Minimal left-right symmetry for electroweak interaction.
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/280690847
Minimal left-right symmetry model for
electroweak interaction
Conference Paper · September 2007
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1 author:
Asan Damanik
Universitas Sanata Dharma
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2noJoglalnternationalPhysics
Conference
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Researchond Educationin Physicsand Nuclear Energyo
September6-9, 2007,Yogyakarta-lndonesia
ORGANIZING
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The Advisors board
.
.
'
.
'
'
.
Prof"lr. Y. Sardjono(P3TM-lndonesia)
Prof.Dr. ShoichiKai(KyushuUniversity-Japan)
Prof.Dr. MuhamadMatSalleh(Universiti
Kebangsaan
Malaysia)
Prof.Suparwoto(UNY-lndonesia)
(UGM-lndonesia)
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Dr.KamsulAbraha(UGM-lndonesia)
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llonaUsuman,M.Kom
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Harsojo,M.Sc.
AgusSupriyanto,
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CONTENTS
ORGANIZING
COMMITTEE
FOREWORDS
CONTENTS
i
ii
iv
PAPERS
Keynofe Speoker
Aulhor(s)
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Nucleor Low ond Regulotionin
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Poge
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Dr.SukormonAminjoyo
2
Prot.Ren-ToiChiong,
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KS06
Dr.BoekJong-Bok
NPPStotusond ProspectIn Koreo
KSOI0
Dr.YoshikiHidoko
Stotisficol
Properties
of
Spoiiotemporollntermittencyin
on ElectroconvectiveSystemof
Nemolics
KSOI2
Prof.Dr.Yoshitsugu
Tomokiyo
Chorocterizotionof NonoStructuresin Moteriolsby
Tronsmission
ElectronMicroscopy
KSOI5
5
Dr.HoriniSosioti
Focusedlon Beom Techniques
And Tronsmission
Electron
MicroscopyStudiesOf Advonced
Moteriols
KS02l
7
Dr.YusrilYusuf
LiquidCrysiolElostomers;SwellingKS026
Dynomics,Electromechonicolond
ElectroopticolEffects
B
Prof.Dr.MuhomcrdMot
Soileh
Fobricotionof Orgonic Light
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KSOI
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2
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B.W.M.Moeskops,S.
Persijn,
H. Nous,F.J.M.
Honen,M.A.J.Wosono,
Muslim,ond W. Rochmoh
Diode-LoserBosedphoto-ocouslic
Spectroscopyin Aimospheric NOz
Detection
NEo4
3
D- Lelonoond M.A.J.
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28 Aripin
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Seplember 6-9, 2007.Yogyokorto-lndonesio
32 Moh. Yosin,S.W.Horun,
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33 Supriyono
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September6-9,2007,yogyakarta_lndonesia
Minimal Left-Right symmetry Modet for ElectroweakInteraction
AsanDananit/''", Mina satriawan2, pramudita Anggraitf, Arief Hermanto2
'Department
of Plrysics,SanataDharma University,
III
USDpaingan, Maguwoharjo,Sleman,yognkarta, Indonesia
$mpus
zDepartmentof physics,
racitty of lviathematicsan{Natural sciences.
'r,,,",ff
fi:!,I:f,y#';;:y;;i{u#;';'rWff
:';*^",,"
Abstratt
Foll_owing the procedure in the Glashow-lYeinberg-Salan(GWS) model
for electroweak
interaction,by using two doubletsand one inducedbidoubletHiggs
fietds as a result oftie interactionsof
the two doublets,we evaluatethe predictive power of the lrftlri7it symnetry nodel basedon S(J(2)1x
SU(2)px U(l) gaugegroup to thegauge bosonsmasses,leptons masses,
and the structure of eharowiak
interaclions-.Byh b.iloublet and doubletHiggsfields haie the contribution to the gauge ioro^
^ r",
a|ter WmeW breaking.Meanwhile,leptonsmassesarise only
from the bidoubletitgtli fuU. Tlw parity
uiolatioytcoild be associatedwith the mixing of the chargei gauge bosow n^sii yron tne
iiaucia
bidoubletHiggs.
Keywofds: Ieft-right symmetrymodel,electroweakinteraction,doubletand bidoubtet.
*Conesponding
author
E-mai I : [email protected]
I. Introductbn
Even though the Glashow-WeinbergSalam(GWS) modelfor electroweakinteraction
based on SU(2[ xU(l\ gauge group very
successfulphenomenologically
[l-3], but many
fundamgntal problems i.e. fie responsible
mechanismfbr generatingthe neutrino masses,
the dolninafion of the V-A over V+A
interactipm 4t low energy, and the responsible
mechanismfor the doubletleptonup.down mass
differenCecould not be explained by GWS
model. The needfor the extensionof the GWS
modelcomesfrom the conclusionthat neutrinos
have a mass as an implication of the detected
neutrinooscillationsphenomenafor both solar
andatmOsphetic
neutrinos[4-10].
ManNtheoriesor models for extension
of the GIWSrnodelhavebeenproposed.Oneof
the intpresipg models is the Left-Right
symmetrymodel basedon SU(2)r x SU(2)xx
U(l) gasge group proposedby many authors
Irl this paper,we use the left-right
[l-15].
symmetrymodel basedon SU(2)r x SU(2)ax
U(l) galhgegroup with two doubletsand one
bidoubletHiggs fields (as a result of the two
doublets interaction) to break the SU(2[ x
SU(2)px U(l) gaugegroupdownto U(l)",. The
leptonfiglds to be represented
as doubletof an
SU(2) for both left and righr fields to makethe
full senseofthe left-rightsymmetrymodel.
THOI5
The paper is organizedas follows: in section II
we presentour main assumptionsfor the leftright symmetrymodel, in sectionIII we evaluate
the gauge bosons masses, in section IV we
evaluate the leptons masses,and finally in
sectionV we give a conclusion
II. The Model
In our model, the left-right symmetry
model for electroweakinteraction basedon the
SU(2)1x SU(2)Rx U(l) gaugegroup wirh the
assumptionsand the particles assignment as
follows:
l. Two primaryHiggsfieldsaredoubletof
su(2):
", =l.;.J'
r-=l;') (r)
u
-(or)
/.-\
2. The secondarybidoubletHiggs field {
could be producedfrom the interaction
of thetwo primaryHiggsfields,that is:
a:a,)=(n' c,l
a=(t.n
'
(2)
V ' = l - 1 , \ r n = l_ l
(3)
l.boc- bodo) (r- ,o )
3. The leptonsfieldsarr doubletof SU(2)
for both left andright fields:
(v )
/v \
\e )t
\e )r
4. Both leptonsand gaugebosonsmasses
are generatedvia symmetry breaking
2noJoga InternationalPhysicsConference
"EnhdncingNetworkond colloborotion
DeveloplngResearchand Educotionin Physicsand NucleorEnergy"
September5-9, 2007,Yogyakarta-tndonesia
when Higgs fields develop its vacuum
expectation values similar to the
symmetrybreakingin the GWSmodel.
By applyingthe aboveassumptions
and
particlesassignment,we could break the leftright symmetrymodelbasedon SU(2)px SU(2h
x U(l) down to U(l),* directly as shown
schematically
below:
where {,
md 4, arethe third components
the
weakisospingenerator:T, =T,12,
Accordingto the Eqs. (a) and (5), the
Higgs fields have the following quantum
numbers:
x r(1,0,t\x
^(0,;,r)p(;,;,0) (q)
andthe leptonsfields fansform as:
SU(2[ x SU(2)axU(l)
1 " 1 .Iob ) * o
(-r^)* 0
III. The GaugeBosonsMasses
From Eq. (4), we can see that the
relevantgaugebosonmasstgrmsas follow:
{
u(l)*
The vacuum exp€ctationvalues of two
doublets and one bidoublet Higgs could
contribute to the gauge bosons masses.
Meanwhile, the leptons masses(in Yukawa
term) only emergefrom the vacuumexpectation
value of bidoublet Higgs, becausethe leptons
fields tp, and wr to be doubletof SU(2),then
only the Yukawa term with bidoublet Higgs
salisfiesgaugeinvariancc. Thus, the complete
Lagrangiandensitycould be reads:
r^*=l(trtr*-.4ttrE,l'
*l(-+r.w*-irt,V^l'(8)
+rl!+tw*-+YB,M'
+r,l(?ww-+yB,M'
By substitutingthe vacuumexpectation
valuesofthe Higgsfields:
/o\,. (o o\
fo),
(o)=|.;,)
r,,)=laJ'
r+)=[a]
into Eq. (8), we obtain:
pi
7 = -! WonV - +Y!*IF tn -+ Bt, Bp'
u* =+lr'tWil * @,11
]*o'(sw)- s'a,f
- s,Bul
* r,a,(ni^l* @,;ll*a,Gwfi
+Vry,8ou- t c.y,n- t ruob,
- t rurb^
+V*yutoo- t c.w,o
*s'b'.*W;"1
.ftr;"|
-@;"ll
*s'(p'- ttrlr;"|
. @kl. @;lt
(4)
(9)
By defining:
+r,]ftar-trw*-+tt,M'
*rlfta,-tr.wu,-+vB,M'
-V(X
(7)
v,Q,o,ol rg^(o,z,o)
I
+l!a,-irww-+tn,V)'
*l$a,-*tw* -ttu,V.l'
(5)
Q=7,,+7,^+!
w; =hQrL+twi\w; =#(wk+iwrt\
-
-pL
cwi-g'BuL r-;-----';
,lc' + c' '
L,X R,d.7-(Cgrpty^+nc)
,"un
sw:n-g'Bun
f--:-----=
,ls' +s' '
" _g' I{ i+gB*, nttR
" _g' W fi+gB*
'
where g, = gn= g are the SU(2) couplinggg'
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
Yukawacoupling.
The elsctric chargeoparator Q satisfiesthe
relations:
,lg"+s"
^IV.F
Z',n=W1,,,,Z',,^=lYk,
m v , =sb
| , * r , = 7sd
, frt=0,
*r" =tbGl*s" ,mz.=+dG' 4" ,
frr" = *'r^ = ilr,, = frr,* =iSr[p'
*f
,
(10)
THOI6
2ndJogiaInternationalPhysicsConference
"EnhancingNetwo* and CalldborotionDeveloplngResearchond Educatlonln Physlcs NuclearEnergy'
ond
September6-9,2007,Yogyakarta-lndonesia
thenEq.(9)rcads:
* m$rw
Lbo,;w ; + mfl^w
|w;
+m|,w;w; +m'j^w;w;
+m|,2*z! +ml"z*zl
interaction)to the electroweakinteractionis only
around0.0157u In this scheme,the domination
of the V-A interactionover 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
gaugebosonsfir?sscS2". in the maximalparity
(ll)
+ m)ArAP+ m),^z'^z'(
violation, only come from the doublet Higgs
freld X, as formulated in the GWS model and
supportedby experimental fact that the boson
massesemergeftom doubletHiggs field.
+ m'",,2'*z'!
or
Lo*=fu|,"
* *;;,yry;w;
I
t
r r \
+@h^+ m;^lY;W;
+ m),zr,z! + m'r^z*zN
lV. The Leptonsmrsses
The leptonsm?rsses
in our model arise
from tho symmetry breaking. The lepton mass
termis the Yukawatermin Eq. (4), that is:
(14)
L,=GV,(|W*
Q2)
+ mlApAt+ m'r,^z'*z';
+ m'r,rz'*Z';
By inserting the vacuum expectationvalue of
bidoublet Higgs, then we obtain the masses:
mu= Gp *l fie - Gs for neutrinoand electron
respectively. In our minimal left-right symmetry
model basedon SU(2[ x SU(2h x U(l) gauge
group the leptonsmasses(neutrino and electron)
arise only from the bidoublet Higgs vacuum
expectationvalues.
As long as we know, for leptonsmass€s
there is no experimental fact that force us to
choose a one kind of multiplet Higgs in the
Yukawaterm exceptdictatedby the requirement
of the Lagrangian density must be gauge
invariance. But, in the boson mass sector, the
representationof the Higgs fields to be SU(2)
doublet theoretically supportedby experimental
fact. Thus, we could use the inducedbidoublet
Higgs field asthe responsiblefield for generating
the leptonsmasses.
From Eq. (10), by following the
standard rnrodel of electroweak interaction
symmetry breaking procedure to the left-right
symmetrymodel and put the value of b : d, we
canseethat the resultedgaugebosonsmassesfor
both left and right bosonsare equal. To make
the left-right symmetry model relevant to the
electroweak phenomen4 many authors
fl4,15,161have takenthe value of b
Minimal left-right symmetry model for
electroweak interaction
Conference Paper · September 2007
READS
12
1 author:
Asan Damanik
Universitas Sanata Dharma
46 PUBLICATIONS 61 CITATIONS
SEE PROFILE
Available from: Asan Damanik
Retrieved on: 22 April 2016
Proceedings
2nd
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of frlothenratics
Foculty
6-8, a007
Septenrber
K*ynute Sp*akers
(BApETEN,
Indonerio)
lr.Suhormon
Aminioyo
(Horea
South
Horeo)
Power
Co.Ltd,
ondNucleor
Hidro
Dr.Boeh
Jong-Boh
(Uniuenity
USA)
USA
snd0FEnergy,
Fh"D
ofFlorido
Frof.
Ren-TaiChiong,
(Krurfru
[Jnivenity,
Sodoti
Dr.Horini
lopon)
(Univenity
Molay:io)
Kebongsan
MotSulleh
Frof,
Dr.Muhumod
winner
200?,Godioh
Modo
Uniuenfu)
owsrd
Brown
Dr.YurilYu:uf
iC.H"
(Kyulhu
Tomohiyo
Uniuenity,
Frof.
Dr.Vofiitrugu
lopsn)
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2noJoglalnternationalPhysics
Conference
"EnhoncingNetwork ond Calloborotion Developing
Researchond Educationin Physicsand Nuclear Energyo
September6-9, 2007,Yogyakarta-lndonesia
ORGANIZING
COMMITTEE
The Advisors board
.
.
'
.
'
'
.
Prof"lr. Y. Sardjono(P3TM-lndonesia)
Prof.Dr. ShoichiKai(KyushuUniversity-Japan)
Prof.Dr. MuhamadMatSalleh(Universiti
Kebangsaan
Malaysia)
Prof.Suparwoto(UNY-lndonesia)
(UGM-lndonesia)
Prof.Dr. Kusminarto
Dr.KamsulAbraha(UGM-lndonesia)
(UGM-lndonesia)
Dr.JaziEkolstianyanto
The Technical Program Committee
Chairperson
:
Dr. Sismanto
Secretary:
Dr. MirzaSatriawan
EdiHartantyo,
M.Si
Treasurer:
Dra.Chotimah,
M.S.
llonaUsuman,M.Kom
Programs:
Dr. KuwatTriyana
Dr.YusrilYusuf
Harsojo,M.Sc.
AgusSupriyanto,
M.Si (UNS)
AriDwiNugraheni,
S.Si
AhmadKusumaatmaja,
S.Si
ScientificProgram:
Dr. Karyono
Dr.M.F.Rosyid
Dr.KamsulAbraha
Dr.AhmadAshari
Publication
:
EkoSulistyo,
M.Si
Mitrayana,
M.Si
Documentation
andAcomodation
:
Dr.AriSetiawan
R. Sumiharto,
M.Kom
M. lkhsan.
M.Si
Exhibition:
FachrudinNugroho,M.Si
2* JoglaInternational
PhysicsConference
'Enhancing
Networkand CollaborationDevelopingResearchandEducationin Physicsand NuclearEnergy"
September6-9, 2007,Yogyakarta-lndonesia
Foreword
On behalfof the organizerof the 2nd Jogjalnternational
PhysicsConference,
I would
liketo give our sinceregratitudeto all the participant
of the conference.I wouldlike to give
our_deepest
appreciation
and gratitudeto all of keynotespeakersof this conference,
nariely
lr. sukarmanAminjoyo,APU (BAPETEN),Dr. Baek Jong-Bok(KoreaHidro and Nuctear
fower co. Ltd.),Prof. Ren-Taichiang (Univ.of Ftoridaand GE EnergyUSA), prof. Dr.
MuhammadMat Salleh(U_nivKebangsaanMalaysia),Prof.Yoshitsugo
Tomokiyo(Kyushu
Univ.Japan),Dr. HariniSosiati(KyushuUniv. Japan),Dr. YoshikiHiOatalXyushu'Univ.
Japan),Dr.YusrilYusuf(GadjahMadaUniv.).
The second Jogja InternationalPhysics Conferenceis the second conference
org.anized
by the PhyslcsDepartmentGadjahMada Universitycontinuing,previouslywas
called,the 1st Jogja RegionalPhysicsConfOrence
20O4.This conferenc6is aim6d for
promoting,
developing,
and disseminating
interdisciplinary
researchftom manydifferentfields
of physics,for the bettermentof humanlives.The conferencewas intendedas a forumfor the
physicistfrom differenlbranchesof physics,and differentcountries,especiallyftom the Asian
and sunoundingregion,to meetand discuss,developingresearchand collaboration.lt is also
intendedas a forumfor disseminationof the latestresearchresultsfrom manydifferentfields
of physics.As Indonesiais cunentlyplanningdevelopingits first powerplanthucbar reactor,
we also hopeto enhanceunderstanding
of the cunent resultin the nuclearreactortheoryand
technology.The theme of the conference is Enhancing Network and Cottabomion Develqing Researchand Educationin Physicsand Nuclear Eneryy. The topics covered in
this conferenceare from very broad spectrumof Physics,such as NuclearEnergy,Atomic
Physics,Theoreticaland MathernaticalPhysics,ComputationalPhysics, Nanote6hnology,
MatedalScience,Geophysics,ElectronicsInstrumentation,Bio and-Medical physics, a'nd
Educational
Physics.
In this conferencethereare 8 papersin the panelsession,presentedby eigth invited
speakerin two days. For the parallelsessionthere are 63 papersto be presentedin the
conference.The presentedpapersconsistof NuclearEnergyand Atomic Physics8 papers,
Theoretical and Mathematical Physics 8 papers computational physics 9 babers,
Nanotechnology
5 papers,MaterialScience6 papers,Geophysics10 paperi, Electronicsand
Instrumentation
17 papers.
The committeeshave worked in ananging the program for the benefit of the
paticipants.The committeehopes that this conferencecould enrich, enhancethe physics
knowlegde,and servedas a forum for individualsto meet and discussthe physics'cunent
from PhysicsD-epartment
of
Psu9s.We sincerelyappreciatethe supportand encouragement
Gadja Mada University, BAPETEN, Atomic and Nuclear laboiatory, Electronics
lnstrurnentations
Laboratory,Geophysicslaboratory,Solid state laboratory,basbs physics
Laboralory,GraduateSchool (Pascasarjana)in Universityof Gadjah Mada, and OS StuOy
frogram. Last but not least I would also give my thanksto the studentvolunteersin physics
Departement.
With sinceregratitude
Chairmanof the 2noJlpC 2007
Dr.Sismanto
znoJoglaIntemationalPhysicsConference
"Enhancins
Network
andcoilaboration
Deveropins
Research
andEducatbrr:X::{;+"i#r:#E1i?;##
Foreword
guests
Distinguished
Honoraryspeakers
Ladiesandgentlemen
Welcometo the 2roJogjaInternational
PhysicsConference.
We gatherheretodayto communicateour scientificactivities,to learnfrom eachother,to find
an opportuni$to collaboratewith each other,and to shareour experience.
The world-wideweb has becomeour closestfriend.No day passeswithoutus accessingthe
Internet. lt was Tim Berners-Lee,a physicist,who initiated the lnternet lifestyle.\Men
Berners-Leedreamed about creating a tool to enable reseachersall over the world to
collaborate,
onlyonewordwasin his mid:shareit, shareit, shareit.
We do not lose anythingwhenwe share.In fact,we enrichour knowledge.
Now,we shareour experiencesto improveour knowledge,to
Physicistshave been knownto initiatenew things.And it will stay that way. Physicistsshould
cultivate freedom. Freedom to think, freedom to try lots of things, freedom to explore
opportunities
fiom philosophy
to engineering.
It was a physicistwho initiate the industrialrevolution.lt was a physicistwho initiatethe
informationrevolution.
We hopeyou havea pleasantstay in Jogjakarta.
FYl, the physicsdepartmentat gadjahmada universitywas foundedin 1955.Now,we have
three B.Sc programs : physics, geophyics,and electronics& instrumentation,a 3-year
diplomaprogramin Electronics
& Instrumentation,
an M.Scand a Ph.Din Physics.
\Mth sinceregratitude
Headof PhysicsDepartment
F)e.Ufod"fr
Dr.JaziEkolstiyanto
"Enhancing Nelwork
2ndJogjo lnternotionolPhysicsConference
and Colloborotion DevelopingReseorchond Educotionin Physicsond Nucleor Energy"
September6-9,2@7,Yogyokorto-lndonesio
CONTENTS
ORGANIZING
COMMITTEE
FOREWORDS
CONTENTS
i
ii
iv
PAPERS
Keynofe Speoker
Aulhor(s)
fille
Nucleor Low ond Regulotionin
Indonesio
Poge
I
Dr.SukormonAminjoyo
2
Prot.Ren-ToiChiong,
Ph.D StobilitySolutionfor InherentlySofe
ESBWR
Operofion
KS06
Dr.BoekJong-Bok
NPPStotusond ProspectIn Koreo
KSOI0
Dr.YoshikiHidoko
Stotisficol
Properties
of
Spoiiotemporollntermittencyin
on ElectroconvectiveSystemof
Nemolics
KSOI2
Prof.Dr.Yoshitsugu
Tomokiyo
Chorocterizotionof NonoStructuresin Moteriolsby
Tronsmission
ElectronMicroscopy
KSOI5
5
Dr.HoriniSosioti
Focusedlon Beom Techniques
And Tronsmission
Electron
MicroscopyStudiesOf Advonced
Moteriols
KS02l
7
Dr.YusrilYusuf
LiquidCrysiolElostomers;SwellingKS026
Dynomics,Electromechonicolond
ElectroopticolEffects
B
Prof.Dr.MuhomcrdMot
Soileh
Fobricotionof Orgonic Light
EmitfingDiodes(OLEDs)
for Flot
PonelDisploys
Porticiponls
NUCTEARENERGYAND ATOMIC PHYSICS
KSOI
KS030
"Enhoncing Nefwork
2.d Jogjo Internolionol PhysicsConference
ond Colloboration Developing Reseorch ond Educotion in PhysicsondN vcleor Energy',
September 6-9,2007.Yogyokorto-lndonesio
I
DoniSoputro
ColculotionOf TotolReoction
CrossSections ForProtonOn l2C,
40Co,9Olr,2OB?b
NucleiAt High
EnergiesTheoreticolly
NEOI
2
Mitroyono,T.Pierero,
B.W.M.Moeskops,S.
Persijn,
H. Nous,F.J.M.
Honen,M.A.J.Wosono,
Muslim,ond W. Rochmoh
Diode-LoserBosedphoto-ocouslic
Spectroscopyin Aimospheric NOz
Detection
NEo4
3
D- Lelonoond M.A.J.
Wosono
Automotizotionof photoocoustic
Spectroscopyfor Anolysisof
MulticomponentGos
NEog
4
TeddyArdionsyoh,SuwondhoArie Proyudho
ond Andong WidiHorto
cellonolysisof spent pwR Fuelsin
FostReoctor
NEl3
5
u. Khoirunnisyoh
ond
D.Soputro
DeterminotionRestitution
Coefficient of BronchingFroction
NEIZ
of DoMeson-+K-n'decav
6
s.T.Persijn,
A.K.Y.
Ngoi,ond speclroscopic
Applicotions
of o
F.J.M.Honen
BroodlyTunoble,ContinuousWoveOpiicolPorometric
Oscillotor
7
Povl.Stothers,Kevin
Thoorghoodond
YohonnesSordjono
plont RemoiningLifeTime
Assessment
for power Generolion
NE2l
NE25
THEORETICAT
AND MATHEMATICAT
PHYSICS
No
Aulhor(s)
9' M. ForchoniRosyid
Iille
Poge
on Thestructureof euontizoote
tHor
TH06
AlgebrosOf The productsOf
SymplecticMonifoldsWith
Polorizotions
l0
Moh. Adhib.u.Aond
KomsulAbroho
Anotyticotstudyof singte-etectron
euontum Wires
II
limothy Siohoonond
Mizo sotriowon
InequivolenlQuontizotionsof A Triviol THol0
Linkof on unknottedcirclesin sr X sz
{,.
. '
'i 12
AsonDomonik,Miao
l, ,,, Soiriowon.promudito
Anggroito,Arief
MinimolLeft-Righf
symmetryModel
for ElectroweoiInteroction
THol5
"Enhoncing Network
2ndJogjo InlernotionolPhysics
Conference
ond Colloborolion Developing Reseorchond Educotbn in Physicsand Nucleor Energy"
September 6-9,2@7, Yogyokorto-lndonesio
Hermonto
l3
BombongHerulswonto
Leorningof MixlureModelsbosed
Clossifiers
usingLobeled ond
UnlobeledDoto
l4
UmiKhoirunnisyoh
Determinotionof Coherent
TH02S
ScotteringAmplitude of ArsenicUsing
SmollAngel NeutronScottering
Theoreticolly
l5
AriefHermonto
A SimpleMethod to Determinethe
Generol-RelotivisticDoppler Shift
with ArbitroryMofionsof Sourceond
Observerin o CosmologicolModel
TH02B
l6
AliYunuR
s ohedi
CreotingA New Plonck'sFormuloof
SpectrolDensityof Block-body
Rodiotionby Meonsof AF(A)
TH030
TH0l9
COMPUTATIONAI.
PHYSICS
No
Author(s)
1 7 FohrudinNugrohoond
PekikNurwontoro
Iitle
Effectsof Angulor Voriotionof
ExternolMogneticFieldto Surfoce
Nucleotionof Rectongulor
SuperconductorMoteriols
Pcge
Cp0l
l8
SimulotionGenerolizedPredictive
Control Modificotion And Controller
PerformonceInfluence
Cp06
ErwoniM.Sortiko
l9 AriefHermonto
UsingComputotionolSystem
of Units CpOlI
to DeriveNoturolond Geomeiricol
Systemof Units
20 Mutio Delinoond
Mohomod lchson
Woter Rocket FunProgromfor
EnhoncingJuniorHighSchool
cP0l3
Supervised
LeorningFromework
of
MixtureModelsfor Clossificotion
TheReconstruction
of Multiple
AcousticSources
thot Fulfillthe
Predetermined
SoundLevelono
CertoinTorgetFieldLocotion
Cp0lZ
2l
Bombong Herulswonto
22 DonielSetiodikorunio
StudentIntereston Studyingphysics
Cp023
"Enhancing Nefwork
2"dJogjo InternotionolPhysicsConference
ond Colloborotion Developing Reseorchond Educotion in Physicsond Nucleor Energy"
Seplember 69, 2007.Yogyokorlo-lndonesio
23 ViskoIndoV
Developmentof TheObject
Thickness
Meosurement
Softwore
CP030
24 PekikNurwontoro
RobustComputotion
of the Gount
Coefficients
CP034
NANOTECHNOTOGY
No
Autho(s)
25 A. Bohtior
26 ldo Sriyonti,Leni
Morlino,Mikrojuddin
Abdulloh,ond
Khoirunijol
27 W.B.Nurdinond K.D.
Schotte
28 Aripin
f$le
Longmuir-Blodgett-Kuhn
Muttiloyer
Filmsof AzobenzeneContoining
PolyomicAcid for LiquidCrystol
Opticol Switching
Poge
NT0l
ElectricolConductivity of Nd-CeOz
NonoporticlesPrepored by Simple
PolymerHeoiingMethod
NT07
Applicotionof Microcononicol
Temperotureto TheSpinCrossover
of Fe-CoCompounds
NTOII
Chorocterizotionond Electricol
Conductivity Behoviourof
PolypynoleConducting Polymer
NT0l6
29 Ahmod Kusumootmojo, structure Dependence of Electricol
Ari Dwi Nugroheni,
Chqrocteristicof Orgonic ThinFilms
Sudormiotiond Kuwot
Bosedon PeryleneDerivotives
Triyorlo
NT020
MATERIAT
SCIENCES
No
Aulhor(s)
30 ArisDoyonond
Susilowoti
3l
susilowotiondAris
Doyon
Ilfle
Poge
ConductivityProperties
of polymer
GelDosimeters
lnodiotedwith
Gommo-Roys
MSOI
opticolProperiiesof polymerFilms
Contoining
Chlorinelnodiotedwith
GommoRoys
Ms06
"Enhoncing Nefwork
2ndJogio InlernotionolPhysicsConference
ond Colloborqtion Developing Reseorchand Educolion rn Physicsond Nucleor Energy"
Seplember 6-9, 2007.Yogyokorto-lndonesio
32 Moh. Yosin,S.W.Horun,
Kusminorto,
Koryono,H.
Ahmod
Constructionof Opticol Fiber
DisplocementSensorUsingon ACModuloted LightSource
MS0lI
33 Supriyono
TheInfluenceof ( Voluein
ShokedownPhenomenofrom
Elostic- PlosticProblems
MSOI4
34 Horsojo
CriticolCunentDensityon Two
Dimensionol
Superconductor
HovingColumnorDefecl
MSOIZ
35 Bombong Murdoko Eko
Joti,lrwonto,Lukmon
Hokim
TheChorocterisotionof Some Liquid
ond SolidStoteMedium to the
Attenuotion
lntensity
levelof Sound MS02l
GEOPHYSICS
No
Author(s)
36 BudiEkoNurcohyoond
Sudormodji
Iille
3D complex seismic Attribut Bosed
on ContinousWovelet Tronsform
37 Sudormoji
SeismicRoyTrocingIn Heterogenous GpO4
Medio Using LineorTroveltime
lnlerpolotion(LTt)Method
38 Edi Hortontyo
A Verificotionof plone Wove
lmplementotionon FiniteVolume
PoissonSolidMedium
GPOIO
39 Novi Rohmowoti,Tjohyo
NugrohoAdji,ond
LonggengWohyu
Sontoso
GroundwoterQuolitychonges Due
io EorthquokeWithinport of Bontul
Regency
Gp0l4
40 Sismonto,Eddy
Hortontyo,ond Agus
Woluyo
Resisfivity
ond RefroctionSeismic
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Minimal Left-Right symmetry Modet for ElectroweakInteraction
AsanDananit/''", Mina satriawan2, pramudita Anggraitf, Arief Hermanto2
'Department
of Plrysics,SanataDharma University,
III
USDpaingan, Maguwoharjo,Sleman,yognkarta, Indonesia
$mpus
zDepartmentof physics,
racitty of lviathematicsan{Natural sciences.
'r,,,",ff
fi:!,I:f,y#';;:y;;i{u#;';'rWff
:';*^",,"
Abstratt
Foll_owing the procedure in the Glashow-lYeinberg-Salan(GWS) model
for electroweak
interaction,by using two doubletsand one inducedbidoubletHiggs
fietds as a result oftie interactionsof
the two doublets,we evaluatethe predictive power of the lrftlri7it symnetry nodel basedon S(J(2)1x
SU(2)px U(l) gaugegroup to thegauge bosonsmasses,leptons masses,
and the structure of eharowiak
interaclions-.Byh b.iloublet and doubletHiggsfields haie the contribution to the gauge ioro^
^ r",
a|ter WmeW breaking.Meanwhile,leptonsmassesarise only
from the bidoubletitgtli fuU. Tlw parity
uiolatioytcoild be associatedwith the mixing of the chargei gauge bosow n^sii yron tne
iiaucia
bidoubletHiggs.
Keywofds: Ieft-right symmetrymodel,electroweakinteraction,doubletand bidoubtet.
*Conesponding
author
E-mai I : [email protected]
I. Introductbn
Even though the Glashow-WeinbergSalam(GWS) modelfor electroweakinteraction
based on SU(2[ xU(l\ gauge group very
successfulphenomenologically
[l-3], but many
fundamgntal problems i.e. fie responsible
mechanismfbr generatingthe neutrino masses,
the dolninafion of the V-A over V+A
interactipm 4t low energy, and the responsible
mechanismfor the doubletleptonup.down mass
differenCecould not be explained by GWS
model. The needfor the extensionof the GWS
modelcomesfrom the conclusionthat neutrinos
have a mass as an implication of the detected
neutrinooscillationsphenomenafor both solar
andatmOsphetic
neutrinos[4-10].
ManNtheoriesor models for extension
of the GIWSrnodelhavebeenproposed.Oneof
the intpresipg models is the Left-Right
symmetrymodel basedon SU(2)r x SU(2)xx
U(l) gasge group proposedby many authors
Irl this paper,we use the left-right
[l-15].
symmetrymodel basedon SU(2)r x SU(2)ax
U(l) galhgegroup with two doubletsand one
bidoubletHiggs fields (as a result of the two
doublets interaction) to break the SU(2[ x
SU(2)px U(l) gaugegroupdownto U(l)",. The
leptonfiglds to be represented
as doubletof an
SU(2) for both left and righr fields to makethe
full senseofthe left-rightsymmetrymodel.
THOI5
The paper is organizedas follows: in section II
we presentour main assumptionsfor the leftright symmetrymodel, in sectionIII we evaluate
the gauge bosons masses, in section IV we
evaluate the leptons masses,and finally in
sectionV we give a conclusion
II. The Model
In our model, the left-right symmetry
model for electroweakinteraction basedon the
SU(2)1x SU(2)Rx U(l) gaugegroup wirh the
assumptionsand the particles assignment as
follows:
l. Two primaryHiggsfieldsaredoubletof
su(2):
", =l.;.J'
r-=l;') (r)
u
-(or)
/.-\
2. The secondarybidoubletHiggs field {
could be producedfrom the interaction
of thetwo primaryHiggsfields,that is:
a:a,)=(n' c,l
a=(t.n
'
(2)
V ' = l - 1 , \ r n = l_ l
(3)
l.boc- bodo) (r- ,o )
3. The leptonsfieldsarr doubletof SU(2)
for both left andright fields:
(v )
/v \
\e )t
\e )r
4. Both leptonsand gaugebosonsmasses
are generatedvia symmetry breaking
2noJoga InternationalPhysicsConference
"EnhdncingNetworkond colloborotion
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September5-9, 2007,Yogyakarta-tndonesia
when Higgs fields develop its vacuum
expectation values similar to the
symmetrybreakingin the GWSmodel.
By applyingthe aboveassumptions
and
particlesassignment,we could break the leftright symmetrymodelbasedon SU(2)px SU(2h
x U(l) down to U(l),* directly as shown
schematically
below:
where {,
md 4, arethe third components
the
weakisospingenerator:T, =T,12,
Accordingto the Eqs. (a) and (5), the
Higgs fields have the following quantum
numbers:
x r(1,0,t\x
^(0,;,r)p(;,;,0) (q)
andthe leptonsfields fansform as:
SU(2[ x SU(2)axU(l)
1 " 1 .Iob ) * o
(-r^)* 0
III. The GaugeBosonsMasses
From Eq. (4), we can see that the
relevantgaugebosonmasstgrmsas follow:
{
u(l)*
The vacuum exp€ctationvalues of two
doublets and one bidoublet Higgs could
contribute to the gauge bosons masses.
Meanwhile, the leptons masses(in Yukawa
term) only emergefrom the vacuumexpectation
value of bidoublet Higgs, becausethe leptons
fields tp, and wr to be doubletof SU(2),then
only the Yukawa term with bidoublet Higgs
salisfiesgaugeinvariancc. Thus, the complete
Lagrangiandensitycould be reads:
r^*=l(trtr*-.4ttrE,l'
*l(-+r.w*-irt,V^l'(8)
+rl!+tw*-+YB,M'
+r,l(?ww-+yB,M'
By substitutingthe vacuumexpectation
valuesofthe Higgsfields:
/o\,. (o o\
fo),
(o)=|.;,)
r,,)=laJ'
r+)=[a]
into Eq. (8), we obtain:
pi
7 = -! WonV - +Y!*IF tn -+ Bt, Bp'
u* =+lr'tWil * @,11
]*o'(sw)- s'a,f
- s,Bul
* r,a,(ni^l* @,;ll*a,Gwfi
+Vry,8ou- t c.y,n- t ruob,
- t rurb^
+V*yutoo- t c.w,o
*s'b'.*W;"1
.ftr;"|
-@;"ll
*s'(p'- ttrlr;"|
. @kl. @;lt
(4)
(9)
By defining:
+r,]ftar-trw*-+tt,M'
*rlfta,-tr.wu,-+vB,M'
-V(X
(7)
v,Q,o,ol rg^(o,z,o)
I
+l!a,-irww-+tn,V)'
*l$a,-*tw* -ttu,V.l'
(5)
Q=7,,+7,^+!
w; =hQrL+twi\w; =#(wk+iwrt\
-
-pL
cwi-g'BuL r-;-----';
,lc' + c' '
L,X R,d.7-(Cgrpty^+nc)
,"un
sw:n-g'Bun
f--:-----=
,ls' +s' '
" _g' I{ i+gB*, nttR
" _g' W fi+gB*
'
where g, = gn= g are the SU(2) couplinggg'
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
Yukawacoupling.
The elsctric chargeoparator Q satisfiesthe
relations:
,lg"+s"
^IV.F
Z',n=W1,,,,Z',,^=lYk,
m v , =sb
| , * r , = 7sd
, frt=0,
*r" =tbGl*s" ,mz.=+dG' 4" ,
frr" = *'r^ = ilr,, = frr,* =iSr[p'
*f
,
(10)
THOI6
2ndJogiaInternationalPhysicsConference
"EnhancingNetwo* and CalldborotionDeveloplngResearchond Educatlonln Physlcs NuclearEnergy'
ond
September6-9,2007,Yogyakarta-lndonesia
thenEq.(9)rcads:
* m$rw
Lbo,;w ; + mfl^w
|w;
+m|,w;w; +m'j^w;w;
+m|,2*z! +ml"z*zl
interaction)to the electroweakinteractionis only
around0.0157u In this scheme,the domination
of the V-A interactionover 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
gaugebosonsfir?sscS2". in the maximalparity
(ll)
+ m)ArAP+ m),^z'^z'(
violation, only come from the doublet Higgs
freld X, as formulated in the GWS model and
supportedby experimental fact that the boson
massesemergeftom doubletHiggs field.
+ m'",,2'*z'!
or
Lo*=fu|,"
* *;;,yry;w;
I
t
r r \
+@h^+ m;^lY;W;
+ m),zr,z! + m'r^z*zN
lV. The Leptonsmrsses
The leptonsm?rsses
in our model arise
from tho symmetry breaking. The lepton mass
termis the Yukawatermin Eq. (4), that is:
(14)
L,=GV,(|W*
Q2)
+ mlApAt+ m'r,^z'*z';
+ m'r,rz'*Z';
By inserting the vacuum expectationvalue of
bidoublet Higgs, then we obtain the masses:
mu= Gp *l fie - Gs for neutrinoand electron
respectively. In our minimal left-right symmetry
model basedon SU(2[ x SU(2h x U(l) gauge
group the leptonsmasses(neutrino and electron)
arise only from the bidoublet Higgs vacuum
expectationvalues.
As long as we know, for leptonsmass€s
there is no experimental fact that force us to
choose a one kind of multiplet Higgs in the
Yukawaterm exceptdictatedby the requirement
of the Lagrangian density must be gauge
invariance. But, in the boson mass sector, the
representationof the Higgs fields to be SU(2)
doublet theoretically supportedby experimental
fact. Thus, we could use the inducedbidoublet
Higgs field asthe responsiblefield for generating
the leptonsmasses.
From Eq. (10), by following the
standard rnrodel of electroweak interaction
symmetry breaking procedure to the left-right
symmetrymodel and put the value of b : d, we
canseethat the resultedgaugebosonsmassesfor
both left and right bosonsare equal. To make
the left-right symmetry model relevant to the
electroweak phenomen4 many authors
fl4,15,161have takenthe value of b