Mediation of Supersymmetry Breaking in Gauge Messenger Model(2)

2.Maximalmixingscenario–asolutiontothe netuningproblem

AsmentionedintheIntroduction,thephysicalHiggsbosonmassreceivesanadditionalcontributionfromstopmixing[13],

24m3GmA2 Ftt222tlogmh MZcos2β+(1 m22π2 t

6whichcorrespondstothemaximalmixing

3/2m(nomixing),scenario.Inthiscasethestopcanbelighter,mt (maximalmixing)=e t

anditcanbeaslightas250～300GeVwhileful llingthephysicalHiggsmassboundfromtheLEP.

InsteadofusingEq.(1.3)asaroughestimateofthecontributionofstopmasstotherunningofm2Huitisinstructivetobemoreprecise.ForgiventanβwecansolveRG22equationsexactlyandexpressEWvaluesofm2Hu,µ,andconsequentlyMZgivenbyEq.(1.2),asfunctionsofallGUTscaleparameters.Fortanβ=10,wehave:

2222MZ 1.9µ2+5.9M3 1.2m2 0.8AtM3+0.2At+···,Hu+1.5mt(2.2)

whereparametersappearingontheright-handsidearetheGUTscaleparameters,wedonotwritethescaleexplicitly.OtherscalarmassesandM1andM2appearwithnegligiblecoe cientsandweneglecttheminourdiscussion.Thecoe cientsinthisexpressiondependonlyontanβ(theydonotchangedramaticallywhenvaryingtanβbetween5and

50)andlog(MGUT/MZ).

LetusalsoexpresstheEWscalevaluesofstopmasssquared,gluinomassandtoptrilinearcouplingfortanβ=10inasimilarway:

22m2 +0.2AtM3 (MZ) 5.0M3+0.6mtt(2.3)

(2.4)

(2.5)M3(MZ) 3M3At(MZ) 2.3M3+0.2At.

Inthecaseofmt thecoe cientsrepresentaveragesofexactcoe cientsthatwouldappear

2.inseparateexpressionsform2 R LandmttFromEqs.(2.2),(2.3)and(2.4),weseetheusualexpectationfromSUSY,MZ mt 1,2 mg ,whenallthesoftSUSYbreakingparametersarecomparable.Furthermore,

We study gauge mediation of supersymmetry breaking in SU(5) supersymmetric grand unified theory with gauge fields as messengers. The generated soft supersymmetry breaking parameters lead to close to maximal mixing scenario for the Higgs mass and highly red

neglectingtermsproportionaltoAtinEqs.(2.5)and

(2.3)

we

nd

that

a

typical

stop

mixing

is

At

ExtremelylargeAtinthecaseofthesamesignasM3contributessigni cantlytotherunningofmt andconsequentlytotherunningofmHu.Therefore,At mt mHu MZisrequiredandtheEWscaleisaresultoflargecancelations.2

We study gauge mediation of supersymmetry breaking in SU(5) supersymmetric grand unified theory with gauge fields as messengers. The generated soft supersymmetry breaking parameters lead to close to maximal mixing scenario for the Higgs mass and highly red

2.1Large(maximal)mixinginmodels

Sincetheradiativelygeneratedmaximalmixingscenariocaninprincipleeliminate netuningofEWSBcompletely,itisdesirabletoseewhetheritispossibletogetevenclosetoitinspeci cmodels.

ItiseasytoseethatthissolutiondoesnotexistinmSUGRA.Asaconsequenceofuniversalitiesingauginoandscalarmasses,whenstopmasssquaredisnegativeenoughtogeneratemaximalstopmixingattheEWscaleradiatively,sleptonsremaintachyonicevenattheEWscalebecausethebinocontributiontotherunningofsleptonmassesissmall.TheEWscalesleptonmassism2e 22

RGeVgivesthefollowinginequality m0+0.15M1/2[17].Imposingtheslepton

massbound100

m20≥ (0.4)2+(100GeV

We study gauge mediation of supersymmetry breaking in SU(5) supersymmetric grand unified theory with gauge fields as messengers. The generated soft supersymmetry breaking parameters lead to close to maximal mixing scenario for the Higgs mass and highly red

N=1vectormultipletVtransformsasanadjointofSU(5),thethreegenerationsofmatter eldsareinchiralmultiplets,3×(10+¯5),andtheHiggs eldsarein5+¯5.Besidesthese,wealsointroduceanadjointchiralmultipletΣ,andweassumethatbothitsscalarcomponent,whichwealsodenoteΣ,andtheauxiliarycomponent,FΣ,getvacuumexpectationvalues.TheVEVofFΣbreaksSUSYandtheSUSYbreakingiscommunicatedtogauginos,squarksandsleptonsthroughgaugeinteractions.ThemassivecomponentsofthegaugemultipletVandΣplaytheroleofmessengers.Thisistheminimal eldcontentweconsider.Inthiscase,thebetafunctioncoe cientoftheuni edgaugecouplingisbG=3andallsoftSUSYbreakingparametersattheGUTscalearecalculableintermsofbGandtheuni edgaugecoupling.

Itisalsopossibletoextendthemessengersectorandintroduce,forexample,apairof

5representationsofSU(5).Additionalmessengersusualmessenger eldsΦandΦcin5and¯

alsochangethebetafunctioncoe cient,bG=3andthespectrumisingeneralgivenintermsofthenumberofmessengers,Nmess,andbG.

Therefore,inthisscenariothemediationofsupersymmetrybreakingisacombinationoftwoe ects:

Gaugemessengercontribution:XandYgaugebosonsandgauginoscontributetothesoftsupersymmetrybreakingterms.TheybecomemassivebytheVEVofΣandgauginomassesgetsplitduetoFΣ.Therefore,themessengerscaleistheGUTscale.Theratio|FΣ

FΣ 4π

Inprincipleitispossibletointroduceanadditionalsingletsuper eld,whoseFcomponentisnon-zero,andwhichcouplestothevector-likemattermessengers.However,weconsideronlytheminimalversioninwhichΦandΦccoupletotheadjointΣbywhichgaugemessengersgottheirmasssplitting.3

We study gauge mediation of supersymmetry breaking in SU(5) supersymmetric grand unified theory with gauge fields as messengers. The generated soft supersymmetry breaking parameters lead to close to maximal mixing scenario for the Higgs mass and highly red

GauginomassesattheGUTscale(αi=αGUT)are(Eq.(A.12)):Mi=[ 2(5 NCi)+Nmess]MSUSY,

whereNCiisthenumberofcolorsofthegaugegroupSU(NCi).Moreexplicitly,

M3=( 4+Nmess)MSUSY,

M2=( 6+Nmess)MSUSY,

M1=( 10+Nmess)MSUSY.(3.3)(3.4)(3.5)

Intheminimalmessengermodel(Nmess=0),thegauginomassesatthemessengerscale(theGUTscale)are

M3= 4MSUSY,

M2= 6MSUSY,

M1= 10MSUSY.(3.6)(3.7)(3.8)

Notethat|M1|>|M2|>|M3|attheGUTscale(|M1|:|M2|:|M3|=2.5:1.5:1).AsaresultofRGevolution,attheweakscalewe nd|M1(MZ)|:|M2(MZ)|:|M3(MZ)|～1:1:2.Thisisquitedi erentfromscenarioswiththeuniversalgauginomassesattheGUTscalewhichleadtogluinoabout7timesheavierthanbinoattheE …… 此处隐藏：5503字，全部文档内容请下载后查看。喜欢就下载吧 ……