Lepton flavor violation in the SUSY seesaw model an update

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

arXiv:hep-ph/0403212v2 11 May 2004

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

2FrankDeppisch,HeinrichP¨as,AndreasRedelbachandReinholdR¨uckl2Neutrinoparameters

Inthelastdecadearatheruniquepictureofneutrinomixinghasemerged.AscanbeseeninFig.1,largetomaximalmixinghasbeenestablishedforsolarandatmosphericneutrinos,whilethethirdangleisstronglyconstrainedbyreactormeasurements.Recently,thispictureofneutrinomixinghasbeenre- nedfurther.TheresultsoftheKamLANDreactorexperimentcon rmedthedisappearanceofsolarelectronneutrinos,whiletheSNOexperimentallowedforthe rsttimetostudybothsolarneutrinoappearanceanddisappearanceviatheseparatemeasurementofchargedcurrent,elasticscatteringandneu-tralcurrentinteractions.Moreover,the rstdataoftheK2Klongbaselineacceleratorexperimentindicateacon rmationofatmosphericneutrinoos-cillations.Atthetimewhenalinearcolliderwillbeinoperation,evenmoreprecisemeasurementsoftheneutrinoparameterswillbeavailablethantoday.Inordertosimulatetheexpectedimprovement,wetakethecentralvaluesof22themasssquareddi erences m2ij=|mi mj|andmixinganglesθijfromthemostrecentglobal ttoexistingdata[10]witherrorsthatindicatetheantic-ipated2σintervalsofrunningandproposedexperimentsasfurtherexplainedin[7]:

.39+0.001+0.4722tan2θ23=1.10+1 0.60,tanθ13=0.006 0.006,tanθ12=0.43 0.22,(1)

+0.36+1.2 5 3 m2eV2, m2eV2.12=6.9 0.36·1013=2.6 1.2·10(2)

Furthermore,forthelightestneutrinomassweassumem1≤0.03eV,wherem1 0eVcorrespondstothecaseofahierarchicalspectrum,whilem1 0.03eVapproachesthedegeneratecase.

3mSUGRAbenchmarkscenarios

ForournumericalinvestigationswefocusonthemSUGRAbenchmarkscenar-iosproposedin[11]forlinearcolliderstudies.ThesemodelsareconsistentwithdirectSUSYsearches,Higgssearches,b→sγ,andastrophysicalconstraints.Recently,theprecisionmeasurementofthecosmicmicrowavebackgroundbytheWMAPexperimentcombinedwithpreviouslyavailabledataprovidedare nedestimateofthedensityofcolddarkmatterintheuniverse.AssumingthatmostofthedarkmatteriscomposedofneutralinoLSPs,thesmallerneutralinorelicdensityledtoashiftofpreviousbenchmarkpoints[12]to-wardslowervaluesoftheuniversalscalarmassm0.Intable1wespecifythemSUGRAparametersofthebenchmarkscenariosB’,C’,G’,andI’.Thesearetheonlymodelsof[11]withleft-handedsleptonswhicharelightenough√tobepair-producedate+e colliderswithc.m.energies

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

Lepton avorviolationintheSUSYseesawmodel:anupdate

Fig.1.Summaryofevidencesforneutrinooscillations[9].

Scenariom0/GeVmχ 0

1/GeV

B’6098

40010291

G’115153

35035310

νcTRMνc

2R+νcTRYνL·H2.3(3)

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

4FrankDeppisch,HeinrichP¨as,AndreasRedelbachandReinholdR¨ucklHere,YνisthematrixofneutrinoYukawacouplings,Mistheright-handedneutrinoMajoranamassmatrix,andLandH2denotetheleft-handedleptonandhypercharge+1/2Higgsdoublets,respectively.Atenergiesmuchbelowthemassscaleoftheright-handedneutrinos,Wνleadstothemassmatrix

1Mν=mTmD=YνTM 1Yν(vsinβ)2,DM(4)

fortheleft-handedneutrinos.Thus,lightneutrinomassesarenaturallyob-tainedifthetypicalscaleoftheMajoranamassmatrixMismuchlargerthan00thescaleoftheDiracmassmatrixmD=Yν H2 ,where H2 =vsinβisthe0 H appropriateHiggsv.e.v.withv=174GeVandtanβ=2

2

2(m )=Aabvcosβ δabmlaµtanβ.lLRab+sin2θW22222 mcos2βsinθW))=(m)+δ(m(m abababZRlalR (8)(9)(10)

2Whenm isrenormalizedfromtheGUTscaleMXtotheelectroweakscaleloneobtains,inmSUGRA,

222m2L=m01+(δmL)MSSM+δmL

222m2R=m01+(δmR)MSSM+δmR(11)(12)

(13)A=A0Yl+δAMSSM+δA,

wherem0isthecommonsoftSUSY-breakingscalarmassandA0thecommontrilinearcoupling.Theterms(δm2L,R)MSSMandδAMSSMarewell-known avor-

diagonalcorrections.Inaddition,theevolutiongenerateso -diagonalterms2inδm2L,RandδAwhichinleading-logapproximationaregivenby[5]

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

Lepton avorviolationintheSUSYseesawmodel:anupdate5

χ

0

iν j

Fig.2.Diagramsforli→ljγintheMSSM

δm2L= 1

16π2

with(YlYν LYν) MX(16)Lij=ln

vsinβdiag

whereRisanunknowncomplexorthogonalmatrix.ForrealRanddegenerateright-handedMajoranamasses,Raswellasφ1andφ2dropoutfromtheproductYν LYν.Usingthentheneutrinodatasketchedinsection2asinputtheresultisevolvedtotheuni cationscaleMX.Inwhatfollowswerefertothisillustrativecasewhichsu cesforthepresentdiscussion.Forsmall2neutrinomasses,m2i mij,theaboveprocedureyields

YνLYνab≈MR m212Ua2Ub2 M2, m1,√m3)U ,(18)+

Upondiagonalization,the avoro -diagonalcorrectionsin(11)-(13)generate avor-violatingcouplingsofthesleptonmasseigenstates. MR.(19)

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

6

FrankDeppisch,HeinrichP¨as,AndreasRedelbachandReinholdR¨uckl

+j

ee+j

e0β i

0β+ i0αe0α

+ + 00 Fig.3.Diagramsfore+e → lbla→ljliχ αχ β

5Chargedlepton avorviolation

Atlowenergies,the avoro -diagonalcorrection(14)inducestheradiativedecaysli→ljγ.FromthephotonpenguindiagramsshowninFig.2withcharginos/sneutrinosorneutralinos/chargedsleptonsintheloop,onederivesthedecayrates[4,5]

Γ(li→ljγ)∝α3m5li2|(δmL)2ij|

Br(µ→eγ)≈α

3 lnm2µ

4 .(21)

Athighenergies,afeasibletestofLFVisprovidedbytheprocesse+e →+ + 00 lbla→ljliχ αχ β.FromtheFeynmangraphsdisplayedinFig.3,onecanseethatLFVcanoccurinproductionanddecayvertices.Forsu cientlynarrowsleptonwidthsΓ landdegeneratemasses,thecross-sectioncanbeapproximatedby

pairσi=j∝2|(δmL)2ij|

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

1√2 χ01(lowerband)at

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

8

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

S+B=3,andassumesanintegratedluminosityof1000fb 1,a

signalcross-sectionof0.1fbcouldonlya ordabackgroundofabout1fb.Whetherornotsuchalowbackgroundcanbeachievedbyapplyingselectronselectioncuts,forexample,ontheacoplanarity,leptonpolarangleandmissingtransversemomentumhastobestudiedinadedicatedsimulation.Forlepton avorconservingprocessesonehasfoundthattheSM√backgroundtosleptonpairproductioncanbereducedtoabout2-3fbat

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

10FrankDeppisch,HeinrichP¨as,AndreasRedelbachandReinholdR¨uckl

ParticularlyinterestingandusefularethecorrelationsbetweenLFVinradiativedecaysandsleptonpairproduction.SuchacorrelationisillustratedinFig.6fore+e →µ+e +2χ 01andBr(µ→eγ).Oneseesthattheneutrinouncertaintiesdropout,whilethesensitivitytothemSUGRAparametersre-mains.Furthermore,whilemodelsC’,G’andI’arebarelya ectedbythechangeinthenewparametersetascomparedtothesetusedin[8],inmodelB’σ(e+e →µ+e +2χ 01)foragivenBr(µ→eγ)isbyafactor10largerthaninthepreviousbenchmarkpointB.Anobservationofµ→eγwithabranch- 11ingratiosmallerthan10 wouldthusbecompatiblewithacross-sectionas+ + lbla→µ+e +2χ 0largeas1fbforee→b,a 1,atleastinmodelC’,G’andB’.Ontheotherhand,nosignalatthefuturePSIsensitivityof10 13wouldconstrainthischanneltolessthan0.1fb.ThecorrelationofBr(τ→µγ)and 7σ(e+e →τ+µ +2χ 0does1)isshowninFig.7.Br(τ→µγ)<3·10

notruleoutcross-sectionsintheτµchannelof1fbandlarger.However,onehastokeepinmindthatthesecorrelationsdependverymuchontheSUSYscenario.

7Conclusions

SUSYseesawmodelsleadingtotheobservedneutrinomassesandmixingscanbetestedbylepton- avorviolatingprocessesinvolvingchargedleptons.Wehavepresentedanupdatedanalysisoftheprospectsforradiativeraredecays+ + li→ljγandsleptonpairproductionanddecaye+e → lbla→ljli+E/.Assumingthemostrecentglobal tstoneutrinooscillationexperiments[10]wehaveillustratedtheimpactoftheuncertaintiesintheneutrinoparameters.Furthermore,usingpost-WMAPmSUGRAscenarios[11]wehaveinvestigatedthedependenceofLFVsignalsonthemSUGRAparameters.ForscenarioB’ourresultscanbesummarizedasfollows.AmeasurementofBr(µ→eγ)≈10 13wouldprobeMRintherange5·1012÷5·1013GeV,whileameasurementofBr(τ→µγ)≈10 8wouldallowtodetermineMR 1015GeVwithinafactorof2.Furthermore,Br(µ→eγ)=10 13÷10 11√impliesσ(e+e →µ+e +2χ 01)=0.02÷2fbat

s=800GeV.Hence,linearcollidersearchesarenicelycomplementarytosearchesforraredecaysatlowenergiesandattheLHC.

Acknowledgements

ThisworkwassupportedbytheBundesministeriumf¨urBildungundForschung(BMBF,Bonn,Germany)underthecontractnumber05HT4WWA2.

We present an update of previous work on charged lepton flavor violation (LFV) in the seesaw model. The most recent neutrino data fits and post WMAP mSUGRA benchmark scenarios are used as input. In this framework we compare the sensitivity of rare radiativ

Lepton avorviolationintheSUSYseesawmodel:anupdate11

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