Can lepton flavor violating interactions explain the atmosph(10)

We investigate whether flavor changing neutrino interactions (FCNIs) can be sufficiently large to provide a viable solution to the atmospheric neutrino problem. Effective operators induced by heavy boson exchange that allow for flavor changing neutrino sca

III.Z-INDUCEDFLAVORCHANGINGNEUTRALCURRENTS

Intheprevioussectionweconsideredmodelswheretheonlymodi cationtotheneutrinosectorisduetonewinteractionsmediatedbyheavybosons.Inthissectionwestudytheoppositescenario,wherenewfermionsareadded,butnoextrabosonsbeyondtheSMonesareneeded.AsanexampleweconsiderZ-inducedFCNCsthatarisewhenintroducingaheavysterileneutrino.SuchSMgaugesinglets,whichappearinmanyextensionsofthestandardmodel,arefrequentlyemployedtoexplainthesmallnessoftheneutrinomassesviathesee-sawmechanism[36].ThebasicideaforZ-inducedFCNCsisthatifaneutrinointeractioneigenstateisalinearcombinationoflightandheavymasseigenstatesthenthee ectivelow-energyinteractioneigenstates,thatconsistonlyoflightmasseigenstates,arenotorthogonaltoeachother[37].ThusthecouplingstotheZ-boson(andinfactalsototheW-boson)havetobemodi edslightly,implyingthatalsothee ectiveHamiltonianthatdescribestheneutrinopropagationinmatterhastobechanged.

InRef.[18]ageneraldiscussionofZ-inducedFCNCsandtheirimpactonneutrinooscil-lationshasbeenpresented.InthecontextoftheANproblemweillustratethemechanismbyconsideringasimpleframeworkwherebesidestheSMneutrinosνµandντthereisonlyonenewgaugesingletνS.(Forsimplicityweassumethattheνedoesnotplayanimportantrolehere.)Theseinteractioneigenstatesareconnectedtothemasseigenstatesbyaunitarytransformation

whereν1andν2denotethelightandνhtheheavymasseigenstates.Theneutrinosthatareproducedinlow-energycharged-currentinteractionstogetherwithchargedleptonsµandτare

Pνµ

PντUµ1νµ ντ = Uτ1US1νS Uµ2Uτ2US2ν1Uµh Uτh ν2 ,νhUSh (3.1) = Uµ1Uτ1Uµ2Uτ2 ν1ν2 ,(3.2)

i.e.wehaveprojectedνµandντontotheν1 ν2plane.Sincethemixingmatrixappearing

PPin(3.2)isonlyasubmatrixoftheunitarymatrixin(3.1),νµandντarenotorthogonalto

eachother

PP νµ|ντ =Uµ1Uτ1+Uµ2Uτ2= UµhUτh(3.3)

andalsonotproperlynormalized.Consequentlythesestatesdonotprovideaproperbasisfortheneutrinooscillationformalism.

ThedescriptionofneutrinooscillationinthepresenceofheavygaugesingletshasbeenworkedoutinRef.[18].Themainresultisthatthee ectivenon-unitarymixinginducesa avoro -diagonalcontributioninthematter-inducedneutrinopotentialVFCNC.Thee ect