Phenomenological Status of Neutrino Mixing
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1 Phenomenological Status of Neutrino Mixing Carlo Giunti INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Università di Torino Neutrino Unbound: SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 1
2 Outline Brief Introduction on Neutrino Masses Solar Neutrinos and KamLAND Atmospheric Neutrinos, KK and MINOS Three-Neutrino Mixing Absolute Scale of Neutrino Masses Tritium Beta-Decay Neutrinoless Double-Beta Decay Cosmology LSND and MiniBooNE Conclusions C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007
3 Standard Model: Massless Neutrinos ÓÓ Ø Ä Ô Î Ú Ô ¼ Ê Ú Ô Standard Model: L c L = (c ) R =µ no Dirac mass term Majorana Neutrino: c Ä D m D L R (no R, ( c ) L ) ( c ) R R =µ Majorana mass term Ä M m M L c L = m M L ( c ) R Standard Model: Majorana mass term not allowed by SU() L U(1) Y (no Higgs triplet) C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 3
4 Extension of the SM: Massive Neutrinos Standard Model can be extended with R (e L e R ; u L u R ; d L d R ; ) L + R µ Dirac neutrino mass term Ä D m D L R µ m D 100 GeV surprise: Majorana neutrino mass for R is allowed! total neutrino mass term Ä D+M L ( c ) L 0 m D m D Ä M R mm R (c ) L R m M R ( c ) R R m M R can be arbitrarily large (not protected by SM symmetries) mr M scale of new physics beyond Standard Model µ mm R md 0 m D diagonalization of µ m 1 ³ (md ), m ³ mr M ν ν 1 see-saw mechanism m D m M R m M R natural explanation of smallness of neutrino masses massive neutrinos are Majorana! [Minkowski, PLB 67 (1977) 4] [Yanagida (1979); Gell-Mann, Ramond, Slansky (1979); Mohapatra, Senjanovic, PRL 44 (1980) 91] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 4
5 Lepton Numbers Standard Model: Lepton numbers are conserved L e L L ( e e ) ( ) ( ) L e L L (( c ) e e + ) (( c ) + ) (( c ) + ) L = L e + L + L ¼ ½¼ md ee m D e m D e er Dirac mass term m D L R el L L me D m D m D R me D m D m D R L e, L, L are not conserved, but L is conserved L( «R) = L( L) µ L = 0 Majorana mass term m M L ( c ) R el L L ¼ ½¼ mm ee m M e m M e me M mm mm me M m M m M L, L e, L, L are not conserved L( c «) = L( ) µ L = ½ (c e ) R () c R ( c ) R ½ C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 5
6 «= U = Two-Neutrino Mixing and Oscillations k=1 cos sin U «k k («= e ) sin cos ν µ ν ϑ ν e ν 1 e = cos 1 + sin = sin 1 + cos m m 1 m m 1 Transition Probability: P e = P e = sin sin m L 4E Survival Probabilities: P ee = P = 1 P e C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 6
7 Solar Neutrinos Solar e Energy Spectrum [J.N. Bahcall, C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 7
8 Homestake+Kam.+GALLEX+SAGE+Super-K+SNO 6 Φ SNO e = cm s 1 Φ SNO e = cm s 1 SNO solved solar neutrino problem Neutrino Physics (April 00) [SNO, PRL 89 (00) , nucl-ex/004008] e oscillations LMA: Large Mixing Angle solution m ³ ev tan ³ s -1 ) cm - 10 ( φ µτ SNO φcc 68% C.L. SNO φnc 68% C.L. SNO φes 68% C.L. SK φes 68% C.L. BS05 φssm 68% C.L. NC φµτ 68%, 95%, 99% C.L φ ( 10 cm - s -1 e ) ) ev -5 (10 m (a) tan θ [SNO, PRC 7 (005) 05550, nucl-ex/05001] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 8
9 BOREXino [BOREXino, arxiv: ] Real-time measurement of 7 Be solar neutrinos (086MeV) + e + e E = 086MeV =µ e ³ 55 Counts/(10 kev day 100 tons) All solar neutrinos 7 Be neutrinos Energy [MeV] Counts/(10 kev day 100 tons) Fit: χ /NDF = 41.9/47 7 Be: 47±7±1 cpd/100 tons 10 Bi+CNO: 15±4±5 cpd/100 tons 85 Kr: ±7±5 cpd/100 tons 10 Po: 0.9±1. cpd/100 tons Energy [kev] n no-osc the = 75 4day 1 (100tons) 1 n exp = day 1 (100tons) 1 n osc the = 49 4day 1 (100tons) 1 (n no-osc the n exp ) n ³ 19 C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 9
10 KamLAND Reactor e e confirmation of LMA (December 00) 53 nuclear power reactors in Japan and Korea Kamioka Mine L ³ 180km E ³ 4MeV short baseline experiment Ratio 1.4 KamLAND data CHOOZ data best-fit osci. 1. best-fit osci. + Expected Geo e st nd 3rd preliminary L 0 /E e (km/mev) [I. Shimizu (KamLAND), TAUP 007] hypothetical single reactor at 180 km C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
11 ) (ev m small matter effect SNO KamLAND KamLAND 95% C.L. 99% C.L % C.L. best fit SNO 95% C.L. 99% C.L % C.L. best fit tan 4 3 preliminary > 6 > 4 KamLAND only tan = 0.56 m = ev LMA II LMA 0 [I. Shimizu (KamLAND), TAUP 007] (marginalized error) ) ev -5 (10 m neutrino effect 3 neutino neutino preliminary sin 1 same result for m C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
12 ) (ev KamLAND tan = KamLAND + Solar % C.L. 99% C.L % C.L. 0.3 global best fit m = ev This result KamLAND + SNO tan = m = ev m : systematic uncertainty.0% dominated by linear energy scale uncertainty m tan ev ) -5 (10 m 7 6 preliminary KamLAND + SNO 95% C.L. 99% C.L % C.L. best fit tan m is measured at.8% precision by KamLAND [I. Shimizu (KamLAND), TAUP 007] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 1
13 Atmospheric Neutrinos e + νe νµ π + p π µ + µ νµ νµ νµ νe e N( + ) N( e + e ) ³ at E 1GeV uncertainty on ratios: 5% uncertainty on fluxes: 30% ratio of ratios dn/dlne, (Kt.yr) sub GeV multi GeV stopping muons through-going muons E ν, GeV (m.yr.ster) -1 R [N( + )N( e + e )] data [N( + )N( e + e )] MC R K sub-gev R K multi-gev = [Kamiokande, PLB 80 (199) 146] = [Kamiokande, PLB 335 (1994) 37] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
14 Super-Kamiokande Up-Down Asymmetry A θ AB z E 1GeV µ isotropic flux of cosmic rays ν α B (A) «( AB z ) = (B) «( AB z ) (A) «(A) «( z ) = (A) ( AB z «( z ) ) = (B) «(z AB ) π θ AB z up N A up-down (SK) = (December 1998) N down N up + N down = [Super-Kamiokande, Phys. Rev. Lett. 81 (1998) 156, hep-ex/ ] 6 MODEL INDEPENDENT EVIDENCE OF DISAPPEARANCE! C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
15 Fit of Super-Kamiokande Atmospheric Data 10 - Measure of CC Int. is Difficult: E th = 35 GeV =µ 0eventsyr -Decay =µ Many Final States m (ev ) 10-3 Best Fit: 99% C.L. 90% C.L. 68% C.L sin θ m = ev sin = live-days (Apr 1996 Jul 001) [Super-Kamiokande, PRD 71 (005) 11005, hep-ex/ ] -Enriched Sample N the = 78 m = ev N exp = N 4 [Super-Kamiokande, PRL 97(006) , hep-ex/ ] Future Check: OPERA ( ) CERN to Gran Sasso (CNGS) L ³ 73 km E ³ 18 GeV [NJP 8 (006) 303, hep-ex/061103] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
16 Kamiokande, Soudan-, MACRO and MINOS m (ev ) Kamiokande up µ 90%CL CDHSW 10 - Kamiokande contained 10-3 Kamiokande up µ 95%CL Kamiokande contained + up µ sin θ [Kamiokande, PRL 81 (1998) 016, hep-ex/ ] [Soudan, PRD 7 (005) 05005, hep-ex/ ] m (ev ) 10-1: Angular distribution : Energy(Low/High) 1+ m (ev ) % C.L. 90 % C.L. - lnl=.3 Best fit MINOS Atmospheric ν 418 days exposure sin θ [MACRO, PLB 566 (003) 35, hep-ex/ ] sin θ [MINOS, PRD 73 (006) 0700, hep-ex/051036] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
17 KK KEK to Kamioka (Super-Kamiokande) L ³ 50km E ³ 13GeV confirmation of atmospheric allowed region (June 00) events/0.gev m [10-3 ev ] rec E ν GeV 1 KK 68% KK 90% KK 99% SK L/E 90% sin (θ) best fit: m = ev sin = 100 [KK, PRD 74 (006) 07003, hep-ex/060603] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
18 MINOS Fermilab to Soudan Mine (Minnesota) L ³ 730km E ³ 35GeV [MINOS, TAUP 007] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
19 Experimental Evidences of Neutrino Oscillations Solar e Reactor e disappearance Atmospheric Accelerator disappearance ¼ ¼ Homestake Kamiokande/Super-K GALLEX/GNO SAGE Super-Kamiokande SNO BOREXino (KamLAND) Kamiokande IMB Super-Kamiokande MACRO Soudan- (KK & MINOS) ½ ½ m SUN = 759 (1 003) 10 5 ev sin SUN = [I. Shimizu (KamLAND), TAUP 007] matm = ev sin ATM = [Fogli et al, PRD 75 (007) , hep-ph/ ] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
20 Three-Neutrino Mixing «L = 3 k=1 U «k kl («= e ) three flavor fields e,, three massive fields 1,, 3 m SUN = m 1 ³ ev m ATM ³ m 31 ³ m 3 ³ ev C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 0
21 Allowed Three-Neutrino Schemes Ñ Ñ ¾ ËÍÆ Ñ ¾ ½ Ñ ¾ ÌÅ Ñ ¾ ÌÅ ¾ Ñ ¾ ËÍÆ ½ normal inverted different signs of m 31 ³ m 3 absolute scale is not determined by neutrino oscillation data C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 1
22 Mixing Matrix ËÍÆ Í ½ Í ¾ Í δm (ev ) 1 Analysis A ν e ν x 90% CL Kamiokande (multi-gev) m 1 m 31 Í Í ½ Í ¾ Í % CL Kamiokande (sub+multi-gev) Í ½ Í ¾ Í ÌÅ 10 - CHOOZ: m CHOOZ = m 31 = m ATM sin CHOOZ = 4U e3 (1 U e3 ) U e for m 10 ev % CL 95% CL SOLAR AND ATMOSPHERIC OSCILLATIONS ARE PRACTICALLY DECOUPLED! sin (θ) [CHOOZ, PLB 466 (1999) 415] see also [Palo Verde, PRD 64 (001) 11001] TWO-NEUTRINO SOLAR and ATMOSPHERIC OSCILLATIONS ARE OK! sin SUN = U e 1 U e3 ³ U e sin ATM = U 3 [Bilenky, C.G, PLB 444 (1998) 379] [Guo, Xing, PRD 67 (003) 05300] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007
23 Standard Parameterization of Mixing Matrix ¼ U = c 3 s 3 0 s 3 c 3 = ¼ 3 ³ ATM ¼ el L L ½¼ ½ ¼ = U e1 U e U e3 U 1 U U 3 U 1 U U 3 c 13 0 s 13 e i Æ s 13 e i Æ13 0 c = CHOOZ ½¼ ½¼ 1L L 3L ½ c 1 s 1 0 s 1 c ³ SUN c 1c 13 s 1c 13 s 13e i Æ 13 s 1c 3 c 1s 3s 13e i Æ 13 c 1c 3 s 1s 3s 13e i Æ 13 s 3c 13 s 1s 3 c 1c 3s 13e i Æ 13 c 1s 3 s 1c 3s 13e i Æ 13 c 3c 13 ½¼ ½¼ e i e i e i e i 3 0 ½ ½ C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 3
24 Global Fit of Oscillation Data: Bilarge Mixing 10 m 1 [10-5 ev ] tan θ 1 sin θ 13 4 m 31 [10-3 ev ] tan θ 3 sin θ 13 [Gonzalez-Garcia, Maltoni, arxiv: ] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 4
25 m 1 = m ev = 6 0(06) 10 3 ev ¼ U 90% = ¼ U 3 = 1 = = = ½ ½ [Gonzalez-Garcia, Maltoni, arxiv: ] future: measure 13 = 0 =µ CP violation, matter effects, mass hierarchy C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 5
26 Absolute Scale of Neutrino Masses normal scheme inverted scheme 10 0 QUASI DEGENERATE 10 0 QUASI DEGENERATE 10 1 m m m1 m [ev ] 10 m m [ev ] m1 NORMAL SCHEME 10 3 m3 INVERTED SCHEME NORMAL HIERARCHY Lightest Mass: m1 [ev ] INVERTED HIERARCHY Lightest Mass: m3 [ev ] 10 0 m = m 1 + m 1 = m 1 + m SUN m 3 = m 1 + m 31 = m 1 + m ATM m 1 = m 3 m 31 = m 3 + m ATM m = m 1 + m 1 ³ m 3 + m ATM Quasi-Degenerate for m 1 ³ m ³ m 3 ³ m Ô m ATM ³ 5 10 ev C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 6
27 3 H 3 He + e + e Tritium Beta-Decay Õ dγ dt = (coscgf) Å F(E)pE (Q T) (Q T) m 3 e Q = M3 H M3 He m e = 1858keV m e = m = k U ek m k K(T) = ÚÙ Ù Ø 3 Kurie plot dγdt = (coscg F) Å F(E)pE (Q T) Õ 1 (Q T) m e K(T) m νe = m νe = 100 ev T Q m νe Q m e ev (95% C.L.) Mainz & Troitsk [Weinheimer, hep-ex/010050] future: KATRIN (start 010) [hep-ex/ ] [hep-ex/ ] sensitivity: m e ³ 0eV C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 7
28 m e = m = U e1 m 1 + U e m + U e3 m NORMAL SCHEME 10 1 INVERTED SCHEME 10 0 Mainz & Troitsk 10 0 Mainz & Troitsk mβ [ev ] 10 1 m3 KATRIN mβ [ev ] 10 1 m1,m KATRIN 10 m 10 m1 m Lightest Mass: m 1 [ev ] Quasi-Degenerate: m 1 ³ m ³ m 3 ³ m =µ m ³ m Lightest Mass: m 3 [ev ] k U ek = m FUTURE: IF m 4 10 ev =µ NORMAL HIERARCHY C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 8
29 Neutrinoless Double-Beta Decay + β As 0 + β 76 3Ge β β Se C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 9
30 Two-Neutrino Double- Decay: L = 0 Æ(A Z) Æ(A Z + ) + e + e + e + e Ï Ù (T 1 ) 1 = G Å second order weak interaction process in the Standard Model Ï Ù Neutrinoless Double- Decay: L = Æ(AZ) Æ(AZ + ) + e + e (T 0 1 ) 1 = G 0 Å 0 m Ï Í Ù effective Majorana mass m = k U ek m k Ñ Í Ï Ù C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
31 Majorana Neutrino Mass? ν 1 ν ν 3 u d s e µ c b τ t m [ev] known natural explanation of smallness of masses New High Energy Scale Å µ both imply See-Saw Mechanism (if R s exist) 5-D Non-Renormaliz. Eff. Operator Majorana masses µ L = µ 0 see-saw type relation m Å EW Å Majorana neutrino masses provide the most accessible window on New Physics Beyond the Standard Model decay C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
32 Effective Majorana Neutrino Mass m = k U ek m k complex U ek µ possible cancellations m = U e1 m 1 + U e e i «m + U e3 e i «3 m 3 «= «3 = ( 3 Æ 13 ) Im[m ββ ] m ββ U e3 e iα 3 m 3 U e e iα m U e1 m 1 Re[m ββ ] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre 007 3
33 Experimental Bounds T y T y Heidelberg-Moscow ( 76 Ge) [EPJA 1 (001) 147] T y T y (90% C.L.) =µ m 03 10eV IGEX ( 76 Ge) [PRD 65 (00) 09007] (90% C.L.) =µ m eV CUORICINO ( 130 Te) [PRL 95 (005) 14501] (90% C.L.) =µ m 0 11eV NEMO 3 ( 100 Mo) [PRL 95 (005) 1830] (90% C.L.) =µ m 07 8eV FUTURE EXPERIMENTS CAMEO, CANDLES, COBRA, EXO, Majorana, XMASS m few10 1 ev CUORE, MOON, GEM, GERDA, SNO++, Super-NEMO m few10 ev C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
34 Bounds from Neutrino Oscillations m = U e1 m 1 + U e e i «m + U e3 e i «3 m NORMAL SCHEME 10 1 INVERTED SCHEME mββ [ev] EXP CP violation mββ [ev] EXP CP violation LightestMass: m 1 [ev] LightestMass: m 3 [ev] 10 1 FUTURE: IF m 10 ev =µ NORMAL HIERARCHY C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
35 Experimental Positive Indication [Klapdor et al., MPLA 16 (001) 409] T 0 1 = ( ) 105 y 65 evidence [MPLA 1 (006) 1547] Counts / kev SSE nb Rosen Primakov Approximation Q=039 kev Energy,keV [PLB 586 (004) 198] [MPLA 1 (006) 1547] the indication must be checked by other experiments m = eV [MPLA 1 (006) 1547] if confirmed, very exciting (Majorana and large mass scale) C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
36 Cosmology H 0 (Hubble Space Telescope Key Project) CMBR (COBE, WMAP, Boomerang, DASI, MAXIMA, VSA, CBI, ACBAR) LSS (dfgrs, SDSS) SNIa (High-z SN Search Team, Supernova Cosmology Project) ΛCDM =µ 3 k=1 m k 0 07eV C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
37 LSND and MiniBooNE m (ev /c 4 ) e Karmen Bugey CCFR NOMAD ) 4 /c (ev m 10 1 e MiniBooNE 90% C.L.y KARMEN 90% C.L. Bugey 90% C.L % (L max -L <.3) 99% (L max -L < 4.6) sin θ [LSND, PRD 64 (001) 11007, hep-ex/ ] m LSND 01eV LSND 90% C.L. LSND 99% C.L sin (θ) [MiniBooNE, PRL 98 (007) 31801, arxiv: ] e is running m LSND m ATM m SUN C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
38 MiniBooNE Low-Energy Anomaly events / MeV ν oscillation analysis threshold MiniBooNE datay expected backgroundgν µ BG + best-fit ν µ ν e ν µ background ν µ background ν e 0.5 excess events / MeV data - expected background best-fit ν µ ν e sin (θ)=0.004, m =1.0 ev sin (θ)=0., m =0.1 ev ν µ ν µ reconstructed E ν (MeV) [MiniBooNE, PRL 98 (007) 31801, arxiv: ] C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
39 Conclusions e with msun ³ ev (solar, KamLAND) with matm ³ ev (atm., KK, MINOS) Bilarge 3-Mixing with U e3 1 (CHOOZ) Decay, Cosmology, 0 Decay =µ m 1eV Exp.: Theory: FUTURE Why lepton mixing = quark mixing? Why only U e3 1? Improve calculation of Å 0! LSND and MiniBooNE Low-Energy Anomaly? Measure U e3 0 µ CP violation, matter eff., mass hierarchy Check 0 signal at Quasi-Degenerate mass scale Improve Decay, Cosmology, 0 Decay measurements LSND and MiniBooNE Low-Energy Anomaly? C. Giunti Neutrino Mixing SIF, XCIII Congresso Nazionale, Pisa, 5 Settembre
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