Gauge bosons in a five-dimensional theory with localized gra

We consider the possibility of gauge bosons living in the recently proposed five-dimensional theory with localized gravity. We study the mass spectrum of the Kaluza-Klein (KK) excitations of the gauge fields and calculate their couplings to the boundaries

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aCERN-TH/99-341Gaugebosonsina ve-dimensionaltheorywithlocalizedgravityAlexPomarol TheoryDivision,CERNCH-1211Geneva23,SwitzerlandAbstractWeconsiderthepossibilityofgaugebosonslivingintherecentlyproposed ve-dimensionaltheorywithlocalizedgravity.WestudythemassspectrumoftheKaluza-Klein(KK)excitationsofthegauge eldsandcalculatetheircouplingstotheboundariesofthe fthdimension.We ndadi erentbehaviourfromthecaseofthegraviton.Inparticular,we ndthatthemasslessmodeisnotlocalized

intheextradimensionandthattheKKexcitationshavesizeablecouplingsto

thetwoboundaries.Wealsodiscusspossiblephenomenologicalimplicationsfor

thecaseofthestandardmodelgaugebosons.

CERN-TH/99-341

November1999

We consider the possibility of gauge bosons living in the recently proposed five-dimensional theory with localized gravity. We study the mass spectrum of the Kaluza-Klein (KK) excitations of the gauge fields and calculate their couplings to the boundaries

I.INTRODUCTION

Ithasbeenrecentlyrealizedthatextradimensionscanplayacrucialroleinthehierarchyproblem.A rstexamplewasgiveninRef.[1]wheretheweaknessofthegravitationalinterac-tionversusthegaugeinteractionswasobtainedbyallowingthegravitontopropagateinsomeextra(andverylarge)dimensions.

AnalternativescenariohasbeenconsideredinRefs.[2,3].Theyassumedanextradimensioncompacti edonasegmentS1/Z2withtwo4Dboundaries.Byadjustingthecosmologicalconstantoftheboundarieswiththeoneinthebulk,theyfoundasolutiontothe5Dmetricoftheform

ds2=e 2kRφηµνdxµdxν R2dφ2,(1)

whereµ=1,..,4,andRistheradiusofthecompact fth-dimensionparametrizedbyφwith0≤φ≤π.kisaparameterrelatedtothecosmologicalconstant[2].Themetric(1)correspondstoasliceofAdS5betweenthetwoboundarieslocatedatφ=0andφ=π.Afterreducingto

234D,one ndsthatthee ective4DPlanckscaleisgivenbyMP=M5(1 e 2kRπ)/kwhereM5is

the5DPlanckmass,thefundamentalscaleinthetheory.Massesonthe4Dboundaryatφ=π,however,appeartobereducedbytheexponentialfactore kRπoftheinducedmetricontheboundary.Therefore,forkR 12andk～M5,onecangeneratetwoscalesforthe eldslivingontheboundaryatφ=π:thePlanckscaleMP M5andtheelectroweakscaleMPe kRπ～TeV.Fieldslivinginthe5Dmetric(1)haveaverypeculiarKaluza-Klein(KK)decomposition.ThemassesoftheKKareexponentiallysuppressedMPe kRπ～TeVandthereforeareverylighteventhoughtheradiusofcompacti cationis(approximately)ofPlanckiansize.TheseKKmodeshaveextensivelybeenstudiedforthecaseofthegraviton[2,4]andascalar eld[5].

InthisletterwewanttoconsiderthecaseofagaugebosonpropagatingintheAdS5slicedescribedabove.WewillstudytheKKdecompositionofthegaugeboson eldandanalyze

We consider the possibility of gauge bosons living in the recently proposed five-dimensional theory with localized gravity. We study the mass spectrum of the Kaluza-Klein (KK) excitations of the gauge fields and calculate their couplings to the boundaries

itsphenomenologicalimplications.Wewillshowthat,unlikethegravitonorthescalar,thezeromodeofthegaugebosonisnotlocalizedinthe5Dtheory.Similartothecaseofa atextradimension,thismasslessgaugebosonspreadsovertheextradimension.AlsotheircorrespondingKKexcitationsbehavedi erentlyfromthoseofthegravitonorscalar.AlthoughtheKKmassesarealsoexponentiallysuppressed,theircouplingstothe eldsontheboundaryatφ=0arenotsuppressed.Theycanthereforeleadtosizeablee ects.Ontheboundary

√atφ=π,wewillshowthatthecouplingoftheKKexcitationsdependslinearlyon

√ggMNRSgFNS M2gRSAS=0, (2)

whereg=Det(gMN),FMNisthegauge- eldstrengthandwedenotewithcapitalLatinlettersthe5DcoordinateM=(µ,φ).Forthemetricofeq.(1),eq.(2)leadsto

ηρν ρ ν+1

√

R e2φ 2kRφ φ+e 2kRφM2 fn=m2nfn.(5)

We consider the possibility of gauge bosons living in the recently proposed five-dimensional theory with localized gravity. We study the mass spectrum of the Kaluza-Klein (KK) excitations of the gauge fields and calculate their couplings to the boundaries

n)ThemncorrespondtothemassesoftheKKexcitationsA(µ.Thesemassesandthecorrespond-

ingeigenfunctionsfncanbefoundsolvingeq(5)withtheboundaryconditionimposedbytheorbifoldS1/Z2(thisrequiresfn(φ)=fn( φ),andthatfnanditsderivativearecontinuousatφ=0andφ=π.).We nd

fn=ekRφ

kekRφ)+bα(mn)Yα(mn

1+M2/k2andbα(mn)are

coe cientsthatful l

Jα(mn

bα(mn)= Yα(mnk

k′mnJα(′(mnYα

2kR2Jα(mn

πRmn.(10)

Fromthecondition(8),onecanobtaintheeigenmassesmn.Letusconsiderseparatelythecaseofa5Dmasslessvectorboson(M=0)andamassiveone(M=0).

A.Massless5Dgaugeboson(M=0case)

InthiscasethelowestmodeisamasslessstateA(0)µwith

We consider the possibility of gauge bosons living in the recently proposed five-dimensional theory with localized gravity. We study the mass spectrum of the Kaluza-Klein (KK) excitations of the gauge fields and calculate their couplings to the boundaries

f0=1.π(11)

Thisisaconstantmode.Therefore,unlikethegravitoncase,itisnotlocalizedinthe fth

√dimension.Itcoupleswithequalstrengthtothetwoboundariesg=g5/

k

k).)(12)

Formn k,wehave

b1(mn) π/2

k

Thesolutionareforn=1,2,...ekRπ) 0.(14)

mn (nπ 0.7)ke kRπ.(15)

WeseethenthatthemassesoftheKKmodesareexponentiallysuppressedandthusmn～TeV(forthecasekR～12thatweareconsidering).Toknowhowtheycoupletotheboundaries,wemustlookattheireigenfunctionsfnnearthe …… 此处隐藏：8683字，全部文档内容请下载后查看。喜欢就下载吧 ……