Minimal left-right symmetry for electroweak interaction.

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Minimal left-right symmetry model for

electroweak interaction

Conference Paper

· September 2007

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12

1 author:

Asan Damanik

Universitas Sanata Dharma

46PUBLICATIONS

61CITATIONS

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K * y n u t e S p * a k e r s

lr. Suhormon

Aminioyo

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Dr.

Boeh

Jong-Boh

(Horea

Hidro

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Nucleor

Power

Co.Ltd,

South

Horeo)

Frof.

Ren-TaiChiong,

Fh"D

(Uniuenity

of Florido

USA

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USA)

Dr.

Horini

Sodoti

(Krurfru

[Jnivenity,

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Frof,

Dr.

Muhumod

Mot

Sulleh

(Univenity

Kebongsan

Molay:io)

Dr.

YurilYu:uf

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Brown

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2no Jogla lnternational Physics Conference "Enhoncing Network ond Calloborotion Developing Research ond Education in Physics and Nuclear Energyo

September 6-9, 2007, Yogyakarta-lndonesia

ORGANIZING

COMMITTEE

The Advisors board

. Prof" lr. Y. Sardjono

(P3TM-lndonesia)

. Prof. Dr. ShoichiKai (Kyushu

University-Japan)

' Prof. Dr. Muhamad

Mat Salleh

(Universiti

Kebangsaan

Malaysia)

. Prof. Suparwoto

(UNY-lndonesia)

'

Prof. Dr. Kusminarto

(UGM-lndonesia)

' Dr. KamsulAbraha(UGM-lndonesia)

. Dr. Jazi Eko lstianyanto

(UGM-lndonesia)

The Technical Program Committee

Chairperson

:

Dr. Sismanto

Secretary:

Dr. Mirza Satriawan

EdiHartantyo,

M.Si

Treasurer

:

Dra. Chotimah,

M.S.

llona Usuman,

M.Kom

Programs:

Dr. Kuwat

Triyana

Dr. YusrilYusuf

Harsojo,

M.Sc.

Agus Supriyanto,

M.Si (UNS)

AriDwiNugraheni,

S.Si

Ahmad Kusumaatmaja,

S.Si

Scientific

Program :

Dr. Karyono

Dr. M.F. Rosyid

Dr. KamsulAbraha

Dr. Ahmad

Ashari

Publication

:

Eko Sulistyo,

M.Si

Mitrayana,

M.Si

Documentation

and Acomodation

:

Dr. AriSetiawan

R. Sumiharto,

M.Kom

M. lkhsan.

M.Si

Exhibition:

2* Jogla International Physics Conference 'Enhancing

Network and Collaboration Developing Research and Education in Physics and Nuclear Energy" September 6-9, 2007, Yogyakarta-lndonesia

Foreword

On behalf

of the organizer

of the 2nd Jogja lnternational

Physics

Conference,

I would

like to give our sincere

gratitude

to all the participant

of the conference. I would like to give

our_deepest

appreciation

and gratitude

to all of keynote

speakers

of this conference,

nariely

lr. sukarman Aminjoyo,

APU (BAPETEN),

Dr. Baek Jong-Bok (Korea Hidro and Nuctear

fower co. Ltd.), Prof. Ren-Tai chiang (Univ. of Ftorida

and GE Energy USA), prof. Dr.

Muhammad

Mat Salleh (U_niv-

Kebangsaan

Malaysia),

Prof. Yoshitsugo

Tomokiyo (Kyushu

Univ. Japan), Dr. Harini Sosiati (Kyushu Univ. Japan), Dr. Yoshiki HiOata lXyushu'Univ.

Japan),

Dr. Yusril

Yusuf (Gadjah

Mada Univ.).

The second Jogja International Physics Conference is the second conference

org.anized

by the Physlcs Department

Gadjah Mada University

continuing,

previously

was

called, the 1st Jogja Regional Physics ConfOrence

20O4. This conferenc6

is aim6d for

promoting,

developing,

and disseminating

interdisciplinary

research

ftom many different

fields

of physics,

for the betterment

of human lives. The conference

was intended

as a forum for the

physicist

from differenl branches of physics, and different countries, especially

ftom the Asian

and sunounding

region, to meet and discuss, developing

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and collaboration.

lt is also

intended

as a forum for dissemination

of the latest research results from many different fields

of physics. As Indonesia

is cunently planning developing

its first power plant hucbar reactor,

we also hope to enhance understanding

of the cunent result in the nuclear reactor theory and

technology. The theme of the conference is Enhancing Network and Cottabomion

-Develqing Research and Education in Physics and Nuclear Eneryy. The topics covered in

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are from very broad spectrum of Physics, such as Nuclear Energy, Atomic

Physics, Theoretical and Mathernatical

Physics, Computational

Physics, Nanote6hnology,

Matedal Science, Geophysics, Electronics Instrumentation,

Bio and- Medical physics, a'nd

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Physics.

In this conference

there are 8 papers in the panel session, presented

by eigth invited

speaker in two days. For the parallel session there are 63 papers to be presented in the

conference.

The presented

papers consist of Nuclear Energy and Atomic Physics 8 papers,

Theoretical and Mathematical Physics 8 papers computational physics 9 babers,

Nanotechnology

5 papers, Material Science 6 papers, Geophysics

10 paperi, Electronics

and

Instrumentation

1 7 papers.

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The committee hopes that this conference could enrich, enhance the physics

knowlegde,

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Psu9s. We sincerely

appreciate

the support and encouragement

from Physics D-epartment

of

Gadja Mada University, BAPETEN, Atomic and Nuclear laboiatory, Electronics

lnstrurnentations

Laboratory,

Geophysics laboratory,

Solid state laboratory, basbs physics

Laboralory,

Graduate School (Pascasarjana)

in University of Gadjah Mada, and OS StuOy

frogram. Last but not least I would also give my thanks to the student volunteers

in physics

Departement.

With sincere gratitude

Chairman

of the 2no

JlpC 2007

zno Jogla Intemational Physics Conference

"Enhancins

Network

and coilaboration

Deveropins

Research

and

Educatbrr:X::{;+"i#r:#E1i?;##

Foreword

Distinguished

guests

Honorary

speakers

Ladies

and gentlemen

Welcome

to the 2ro Jogja International

Physics

Conference.

We gather here today to communicate

our scientific

activities,

to learn from each other, to find

an opportuni$ to collaborate

with each other, and to share our experience.

The world-wide

web has become our closest friend. No day passes without us accessing

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Internet. lt was Tim Berners-Lee, a physicist, who initiated the lnternet lifestyle. \Men

Berners-Lee dreamed about creating a tool to enable reseachers all over the world to

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only one wordwas in his mid: share it, share it, share it.

We do not lose anything

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Physicists

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We hope you have a pleasant

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FYl, the physics department

at gadjah mada university

was founded in 1955. Now, we have

three B.Sc programs : physics, geophyics, and electronics & instrumentation,

a 3-year

diploma

program

in Electronics

& Instrumentation,

an M.Sc and a Ph.D in Physics.

\Mth sincere gratitude

Head of Physics Department

F)e.Ufod"fr

2nd Jogjo lnternotionol Physics Conference "Enhancing Nelwork and Colloborotion Developing Reseorch ond Educotion in Physics ond Nucleor Energy" September 6-9, 2@7, Yogyokorto-lndonesio

CONTENTS

ORGANIZING

COMMITTEE

FOREWORDS

CONTENTS

PAPERS

Keynofe Speoker

i

ii

iv

Aulhor(s)

fille

Poge

I

Dr. Sukormon Aminjoyo

2 Prot. Ren-ToiChiong,

Ph.D

Nucleor Low ond Regulotion in

Indonesio

Stobility

Solution

for Inherently

Sofe

KS06

ESBWR

Operofion

NPP

Stotus

ond Prospect

In Koreo

KSOI0

Stotisficol

Properties

of

KSOI2

Spoiiotemporol lntermittency in

on Electroconvective

System

of

Nemolics

Chorocterizotion

of

Nono-Structures

in Moteriols by

Tronsmission

Electron Microscopy

Focused lon Beom Techniques

KS02l

And Tronsmission

Electron

Microscopy Studies

Of Advonced

Moteriols

LiquidCrysiolElostomers;Swelling KS026

Dynomics, Electromechonicol ond

Electroopticol Effects

Fobricotion of Orgonic Light

KS030

Emitfing

Diodes (OLEDs)

for Flot

PonelDisploys

Dr. Boek Jong-Bok

Dr. YoshikiHidoko

Prof. Dr. Yoshitsugu

Tomokiyo

5 Dr. HoriniSosioti

7 Dr. YusrilYusuf

B Prof. Dr. Muhomcrd

Mot

Soileh

KSOI

KSOI

5

Porticiponls

2.d Jogjo Internolionol Physics Conference "Enhoncing Nefwork ond Colloboration Developing Reseorch ond Educotion in Physics ondN vcleor Energy',

September 6-9, 2007. Yogyokorto-lndonesio

I

DoniSoputro

Colculotion

Of TotolReoction

NEOI

Cross

Sections For Proton On l2C,

40Co, 9Olr,2OB?b

Nuclei At High

Energies

Theoreticolly

2

Mitroyono, T. Pierero,

Diode-Loser

Bosed photo-ocouslic NEo4

B.W.M.

Moeskops,

S.

Spectroscopy in Aimospheric NOz

Persijn,

H. Nous, F.J.M.

Detection

Honen, M.A.J.

Wosono,

Muslim,

ond W. Rochmoh

3

D- Lelono ond M.A.J.

Automotizotion

of photoocoustic

NEog

Wosono

Spectroscopy for Anolysis

of

Multicomponent

Gos

4 Teddy Ardionsyoh, -

cellonolysis

of spent pwR Fuels

in

NEl3

Suwondho

Arie Proyudho Fost Reoctor

ond Andong WidiHorto

5

u. Khoirunnisyoh

ond

Determinotion

Restitution

NEIZ

D.Soputro

Coefficient of Bronching Froction

of DoMeson-+ K-n'decav

6 s.T.

Persijn,

A.K.Y.

Ngoi,

ond speclroscopic

Applicotions

of o

NE2l

F.J.M.

Honen

Broodly

Tuno

ble,

Continuous-Wove Opiicol Porometric

Oscillotor

7 Povl. Stothers,

Kevin

plont Remoining Life Time

NE25

Thoorghood ond

Assessment

for power Generolion

Yohonnes

Sordjono

THEORETICAT

AND MATHEMATICAT

PHYSICS

No

Aulhor(s)

Iille

Poge

9' M. ForchoniRosyid

on The

structure

of euontizoote

tHor

Algebros Of The products Of

Symplectic Monifolds With

Polorizotions

l0 Moh. Adhib.u.A ond

Anotyticotstudy

of singte-etectron

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I I limothy Siohoon ond

Inequivolenl Quontizotions

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' 12 Ason Domonik, Miao

Minimol

Left-Righf

symmetry

Model

THol5

l,

,,, Soiriowon.

promudito

for Electroweoi

Interoction

2nd Jogjo Inlernotionol Physics Conference "Enhoncing Network ond Colloborolion Developing Reseorch ond Educotbn in Physics and Nucleor Energy" September 6-9, 2@7, Y ogyokorto-lndonesio

Hermonto

l3 Bombong

Heru

lswonto

l4 UmiKhoirunnisyoh

l5 Arief Hermonto

l 6 A l i Y u n u s

R o h e d i

Leorning

of Mixlure

Models bosed

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Clossifiers

using Lobeled ond

Unlobeled

Doto

Determinotion

of Coherent

TH02S

Scottering Amplitude of Arsenic Using

Smoll

Angel Neutron

Scottering

Theoreticolly

A Simple Method to Determine the

TH02B

Generol -Relotivistic

Doppler Shift

with Arbitrory Mofions of Source ond

Observer in o Cosmologicol Model

Creoting A New Plonck's

Formulo

of

TH030

Spectrol Density

of Block-body

Rodiotion by Meons of AF(A)

COMPUTATIONAI.

PHYSICS

No

Author(s)

Iitle

Pcge

1 7 Fohrudin

Nugroho ond

Pekik Nurwontoro

Effects of Angulor Voriotion of

ExternolMognetic Field to Surfoce

Cp0l

Nucleotion

of Rectongulor

Superconductor Moteriols

Simulotion

Generolized Predictive

Cp06

Control Modificotion And Controller

Performonce Influence

Using

ComputotionolSystem

of Units CpOl I

to Derive Noturolond Geomeiricol

System

of Units

Woter Rocket Fun Progrom for

Enhoncing

Junior High School

Student

Interest

on Studying

physics

Supervised

Leorning

Fromework

of

Cp0l Z

Mixture

Models

for Clossificotion

The Reconstruction

of Multiple

Cp023

Acoustic

Sources

thot Fulfillthe

Predetermined

Sound

Levelon o

Certoin

Torget

Field

Locotion

l8 ErwoniM. Sortiko

l9 Arief Hermonto

20 Mutio Delino ond

Mohomod lchson

2l Bombong Heru lswonto

22 Doniel Setiodikorunio

2"d Jogjo Internotionol Physics Conference "Enhancing Nefwork ond Colloborotion Developing Reseorch ond Educotion in Physics ond Nucleor Energy" Seplember 69, 2007. Yogyokorlo-lndonesio

23 Visko

Indo V

Development

of The Object

CP030

Thickness

Meosurement

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24 Pekik

Nurwontoro

Robust

Computotion

of the Gount

CP034

Coefficients

NANOTECHNOTOGY

No

Autho(s)

f$le

Poge

25 A. Bohtior

Longmuir-Blodgett-Kuhn

Muttiloyer

NT0l

Films

of Azobenzene Contoining

Polyomic Acid for Liquid Crystol

Opticol Switching

26 ldo Sriyonti, Leni

Electricol Conductivity of Nd-CeOz

NT07

Morlino, Mikrojuddin

Nonoporticles Prepored by Simple

Abdulloh, ond

Polymer

Heoiing Method

Khoirunijol

27 W.B.

Nurdin

ond K.D.

Applicotion of Microcononicol

NTOI

I

Schotte

Temperoture to The Spin Crossover

of Fe-Co Compounds

28 Aripin

Chorocterizotion

ond Electricol

NT0l6

Conductivity Behoviour of

Polypynole Conducting Polymer

29 Ahmod Kusumootmojo, structure Dependence of Electricol NT020

Ari Dwi Nugroheni,

Chqrocteristic of Orgonic Thin Films

Sudormiotiond Kuwot

Bosed on Perylene Derivotives

Triyorlo

MATERIAT

SCIENCES

No

Aulhor(s)

Ilfle

Poge

30 Aris

Doyon ond

Conductivity

Properties

of polymer

MSOI

Susilowoti

GelDosimeters

lnodioted with

Gommo-Roys

3l susilowotiond

Aris

opticolProperiies

of polymer

Films

Ms06

Doyon

Contoining

Chlorine

lnodioted

with

2nd Jogio Inlernotionol Physics Conference "Enhoncing Nefwork ond Colloborqtion Developing Reseorch and Educolion rn Physics ond Nucleor Energy" Seplember 6-9 , 2007. Yogyokorto-lndonesio

32 Moh. Yosin,

S.W.

Horun, Construction

of Opticol Fiber

MS0l I

Kusminorto,

Koryono,

H. Displocement

Sensor

Using

on

AC-Ahmod

33 Supriyono

Moduloted Light Source

The Influence

of ( Volue in

MSOI4

Shokedown

Phenomeno

from

Elostic

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CriticolCunent

Density

on Two

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Dimensionol

Superconductor

Hoving Columnor Defecl

34 Horsojo

35 Bombong Murdoko Eko The Chorocterisotion

of Some Liquid

Joti, lrwonto, Lukmon

ond Solid

Stote Medium to the

Hokim

Attenuotion

lntensity

levelof Sound MS02l

GEOPHYSICS

No

Author(s)

Iille

Poge

36 Budi Eko Nurcohyo ond

3D complex seismic Attribut Bosed

GpOr

Sudormodji

on Continous Wovelet Tronsform

37 Sudormoji

Seismic

Roy Trocing In Heterogenous GpO4

Medio Using Lineor Troveltime

lnlerpolotion

(LTt)

Method

38 Edi Hortontyo

A Verificotion of plone Wove

GPOIO

lmplementotion on Finite Volume

Poisson

Solid Medium

39 Novi Rohmowoti,

Tjohyo Groundwoter

Quolity chonges Due

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Within

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40 Sismonto,

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Condisewu complex by meons

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42 Sudormoji,

Budi Eko

Applicotion of Instonloneous

GpO29

Nurcohyo ond Rossy

Bondwidth For Hydrocorbon Trop

Septo Brion Khrismo

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2"d Jogjo Infernotionol Physics Conference "Enhancing Netwo* ond Colloborotion Developing Reseorch ond Educolion in Physics ondN ucleor Energy" Sepiember 6-9 , 2007, Yogyokorto-lndonesio

43 Udi Hormoko

44 W. Suryonto,

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Ulrich Schreiber

Hydrothermol

Model of Meropi

Volcono, Centrol Jovo, lndonesio

Whot con be leorned from tilt

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ETECTRONICS

AN D INSTRUMENTATION

46

47

48

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Donong Lelono ond

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llono Usumon

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49 lrwondi

Tri Kuntoro Priyombodo,

Proyoto, Jol Eko

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Setio Wirowon, Suryo

Guritno ond Agus

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Title

A Comporison Study of The

Performonce of The lmoge Retrievol

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September 6-9, 2007, yogyokorto-lndonesio

54 R. Sumihorfo,

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55 wini Rizkiningoyuond

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Minimal Left-Right symmetry Modet for Electroweak Interaction

Asan Dananit/''", Mina satriawan2 , pramudita Anggraitf, Arief Hermanto2_'Department of Plrysics, Sanata Dharma University,

$mpus III USD _zDepartment paingan, Maguwoharjo, Sleman, yognkarta, Indonesia of physics, racitty of lviathematics an{Natural sciences.

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Foll_owing the procedure in the Glashow-lYeinberg-Salan (GWS) model for electroweak interaction, by using two doublets and one induced bidoublet Higgs fietds as a result oftie interactions of the two doublets, we evaluate the predictive power of the lrftlri7it symnetry nodel based on S(J(2)1 x SU(2)p x U(l) gauge group to the gauge bosons masses, leptons masses, and the structure of eharowiak interaclions-. Byh b.iloublet and doublet Higgs fields haie the contribution to the gauge ioro^ ^ r", a|ter WmeW breaking. Meanwhile, leptons masses _{arise only from the bidoublet itgtli fuU. Tlw parity} uiolatioyt coild be associated with the mixing of the chargei gauge bosow n^sii yron tne iiaucia bidoublet Higgs.

Keywofds: Ieft-right symmetry model, electroweak interaction, doublet and bidoubtet. *Conesponding _author

E- ma i I : d.asur@lycos.oom I. Introductbn

Even though the Glashow-Weinberg-Salam (GWS) model for electroweak interaction based on SU(2[ xU(l\ gauge group very successful phenomenologically _{[l-3], but many} fundamgntal problems i.e. fie responsible mechanism fbr generating the neutrino masses, the dolninafion of the V-A over V+A interactipm 4t low energy, and the responsible mechanism for the doublet lepton up.down mass differenCe could not be explained by GWS model. The need for the extension of the GWS model comes from the conclusion that neutrinos have a mass as an implication of the detected neutrino oscillations phenomena _{for both solar} and atmOsphetic neutrinos _[4-10].

ManN theories or models for extension of the GIWS _{rnodel have been proposed. One of} the intpresipg models is the Left-Right symmetry model based on SU(2)r x SU(2)x x U(l) gasge group proposed by many authors [l-15]. Irl this paper, we use the left-right symmetry model based on SU(2)r x SU(2)a x U(l) galhge _{group with two doublets and one} bidoublet Higgs fields (as a result of the two doublets interaction) to break the SU(2[ x SU(2)p _{x U(l) gauge group down to U(l)",. The} lepton figlds to be represented as doublet of an SU(2) for both left and righr fields to make the full sense ofthe left-right symmetry model.

The paper is organized as follows: in section II we present our main assumptions for the left-right symmetry model, in section III we evaluate the gauge bosons masses, in section IV we evaluate the leptons masses, and finally in section V we give a conclusion

II. The Model

In our model, the left-right symmetry model for electroweak interaction based on the SU(2)1 x SU(2)R x U(l) gauge group wirh the assumptions and the particles assignment as follows:

l. Two primary Higgs fields are doublet of

su(2):

u - ( o r ) / . - \

", =l.;.J'

r-=l;') (r)

2. The secondary _{bidoublet Higgs field {} could be produced from the interaction of the two primary Higgs fields, that is:

a=(t.n

'

a:a,)=(n' c,l (2)

l.boc- bodo _{) (r- ,o )} 3. The leptons fields arr doublet of SU(2)

for both left and right fields: ( v ) _{/ v \}

V ' = l - 1 , \ r n = l

_ l ( 3 )

\ e ) t \ e ) r

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when Higgs fields develop its vacuum expectation values similar to the symmetry breaking in the GWS model. By applying the above assumptions and particles assignment, we could break the left-right symmetry model based on SU(2)p x SU(2h x U(l) down to U(l),* directly as shown schematically below:

The vacuum exp€ctation values of two doublets and one bidoublet Higgs could contribute to the gauge bosons masses. Meanwhile, the leptons masses (in Yukawa term) only emerge from the vacuum expectation value of bidoublet Higgs, because the leptons fields tp, and wr to be doublet of SU(2), then only the Yukawa term with bidoublet Higgs salisfies gauge invariancc. Thus, the complete Lagrangian density could be reads:

7 = -! WonV pi - _+Y!*IF tn -+ B _{t, Bp'}

+V

ry, 8o

u - t c.y,n

- t ruob,

+V

*yu

to o - t c.w,o

- t rurb ^

+l!a,-irww-+tn,V)'

*l$a,

-*tw* -ttu,V.l'

+r,]ftar-trw*-+tt,M'

*rlfta,-tr.wu,-+vB,M'

-V(X

L,X R,d.7-(Cgrpty^ +nc) where g, = gn= g are the SU(2) couplingg g' is the U(1) coupling, Tu(lr=Q,I,2,3) are the Dirac matrices, T's are the Pauli spin matrices,fl;gr,X^,q; is the Higgs potential, Y is the hypercharge (I =B-L), and G is the Yukawa coupling.

The elsctric charge oparator Q satisfies the relations:

SU(2[ x SU(2)ax U(l) I

1 " 1 . o

I b ) * o

(-r^) * 0

{

u(l)*

Q =7,,

+7,^

+!

(5)

where {, md 4, are the third components the weak isospin generator: T, =T,12,

According to the Eqs. (a) and (5), the Higgs fields have the following quantum numbers:

x r(1,0,t\x

^(0,;,r)p(;,;,0) (q)

and the leptons fields fansform as:

v,Q,o,ol rg^(o,z,o) (7)

III. The Gauge Bosons Masses

From Eq. (4), we can see that the relevant gauge boson mass tgrms as follow:

r^*=l(trtr*-.4ttrE,l'

*l(-+r.w*-irt,V^l'

(8)

+rl!+tw*-+YB,M'

+r,l(?ww-+yB,M'

By substituting the vacuum expectation values ofthe Higgs fields:

f o ) ,

/ o \ , . ( o o \

r,,)=laJ'

r+)=[a]

(o)=|.;,)

into Eq. (8), we obtain:

u* = +lr't Wil * @,11

]* o'

(sw)

- s' a ,f

* r, a, (ni^l

* @,;ll*

a,

Gwfi

- s, B

ul

By defining:

(9)

w

; = hQrL + tw

i\w; = #(wk + iw

rt\

-

cwi-g'BuL -

sw:n-g'Bun

-pL _{r-;---'; ,"un f--:---=}

, l c ' + c ' '

, l s ' + s ' '

" _ g ' I { i + g B * " _ g ' W f i + g B *

_{, nttR}

,lg" + s"

^IV.F

'

Z',n

=W1,,,,

Z',,^

=lYk,

sb

sd

m v , = | , * r , = 7 ,

f r t = 0 ,

* s'b'

.*W;"1

.ftr;"|

-@;"ll

* s' (p'

- ttrlr;"|

. @kl

. @;lt

(4)

*r" =tbGl*s" ,mz.

=+dG' 4" ,

= *'r^ = ilr,, = frr,* =iSr[p' *f ,

frr"

THOI6

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then Eq.(9) rcads:

Lbo,-

* m$rw

;w ; + mfl^w

|w;

+m|,w;w; +m'j^w;w;

+m|,2*z! +ml"z*zl

(ll)

+ m)ArAP

+ m),^z'^z'(

+ m'",,2'*z'!

or

Lo* =fu|,"

* *;;,yry;w;

I t r r \

+@h^

+ m;^lY;W;

+ m),zr,z! + m'r^z*zN Q2)

+ mlApAt + m'r,^z'*z';

+ m'r,rz'*Z';

From Eq. (10), by following the standard rnrodel of electroweak interaction symmetry breaking procedure to the left-right symmetry model and put the value of b : d, we can see that the resulted gauge bosons masses for both left and right bosons are equal. To make the left-right symmetry model relevant to the electroweak phenomen4 many authors fl4,15,161 have taken the value of b<<d. The difference values of the 6 and d can be associatred with the parity violation.

The gauge bosons masses problem in our modcl, especially for charged bosons masses arise fr,orn bldoublet Higgs vacuum expectation values, could be resolved by defining:

f,r; l=fcos0

-sinoYr",

t0t) 63)

l^i" ) [sin0 cosl )rn*^(Q))

where the angle 0 associated with parity violation, _{m*,(Q) and a*,161we massesofthe} left and right lll bosons from bidoublet Higgs fields. From Eq. (13) we can see that the maxim4l parity violation occur for 0 = 450 such that the total charged right bosons masses

^*rrary large compared to the left bosons [lassoS mr,, . For example, if we take values of the l{t and I(x bosons masses from doublet Ne mvr. =12". -glQgv,then the reasonable valrcs for gauge bosons W from induced bidoublet are rnn,(Q)= nv^(q)= 6724 GeVor mr,(Q)=m*^(@)o7TeV. If we take 0 =4So, then tho rigtrt charge-cun€nt conffibution (V+A

interaction) to the electroweak interaction is only around 0.015 7u In this scheme, the domination of the V-A interaction over V+A interaction for charged curent at low energy could be understood as an implication of the very massiveness _{of the mn^compared to m*,, The} gauge bosons fir?sscS 2". in the maximal parity violation, only come from the doublet Higgs freld X, as formulated in the GWS model and supported by experimental fact that the boson masses emerge ftom doublet Higgs field. lV. The Leptons mrsses

The leptons m?rsses in our model arise from tho symmetry breaking. The lepton mass term is the Yukawaterm in Eq. (4), that is:

L, =GV,(|W*

( 1 4 ) By inserting the vacuum expectation value of bidoublet Higgs, then we obtain the masses:

mu = Gp *l fie - Gs for neutrino and electron respectively. In our minimal left-right symmetry model based on SU(2[ x SU(2h x U(l) gauge group the leptons masses (neutrino and electron) arise only from the bidoublet Higgs vacuum expectation values.

As long as we know, for leptons mass€s there is no experimental fact that force us to choose a one kind of multiplet Higgs in the Yukawa term except dictated by the requirement of the Lagrangian density must be gauge invariance. But, in the boson mass sector, the representation of the Higgs fields to be SU(2) doublet theoretically supported by experimental fact. Thus, we could use the induced bidoublet Higgs field as the responsible field for generating the leptons masses.

V. Conclusion

By using the minimal content of the particles (two primary doubles Higgs, one induced bidoublet Higgs (secondary Higgs), and two lepton fields) involve in the left-right symmetry model based on SU(2L x SU(2)a x U(l) gauge group, the domination of the V-A interaction over V+A interaction at low enerry, the neutrino mass and the electron mass arise naturally. The parity violation in our model related to the mixing of the bosons masses arise from the induced bidoublet Higgs.

VI. References

4. 5 . 6. 7:

"Enhancins _{Network ahd cotlaboration Devetopins Rese"rro "^o')7,f;jil?:if;:;:t"ii";::;::'#tr;}

September 6-9, 2007, Yogyakarta-lndonesia

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