For massive neutrinos one could introduce in analogy to the quark mixing a mixing matrix describing the relation between mass and flavor states:
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- Cameron Shaw
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1 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon. wr 4. Nurno Oscllaons τ τ τ τ For assv nurnos on could nroduc n analogy o h quark xng a xng arx dscrbng h rlaon bwn ass and flavor sas: Consan for asslss : xng s quson of convnon *, hr wll b a xng of h flavor sas wh. assv nurnos dvlo dffrnly n. for asss << : 4. Two-Flavor xng for slcy cos sn sn cos T dvlon for an nally ur > ba: [ ] [ ] sn cos sn cos sn cos xng robably: P cos sn cos, ] [ ] [ 4 ] [.7 sn sn 4 sn sn, k GV V P : w/ / sa h s assung Dfn onu ; sa for all ass gnsa coonns
2 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon Sarch for Nurno Oscllaons PDG 996 xcluson los P, sn sn 4 Dsaaranc: I Wh known nurno flux: asurn of flux a dsanc : racor xrns, II asur nurno flux a oson and vrfy flux afr dsanc. Aaranc: s nurno ba of y A and sarch a dsanc for nurnos of y B. or sascs Basln longr xcludd Obsrvaon of Nurno Oscllaons Nurno sourc Solar nurnos Aoshrc nurnos Acclraor acor xrn ado-chcal x.: HosakClx., GAX, SAG, War xrns: SurKaokand, IB War: SNO SurKaokand SDN No confrd KK KaAND, CHOOZ Cons Frs obsrvaon of nurno dsaaranc das or han yars ago: Solar nurno robl Confr dsaaranc of solar nurnos la solar nurno xrn : rovs h oscllaon of solar Oscllaon sgnal uch dsud sgnal Clar dsaaranc sgnal Clar dsaaranc sgnal. wr
3 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon 4. Aoshrc nurno robl Cosc radaon: Ar showr ± N π, K ± π, K ± ± ± ± ± xac calculaon:. <GV For largr nrgs >. Nurno dcon wh war dcors [ ~OGV] War lasc scarng acv arg x X Z x X Chrnkov gh W Chargd currn Knacal l for : > Dcon of Chrnkov hoons: Phoo ullr xrns: Sur-Kaokand IB Soudan-. wr
4 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon Sur-Kaokand args arfcal war dcor 5 k nl h accdn: PTs 5 c ubs!: 4% of surfac covrd wh hoo-cahod Back n oraon snc Chrnkov con: cos n 4 o Sod uon xrn can dsngush lcron and uon vns, can asur nrgy. wr 4
5 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon ao of uon o lcron nurnos Prdcon wh oscllaon Too fw uon nurnos obsrvd Can b xland by oscllaon. Znh angl dndnc of h nurno flux Thorcal rdcon w/o oscllaon w/ oscllaon ~5 k ~ k dfc dnds on angl flux okay Oscllaon: τ. wr 5
6 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon Oscllaon arn of aoshrc nurnos Nurno 4 allowd τ xng of aos. nurnos.4 ±.4 V sn C.. 4. Solar nurno robl Nurno roducon. wr 6
7 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon Nurno nrgy scru Sag, Gallx Hosak -body dcays Nurno xrns: Cl dcors 7 Cl 7 Ar, 7 Ar 7 Cl C >.8 V Ga dcors 7 Ga 7 G >. V H O dcors lasc scarng: >5 V dcon ado-chcal xrns: Hosak n, 4 undrground 65 of C Cl 4 rchlorohln.x aos of 7 Cl s 6 Ar and 8 Ar o carry-ou h fw aos of 7 Ar ~ ao/day Coun radoacv 7 Ar dcays Hosak, SAG, GAX Hosak Cl xrn SS rdcon. wr 7
8 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon Solar Nurno Probl: xrnal suary >.8 V > 5 V >. V > 5 V Nurno dsaaranc CC S CC S Can on asur h oscllad nurnos?? Th Nobl Prz n Physcs ayond Davs Jr. asaosh Koshba ccardo Gacon "for onrng conrbuons o asrohyscs, n arcular for h dcon of cosc nurnos" "for onrng conrbuons o asrohyscs, whch hav ld o h dscovry of cosc X-ray sourcs". wr 8
9 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon Sudbury Nurno Obsrvaory 6 radus ransarn acrylc vssl of havy war D O 9456 nward lookng hoo ullrs Add of NaCl o dc nurons Nurno dcon wh SNO Chargd currn σ σ τ φ φ lasc scarng.54 σ σ σ τ φ φ φ φ / 6 τ n x W Z W x Chrnkov gh Chrnkov gh Nural currn σ σ σ τ φ φ φ φ τ n Z n 5 Nuron 6 Cl n, γ Cl. wr 9
10 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon SNO vdnc for Nurno Oscllaon lcron nurno flux s oo low: P 5 ± % Toal flux of nurnos s corrc. Inrrd as or τ oscllaon Bu n cas of sl vacuu oszllaon : P sn 5%? Nurno oscllaons n ar: SW-ffc Nurno oscllaon n vacuu: khav, Srnov 986, Wolfnsn 976 dvlon of ass gnsas d d Wh unary ransforaon on obans for h flavor oscllaon n vaccu: d d T T 4 cos sn cos sn sn cos sn cos. wr
11 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon. wr Nurnos n ar: x x Z lcron nurnos suffr an addonal onal V affcng h forward scarng alud whch lads o chang n h ffcv ass for : N G V V F W N lcron dnsy F N G V G N a F Nurno oscllaon n ar: cos sn sn cos on dfn h ar ass gnsas whch on obans by dagonalzng T Go h oos drcon T sn cos a N G F
12 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon cos sn wh sn cos sn sn cos a sn sn 4 sn sn 4 ar xng angl can go hrough a rsonanc: cos a.. N cos G F a G N / F As n h cor of h sun, N s largr han h crcal dnsy h rsonanc condon wll always b fulflld: oscllaon largly odfd by ar. xlans P 5 ± % obsrvd wh SNO Saus of oscllaon asurns xcludd Aos x.4 ±.4 V sn C.. allowd allowd SolarKaAND x A larg xng angl: SW ffc ncssary ong basln any racors xrn 8. ±.6 sn.8 5 V Dffrn oscllaon arn for dffrn nurnos wha can w larn abou h asss??. wr
13 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon 4.4 Nurno asss cc sc css ss ccs c c c s s c s s s c s s s c s c c whr c cos, s sn j a sol j j j ~ 8. 5 V ~.4 V ~ 8. 5 V ~.4 V Absolu nurno asss ar no known! Nurno asss n h Sandard odl Nurno ass r: h Drac ass r Hggs D h sa as for chargd lons: ~ ψ ψ asss of nurnos hrough Yukawa coulng o Hggs: λ υ Fro h vacuu xcaon valu of h Hggs, υ 46 GV, follows ha h Yukawa coulng us b xrly sall < - o gnra h sall nurno asss. unnaural Drac ass rs ly xsnc of rgh lf -handd an nurnos. nal xnson of h Sandard odl: Inroduc sngls of rgh lf-handd annurnos whch do no coul o chargd and nural currns. on nubrs: and τ ar no consrvd. s consrvd!! Bu why ar h nurno asss so sall?. wr
14 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon ajorana Nurnos nlk h chargd lons, nurnos could b hr own an-arcls: ajorana-ass rs n addon o Drac ass rs ossbl: h Hggs ajorana Nurnos ajorana ass r,, c. c., ass r volas on flavor consrvaon: ± ajorana characr can b chckd n nurnolss doubl ba dcay : Can w rov ha nurno s a Drac arcl Sarch for nrgy scru Granu dcay xal Klador-Klngrohaus 4?. wr 4
15 Advancd Parcl Physcs: IX. Flavor Oscllaon and CP Volaon Ssaw chans o gnra lgh nurnos If nurnos ar ajorana arcls: Inroduc n addon o h Drac ass r also a ajorana ass r for h rgh-handd nurno sngl:, D, c. c. D, Ssaw odl: Assu ajorana ass of h rgh-handd nurno vry havy, ajorana ass of lf handd nurno. Solvng h ass arx on obans a sall ass for H nurnos D h x Ssaw ass r for lgh nurno Sall nurno asss can b xland bu how larg s 5 GV? h h h Th nd. wr 5
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