Decay of Charged Higgs boson in a scenario of SUSY breaking inspired neutrino mass

DecayofChargedHiggsbosoninascenarioofSUSY

breakinginspiredneutrinomass

Gi-CholChoa),SatoruKanekoa)∗andAyaOmoteb)

a)

DepartmentofPhysics,OchanomizuUniversity,Tokyo112-8610,Japan

b)

GraduateSchoolofHumanitiesandSciences,OchanomizuUniversity,Tokyo,

112-8610,Japan

Abstract

Insomeclassofsupersymmetricmodels,smallneutrinomassisgivenasaconsequenceofthesupersymmetry(SUSY)breaking.Phenomenologicallyinterestingfeaturesofthisscenarioareasfollows:(i)theright-handedsneutrinomasscouldbeaslowasTeVscaleduetotheGiudice-Masieromechanism,and(ii)ascalartrilinearinteractionofHiggs-slepton-(right-handed)sneu-trinocouldbesizablewithoutsuppressionbythesmallneutrinoYukawacoupling.Westudysomephenomenologicalaspectsofthisscenariofocusingonthescalartrilinearinteraction.Weshowthatthe1-loopcorrectionbysneutrinoexchangetothelightestHiggsbosonmassdestruc-tivelyinterfereswithtop-stopcontributionsintheminimalSUSYStandardModel.WefindthatadecayofchargedHiggsbosonintosneutrinoandchargedsleptonissizablyenhancedandhenceitgivesrisetoadistinctivesignalatfuturecolliderexperimentsinsomeparameterspace.

1Introduction

SmallnessofneutrinomassisoneoftheimportantcluestophysicsbeyondtheStandardModel(SM).Anattractiveexplanationontheoriginofsmallneutrinomassistheseesawmechanism[1].Intheseesawmechanism,aheavyright-handedneutrinoisintroducedanditcouplestoSU(2)LdoubletneutrinoandHiggsbosonthroughtheYukawacouplingYν.Afterdiagonalizingtheneutrinomassmatrix,asmallermasseigenvalueofneutrino,mν,isgivenby

mν≃(Yνv)2/mN,

(1)

wheremNandvarethemassofright-handedneutrinoandthevacuumexpectationvalue(v.e.v.)oftheHiggsboson,respectively.IftheYukawacouplingYνisoforderunity,beconsistentwithresultsofneutrinoexperiments.Thenonemaycomplainthelargehierarchybetweenthescaleoftheseesawmechanism(mN)andtheelectroweakscale(v).Furthermoreitishopelesstoconfirmtheseesawmechanismthroughsearchingfortheright-handedneutrinoatcolliderexperiments(atrialtotesttheseesawmechanismwithhypotheticaloutcomeoffutureexperimentsisproposedinref.[3]).Thusitmaybeworthconsideringapossibilitytolowerthescaleofseesawmechanism(scaleofright-handedneutrino)aslowastestableatcolliderexperiments,say,O(100GeV−1TeV),oralternativetotheseesawmechanismfromaphenomenologicalpointofview.

Ithasbeenarguedpossibilitiestoexplainthesmallneutrinomassasaconsequenceofsupersymmetry(SUSY)breakinginrefs.[4,5,6].Somephenomenologicallyviablepointsofthisclassofmodelsare(i)light(TeVscale)right-handedsneutrinoduetotheGiudice-Masieromechanism[7]and(ii)enhancementofscalartrilinearinteractionamongtheright-handedsneutrino,left-handedsleptonandHiggsbosons.Both(i)and(ii)canbe,forexample,realizedasfollows.LetusfirstintroduceachiralsuperfieldXwhichisaSMgaugesingletbutchargedunderacertainglobalsymmetry.Thisglobalsymmetrymayallownon-renormalizableoperatorssuchas

XX†

theright-handedneutrinoshouldbeheavyenough,say,mN∼1011GeV/(mν/1eV),to

MP

LHuN,(3)

wheredimensionlesscouplingswithO(1)magnitudearesuppressed.In(2)and(3),LandNdenotetheleft-handedleptonandright-handedneutrinosuperfields,respectively.

2

TheHiggssuperfieldwiththehyperchargeY=1/2isrepresentedbyHu,andMPisthereducedPlanckmass.SupposethattheF-componentoftheXfielddevelopsav.e.v.󰀏F󰀐∼m3/2MPduetotheSUSYbreaking,wherem3/2isthegravitinomass.ThentheD-componentof(2)leadstotheright-handedsneutrinomassas

󰀁

XX†

MP

LHuN

󰀌

F

→AνℓH

Notethatbothm󰀉ν󰀉uRandAνareoforderthegravitinoν󰀉R.(5)

mass∼O(TeV).Moreoverthescalartrilinearinteractionisnotsuppressedifadimensionlesscouplingin(3)isoforder

unity.

IntheminialSUSYSM(MSSM),theSUSYbreakingscalartrilinearinteractionsofsquarkorsleptonsareparametrizedbyAfYf,whereAfandYfarethescalartrilinearcouplingandtheYukawacouplingforflavorf,respectively.Thescalarthree-pointverticesare,therefore,suppressedbysmallYukawacouplingsforthefirsttwogenerationsofsquarksandsleptons.Inthemodelsofrefs.[4,5,6],however,thescalartrilinearinteractionoftheright-handedsneutrinoisnotsuppressedbytheneutrinoYukawacoupling,asmentionedabove.

Afewcommentsonthisclassofmodelsareinorder.Inaseriesofnon-renormalizable

operators((2),(3),etc),therearelepton-numberviolatingoperatorsingeneral.Ifsuchoperatorsareforbiddenbyanappropriatediscretesymmetry,theseesawmechanismdoesnotworkandtheDiracneutrinomassshouldbegivenby(3)withtheA-componentv.e.v.󰀏A󰀐oftheX-field.Then,tosatisfytheexperimentallimit,arelation󰀏A󰀐≪

󰀈

ofchargedHiggsboson[4].OwingtoAν,thedecayofchargedHiggsbosonintothesneutrinoandselectroncouldbeenhancedascomparedtotheMSSM.Wefindthat,insomeparameterspace,thebranchingratioofthisdecaymodecanbeaslargeas10%,anditmaybedetectableatfuturelinearcolliderexperiments.Inourstudy,weneglectthegenerationmixinginboththeleft-andright-handedsneutrinosforsimplicity.Al-thoughthisscenariohasapossibilityiftheneutrinoisMajoranaorDirac,ourstudyisavailableinbothcasesiftheSUSYbreakingB-termofsneutrinointheMajoranacaseisassumedtobesmallenoughsothat,inadditiontosuppressthe1-loopcorrectiontothemassoflighterneutrino,thesneutrinomassmatrixhascommonstructureinbothcases.

2MassandInteractions

Wefirstreviewthesneutrinomassesandinteractionstofixournotation.WhentheSUSYbreakingB-termofsneutrinoisneglected,themassmatrixofsneutrinosina

󰀉L,ν󰀉R)isgivenbybasisof(ν

2

Mν˜=2m󰀉ν

󰀁

L

=m2L+

2m󰀉AνvsinβνL

2Aνvsinβm󰀉ν

R

󰀃

,(6)

1

anunitarymatrixU󰀉ν:

󰀂

2+v2≈246GeV.Themassmatrix(6)canbediagonalizedusingvud

2(7)satisfiesthefollowingIntheMSSM,thesneutrinomassisgivenby(7).Notethatm󰀉ν

L

2

Uν=diag(m󰀉U󰀉ν1,m󰀉ν2),νM󰀉ν󰀉

󰀄†

(m󰀉ν1(8)

󰀉LduetotheSU(2)Lsymmetry:relationwiththemassofleft-handedselectrone

222m2e˜L−mν˜L=(−1+sW)mZcos2β.

(9)

Sincecos2β<1fortanβ>1,themassofsneutrinointheMSSMisalwayssmallerthantheselectronmasswhentanβ>1.Ontheotherhand,thelightersneutrinomass(8)isindependentoftheselectronmassandcanbemuchlighterthanthesneutrinointheMSSM.

4

350(a)150300250(b)m~= 180[GeV]eL m~ [GeV]ν1Aν [GeV]m~= 180 [GeV]eL 200m~= 150[GeV]eL 100m~= 150 [GeV]eL 150100m~= 120[GeV]eL m~= 120 [GeV]eL 50050050Aν [GeV]10001234652m~/m2νR~νL78910Figure1:(a):Thelightersneutrinomassm󰀉ν1asafunctionofAνfortanβ=3.Three

linescorrespondtom󰀉eL=120GeV(solid),150GeV(dashed)and180GeV(dotted).The

2=m2.(b):ThecouplingAasafunctionofaratioresultsareobtainedbytakingm󰀉ννL󰀉νR

2/m2fortanβ=3.m󰀉ν󰀉ν

R

L

3.Threelinescorrespondtom󰀉eL=120GeV(solid),150GeV(dashed)and180GeV

(dotted).Fortheright-handedsneutrinomass,wetakem󰀉νR=m󰀉νLforconvenience.sneutrinomuchlighterthanthatintheMSSM.

InFig.1(a),weshowthelightersneutrinomassm󰀉ν1asafunctionofAνfortanβ=

Notethatthemassm󰀉ν1atAν=0correspondstothatintheMSSM.Thefiguretells

R

L

usthatthelargeleft-rightmixingofsneutrinowhichisinducedbylargeAν,makesa

2/m2.ThreelinesFig.1(b)showsthetrilinearcouplingAνasafunctionofm󰀉ν󰀉ν

correspondtodifferentvaluesoftheselectronmassasFig.1(a).Thelightersneutrinomassm󰀉ν1isfixedat80GeV.ItcanbeseenfromthefigurethatthecouplingAνincreasesbosons.ForsimplicitywetakealimitoflargepseudoscalarmassmA.Thenthelight-estHiggsbosonhcanbeapproximatelyidentifiedwiththeSMHiggs.Theinteraction

󰀉−H−)arethengivenasfollows:󰀉i−ℓslepton-chargedHiggsboson(ν󰀉i−ν󰀉j−hinteraction:•ν

󰀉i−ν󰀉j−h)andsneutrino-Lagrangiansofsneutrino-sneutrino-lightestHiggsboson(ν

2/m2islargerthanone.whenm󰀉ν󰀉ν

R

L

NextwesummarizetheinteractionLagrangianofsneutrino,sleptonandHiggs

L=Aν

󰀆

i,j

∗∗

󰀉jh+h.c.󰀉i(U󰀉νν)1i(U󰀉ν)2jν

(i,j=1,2),(10)

5

14010.99135tanβ = 30,m~ = 300GeVeL0.980.97tanβ = 30,m~= 300GeVeL130tanβ = 30,mh [GeV]m~ = 500GeVeLRh0.960.950.94tanβ = 3m~= 300GeVeLtanβ = 30m~= 500GeVeL125tanβ = 3,meL~ = 300GeV120tanβ = 3,0.93115(a)050010001500Aν [GeV]m~ = 500GeVeL0.920.91(b)tanβ = 3m~= 500GeVeL050010001500Aν [GeV]200011020000.9Figure2:(a)ThelightestHiggsbosonmassmhasafunctionofAν.Eachlinecorrespondtocombinationsoftanβ=3,30andm󰀉eL=300,500GeVasindicated.The1-loopcorrectionfromthetop-stoploopisevaluatedfollowingref.[13]usingthestopmassm󰀉=1TeV.TheHiggsmassmhatAν=0correspondstotheMSSMprediction.(b)t

TheratioRhdefinedineq.(17)asafunctionofAν.

󰀉−H−interaction:󰀉i−ℓ•ν

νiℓH∗󰀉+

󰀉iL=g󰀉νℓH+h.c.,

󰀂󰀄∗g∗νi󰀉ℓH−

msin2βU󰀉=Aνcosβ(U󰀉)−g󰀉Wν1iν2i

2

−

󰀉

(11)

(i=1,2).

(12)

3SneutrinocontributiontothelightestHiggsbosonmass

ItisknownthatthelightestHiggsbosonmassmhreceiveslarge1-loopcorrectionsmainlyfromthetopquarkandthestopexchangingdiagram[9,10,11].InthescenarioofTeV

󰀉RwithsizableAν,theν󰀉L-ν󰀉R-hinteraction(10)couldgiveanewcontributiontoscaleν

thelightestHiggsbosonmassat1-looplevel.Usingtherenormalizationgroupmethodusedinref.[10],weevaluatethesneutrinocontributiontomh.

LetustakethelargelimitoftheSUSYbreakingmassscalemSUSYsothatphysicsbelowmSUSYisdescribedbytheStandardModel.ThenthelightestHiggsbosonmassmhissimplyparametrizedby

2

m2h=λv,

(13)

whereλisaquarticcouplingintheHiggspotential.Notethatthequarticcouplingatthetreelevel,λtree,satisfiestheSUSYrelation

λtree=

1

wheregYandgaretheU(1)YandSU(2)Lgaugecouplings,respectively.TheradiativecorrectionstothequarticcouplingλintheMSSMcanbefoundin,forexample,ref.[10].InthescenariooflargeAν,theinteraction(10)givesrisetothesneutrinoexchangingboxdiagramasthe1-loopcorrectiontothequarticcouplingλ.Thesneutrinocontribution,λ󰀉ν,canbeevaluatedas

λ󰀉ν=−

A4ν

222(m21−m2)(m3−m4)

󰀅

2m21+m3

m1m2

󰀇

+

2m22+m4

m2(16)

−

2m21+m4

m1

−

2m22+m3

.

InFig.2(a),wedepicttheAνdependenceofthelightestHiggsbosonmassmh.Wealsocompare,inFig.2(b),aratiooftheHiggsbosonmassinourscenarioandintheMSSMwhichisdefinedas

Rh≡

mh

16

mSUSY

󰀌4

<0.(18)

Theminussigninr.h.s.of(18)istheoriginthatmhisloweredviathesneutrinocontribution.Fig.2(b)showsthatthenegativecontributiontomhfromthesneutrinodiagramislessthan5%forAν<∼1TeV.

4DecayofchargedHiggsboson

󰀉=e󰀉couldbeadistinctiveprocessofourscenariobecausethatsuchparticular,acaseofℓ

󰀉,whereH−standsforachargedHiggsboson.In󰀉+ℓNextweexamineadecayH−→ν

7

processisstronglysuppressedintheMSSMduetotheelectronYukawacoupling.So,

󰀉=e󰀉inthefollowingstudy.IntheMSSM,itisknownthat,weconsideronlythecaseofℓ−formH−>∼200GeV,Hdominantlydecaysintothetopandbottomquarksowingtothe

sizableYukawacouplings(forareviewofvariousdecaychannelsofthechargedHiggs

regionbecausethatthedecayvertexisproportionaltoAνcosβ(12).Thedecaywidth

bosoninthesupersymmetricmodels,seeref.[12]).Theτ+ντmodeissubdominant

forlargetanβ(>∼10)duetothetau-Yukawacoupling.Ontheotherhand,whenAνis

󰀉1+e󰀉ismuchenhancedinsmalltanβsizable,itisexpectedthatthedecaymodeH−→ν

ofH−→󰀉ν

1+e󰀉isgivenasfollows:Γ(H−→󰀉ν

1+e󰀉)=1

m,

H−

󰀌2󰀋

m󰀉e

󰀉modecouldbeas󰀉+ℓItcanbeseenfromFig.3thatthebranchingratioofH−→ν

largeas10%forsmalltanβ(<∼7).IntheMSSM,thechargedHiggsbosoncandecayinto󰀉Lande󰀉R.Forcomparison,wefixthemassofe󰀉Rasm󰀉νeR=m󰀉eL=200GeV.Thenthe󰀉LduetotheSU(2)Lrelation(9)(notethatm󰀉muchlighterthaneeR=m󰀉eL=200GeV).

󰀉L+e󰀉Riskinematicallyforbiddenbecausethesneutrinoν󰀉LcannotbedecaymodeH−→ν

Therefore,ifthechargedHiggsbosonmassdoesnotdiffersomuchfromthemassesof

󰀉L+e󰀉RintheMSSMisstronglysuppressed.chargedsleptons,thedecayH−→ν

󰀉LdominantlydecaysintothelightestneutralinotheinputsusedinFig.3,theselectrone

󰀉1+e󰀉Linsomedetail.ForourchoiceofNextwestudyasignalofthedecayH−→ν

roughly10%forsmalltanβregion,aprobabilitywhichwefindanelectronfromthiselectronisalsocomingoutfromtheWbosonofthedecayH−→W+h,andthe

󰀉−+χ󰀉0.FromFig.3wefindthatBr(H−→W+h)andtheleptonicdecayoftheWbosonisknownasBr(W→ν+e)<∼10.8%[14].ItleadstoBr(H−→W+h)×Br(W→ν+e)<∼0.3%.IncaseofFig.3(a),therefore,

󰀉−+χ󰀉0,thethebackgroundfromH−→W+hismuchsuppressed.IncaseofH−→χ

󰀉1+e󰀉L)×Br(e󰀉L→e+χ󰀉0decaymodecanbeestimatedasBr(H−→ν1)≃10%.The

󰀉L→χ󰀉0󰀉1+e󰀉Lmodeisandanelectron,e1+e.Then,sincethebranchingratiooftheν

󰀉−+χ󰀉0)×Br(χ󰀉−→e+ν󰀉)isabout0.3%.pereachleptonflavor.ThusBr(H−→χ

󰀉−+χ󰀉0)isabout1%andBr(χ󰀉−→e+ν󰀉)isroughly30%branchingratioisBr(H−→χ

AsshowninFig.3(b),however,ifthelightercharginoisdominantlygaugino,the

branchingratioofthechargino-neutralinomodeincreases,sothatthebranchingratio

󰀉−+χ󰀉0modeofthechargedHiggsdecayasBr(H−→theelectronisfoundintheχ

󰀉1+e󰀉Lisrelativelydecreased.InthiscaseweestimatetheprobabilitythatofH−→ν

󰀉L+ν󰀉1decay.Weconcludethat,eveninourspecificchoiceofiscomingoutfromthee

󰀉−+χ󰀉0modecouldbeaseriousbackgroundtosearchthedecayparameterset,theχ

󰀉1+e󰀉Lwhenthecharginoandneutralinoarealmostgauginos.H−→ν

󰀉RwithunsuppressedWewouldliketodiscussthetestabilityofthescenariooflightν

󰀉−+χ󰀉0)×Br(χ󰀉−→e+ν󰀉)≃10%.Thiscompeteswiththeprobabilitythatanelectronχ

pointistoidentifythattheobservedelectroncomesfromH−.ItcouldbeachievedusingthepairproductionofthechargedHiggsbosons.InapairproductionofthechargedHiggs,oneofthechargedHiggsbosonscanbeidentifiedusingthet+bmode.ThenifanelectronisobservedinthechargedHiggspairproductionitmustbeidentifiedasone

󰀉1+e󰀉L.Forexample,atthefromthedecayofanotherchargedHiggsthroughH−→ν

󰀉1+e󰀉L→e+EAνatfuturecolliderexperimentsusingthedecayH−→νT.Animportant

e+e−linearcollider(ILC),thetypicalsizeofthecrosssectionofthechargedHiggsboson

9

1t + b1∼− + χ∼0χt + bτ + νBranching ratio0.1W + h (MSSM)Branching ratio0.1τ + νW + h (ν)W + h0.01−∼0∼χ + χ(MSSM)~∼e + ν1∼∼e + ν10.01(a)46810121416tanβ182022244W + h(ν)(b)8101214tanβ161820226Figure3:ThebranchingratiosofchargedHiggsbosondecayformH−=350GeV.Thedecaymodeintosneutrinoandselectronisfoundforme˜L=200GeV,mν˜1=50GeV,Aν=

=150GeVwithM2/µ=5500GeV.Thechargino-neutralinomodeisobtainedformχ󰀉−1

(a)and1(b).

pairisO(1−10)(fb)formH−=O(100GeV)[12].Assumingtheintegratedluminosityas100fb−1,itisexpectedthat100∼1000chargedHiggspairsareproducedinayear.Fig.3(a)tellsusthat,whentanβ=3,onlyfewelectronsappearfrom1000charged

󰀉+ν󰀉1HiggsbosonsintheMSSM(theW+hmode),whileabout160electronsfromthee

modeisexpectedinourscenario.Therefore,anexcessofelectronsfromthechargedHiggsdecaycouldbeasignaloftheTeVscaleright-handedsneutrinowithunsuppressedtrilinearcouplingAν.

5Summary

Inthispaper,wehavestudiedphenomenologyofthescenarioofTeVscaleright-handedsneutrinoinspiredbymodelsofSUSYbreakinginspiredneutrinomass[4,5,6].TheimportantpredictionofthisscenarioisthatthesneutrinotrilinearcouplingAνcouldbesizableandisnotsuppressedbytheneutrinoYukawacoupling.Weexaminedtwophenomenologicalconsequencesofthisscenario.Wefoundthatthesneutrinocontribu-tiontothelightestHiggsbosonmassisdestructivelyinterfereswiththeordinaryMSSMcontributions.ThusthelightestHiggsbosonmassmaybeloweredinthismodelviasneutrinoexchangewithlargeAν.ThelargeAνalsoaffectsthedecayofchargedHiggsinsomeparameterregionandthebranchingratioisroughly∼10%forsmalltanβ.In

󰀉1+e󰀉Lcouldbesubdominantdecaymodeboson.ItisshownthattheprocessH−→ν

10

suchparameterregion,weexpectthatroughly200electronsperyearfromthechargedHiggsdecayattheILCexperimentswiththeintegratedluminosity100fb−1.OntheotherhandtheMSSMpredictsonlyfewelectronsfromthechargedHiggsdecay.TheexcessoftheelectronsinthechargedHiggsdecay,therefore,couldbeasignalofthe

󰀉Rscenario.TeVν

Acknowledgments

TheworkofG.C.C.wassupportedinpartbytheGrant-in-AidforScienceResearch,MinistryofEducation,ScienceandCulture,Japan(No.K175402386).TheworkofS.K.wassupportedbytheJapanSocietyofPromotionofScience.

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