tuning

Higgs mass

Needed TreeContribution

Top

Gauge Higgs=

Cutoff scale Λ = 10TeVTree

2~ (2000 )GeV

2~ (700 )GeV 2~ (500 )GeV

2~ (200 )GeV


So we need incredible fine tuning to explain why the Higgs mass (~Weak scale order) is so much lighter than other mass parameter scales (Planck, GUT or Heavy Majorana scale) when we take the Cutoff scale Λ as P or G or H.

This is not NATURAL. (NATURALNESS problem)

In order to solve the hierarchy problem naturally (without fine tuning), we can expect that there exist at least the new physics beyond the Standard Model if we accept the big-desert between weak energy scale and P or G or H. .

LEP and Tevatron have probed directly up to a few hundred GeV, and indirectly between 1 and 10 TeV through the precision measurements.


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 ^17 GeVPlanck scale-

strong gravity

GUT- coupling

unification

Heavy right-handed

Majorana for Seesaw

Mechanism


h top

t

t

h

thh

stop t

2 22

38 t

22

316 t

2

t t Cancellation condition:

One well-known solutionSupersymmetry


Alternative models IComposite Higgs - Little Higgs (from UV completion) - Tecnicolor (new Strong-type interation)

Extra dimension- Large extra dimension (ADD) - Universal extra dimension (UED)- Small extra dimension - With the warped spacetime (RS)


- Higgsless no zero modes SM gauge bosons = First excited modes

- Gauge Higgs Unification(GHU)

Alternative models II

Brief introduction to GHU• - Gauge Higgs Unification SM gauge bosons = Zero modes Needs Higgs mechanism in order to break the

EWSB. but there is no Higgs potential in 5D. or Hosotani mechanism. too low Higgs mass (or top quark mass) with VEV which is proportional to 1/R.


Unification of gravity (s=2) & electromagnetic (s=1) Kaluza-Klein gravity the-ory

Unified theory of gauge (s=1) & Higgs (s=0) Gauge-Higgs unification

4D space-time 4D gauge-field Higgs 5D gauge field extra dimen-sion

Higher dimensional Gauge Theory

Zero mode

The pioneer works of GHU :・N.S. Manton, Nucl. Phys. 58(’79)141. ・ Y.　Hosotani, Phys. Lett. B126 (‘83) 309 ``Hosotani mechanism”



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 Ag g g g A

G g g g g Ag gg g AA AA A

Kaluza-Klein gravity the-ory

Gauge-Higgs unification

0

1

2

3

M

AA

A AA

In addition the scenario may also shed some light on the arbitrariness problem in the interactions of Higgs.

・ The quantum correction to mH is finite because of the higher dimensional gauge symmetry.

An interesting solution to solve the hierarchy problem without the supersymmetry.

Advantage of the GHU



Toy example – 5D SU(3) 1 2/S Z

ORBIFOLD BOUNDARY CONDITIONS

PURE HIGHER-DIMENSIONAL GAUGE THEORYA

5A


We only focus on the zero modes,

After we integrate out fifth dimension,Volume factor

0 0 0 00

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

A Z A

And rescale the gauge field,

RELATION BETWEEN 4D AND 5D GAUGE COU-PLINGS


Adding to brane kinetic terms

We can easily understand that these terms can give a modification to the gauge couplings without big change of given models.

U(1)SU(2)

From the effective Lagrangian, we can expect this relation

Similarly, for the U(1) cou-pling


Final 4D effective La-grangian

g gWeak mixing angle

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 con-stants of given Lie group (or Lie algebra) regardless of volume fac-tor Z if there are no brane kinetic terms in given models.

NO MASS TERM OF THE HIGGS

BECAUSE OF HIGHER DI-MENSIONAL GAUGE SYM-

METRY


Problems in the toy modelWrong 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

exp1tan3


GoalsStability of the electroweak scale (from the quadratic divergences – Gauge hierarchy problem)

Higgs potential - to trigger the electroweak symmetry breaking

Correct weak mixing


Possible answers for these problems

Wrong weak mixing angle- 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

(3) (2 |1)SU SU

Abandon the gauge coupling unifi-cation scheme .


No Higgs potential (to trigger the EWSB). - Using a non-simply connected extra-

dimension ( the fluctuation of the AB type phase – loop quantum correction)

- Using a 6D (or more) pure gauge the-ory.

- Using a background field like a mono-pole in extra dimensional space.

256( )L tr F

25~ [ , ]BL A A


Phenomenologically viable models

To find phenomenologically viable models they demand following 4 constraints:

(1) three massive gauge bosons W+,W, Z0 at the electroweak scale(2) rho =1 at tree level (3) existence of representations that can contain all Standard Model(SM) particle, especially hyper charge 1/6.(4) correct weak mixing angle.

Alfredo Aranda and Jose Wudka, PRD 82, 096005

(0) simple group ~ the gauge coupling unification.


POSSIBLE ALL GROUPS THAT SATISFY (0), (1), (2), (3) CONSTRAINTS EXCEPT (4) – WEAK MIXING ANGLE

Simple rootscor. to SU(2) One cartan

generator cor. to U(1)

Any GHU model can not explain correct weak mix-ing angle.


Higgs potential in 6DNOTATIONS OF LIE ALGEBRA SU(2) AND U(1)

SU(2) generatorsU(1) generator

COMMUTATION RELATIONS

ORTHONORMAL BASIS


A GENERAL FORM OF ZERO MODES IN TERMS OF GENERATORS OF LIE ALGEBRA

2tr [ , ]nA A

We focus on the mass term,

and the mixing angle,

From previous toy example, we can easily expect that our brane kinetic terms can modify the coupling constants, that is, the mixing angle,


FROM EXPERIMENTAL VALUE OF WEAK MIXING ANGLE,

VALUES OF C1 AND C2 WHICH ARE CONSISTENT WITH THE

PRESENT EXPERIMENT VALUE OF THE WEAK MIXING ANGLE

AND EACH GROUP THEORETIC NUMERICAL

FACTOR IN 6 DIMENSIONAL SU(3) AND E6 GAUGE HIGGS UNIFICATION MODELS

ON S2/ Z2.

STRAIGHT, DASHED AND DOTTED LINES CORRESPOND TO THE COM-

PACTIFICATION SCALES 5, 10 AND 20 TEV, RESPECTIVELY.


HIGGS POTENTIAL,

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

H Wg vM v M

24,2Dg

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

We can rewrite the equation with previous relation,

NAMBU-GOLDSTONE BOSON MODES ~

MASSLESS (FLAT DIRECTION)

RADIAL MODES ~MASSIVE

4H DM g v 4

1

DW

g vMZ


Numerical results.1. POSSIBLE GAUGE GROUPS AND HIGGS MASS

UNDER PRESENCE OF BRANE KINETIC TERMS

All masses are smaller than 114.4 GeV.


2. THE HIGGS MASS OF EACH GROUP AS A FUNCTION OF C2 ON THE COMPACTIFICATION SCALE MC=1, 5 AND 10 TEV

| IN THE 6 DIMENSIONAL GHU

MODEL ON S2/ Z2.


3. THE HIGGS MASS OF EACH GROUPAS A FUNCTION OF C2

ON THE COMPACTIFICATION SCALE MC=1, 5 AND 10 TEV

IN THE 6 DIMENSIONAL GHU MODEL

ON T2/ Z3.


4. VOLUME FACTORS AND SLOPES OF SEVERAL EXAMPLES IN 6D, 7D AND 8D


3. THE HIGGS MASS OF EACH GROUPAS A FUNCTION OF C2

ON THE COMPACTIFICATION SCALE MC=1, 5 AND 10 TEV

IN THE 7 DIMENSIONAL MODEL ON

S3/ Z2(TOP) AND

8 DIMENSIONAL T4/Z2

(BOTTOM) .


Summary

Weak Mixing Angle and Higgs Mass in Gauge-Higgs Unification Models with Brane Kinetic Terms

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