Status of Neutrino Masses and Mixing

Transcription

1 Status of Neutrino Masses and Mixing Carlo Giunti INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Università di Torino POSTECH, Pohang, Korea, October 004 Introduction to Neutrino Mass, Mixing and Oscillations Solar ν e ν µ, ν τ + Atmospheric ν µ ν τ = Three-Neutrino Mixing Absolute Scale of Neutrino Masses Cosmological Bound on Neutrino Masses Neutrinoless Double-β Decay Majorana Mass Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004

2 Neutrino Mass Standard Model: ν L, ν R = no Dirac mass term ν L ν R (no ν R, ν L ) Majorana neutrino: ν = ν = ν R = ν R = Majorana mass term ν L ν R Standard Model: Majorana mass term is not allowed by SU() L U() Y (no Higgs triplet) Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004

3 Standard Model: Lepton numbers are conserved L e L µ L τ (ν e, e ) ( νµ, µ ) L e L µ L τ ( ν e, e + ) 0 0 ( νµ, µ +) 0 0 L = L e + L µ + L τ (ν τ, τ ) ( ν τ, τ + ) 0 0 Dirac mass = L e, L µ, L τ are not conserved, M = but L is conserved (ν ν) m ee m eµ m eτ m µe m µµ m µτ m τe m τµ m ττ Majorana mass = L, L e, L µ, L τ are not conserved (ν = ν L(ν) = L( ν)) Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 3

4 no reason not to extend the Standard Model with ν R (e L, e R ; u L, u R ; d L, d R ;... ) ν L + ν R = Dirac neutrino mass term ν L ν R (as all other particles) surprise: also Majorana neutrino mass for ν R is allowed! Lagrangian neutrino mass term ( ) 0 m D ν R ν L ν L m D m M R ν R m D 00 GeV, but m M R can be arbitrarily large (not protected by any symmetry) natural that m M R scale of new physics beyond the Standard Model = mm R md diagonalization of 0 m D m D m M R = m (md ), m m M R m M R ν ν see-saw mechanism natural explanation of smallness of neutrino masses massive neutrinos are Majorana! [Minkowski, Phys. Lett. B 67 (977) 4] [Yanagida, 979] [Gell-Mann, Ramond, Slansky, 979] [Mohapatra, Senjanovic, Phys. Rev. Lett. 44 (980) 9] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 4

5 Neutrino Oscillations [Pontecorvo, Sov. Phys. JETP 6 (957) 49] [Pontecorvo, Sov. Phys. JETP 7 (958) 7] [Gribov, Pontecorvo, Phys. Lett. B 8 (969) 49] [Eliezer,Swift, Nucl. Phys. B 05 (976) 45] [Fritzsch, Minkowski,Phys. Lett. B 6 (976) 7] [Bilenky, Pontecorvo, Sov. J. Nucl. Phys. 4 (976) 36] [Bilenky, Pontecorvo, Nuovo Cim. Lett. 7 (976) 56] [Bilenky, Pontecorvo, Phys. Rept. 4 (978) 5] α = e, µ, τ ν α = U αk ν k ν k m k Neutrino Mixing k ν α (x, t) = ν k (x, t) = e ie kt+ip k x ν k = ν α (x, t) = β=e,µ,τ U αk e ie kt+ip k x U βk ν β k } {{ } να ν β (x,t) U αk e ie kt+ip k x ν k k ν k = U βk ν β β=e,µ,τ Transition Probability P να ν β (x, t) = ν β ν α (x, t) = να νβ(x, t) = U αk e ie kt+ip k x U βk k Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 5

6 ultrarelativistic neutrinos = t x = L source-detector distance E k t p k x ( E k p k ) L = E k p k E k + p k L = m k E k + p k L m k E L P να ν β (L, E) = = U αk e im k LE U βk k U αk U βk constant term k m + Re U αk U βk U αj U βj exp i kj L E k>j m kj m k m j oscillating term coherence [Nussinov, Phys. Lett. B 63 (976) 0] [Kayser, Phys. Rev. D 4 (98) 0], [Giunti, Kim, Lee, Phys. Rev. D44 (99) 3635] [Kiers,Nussinov, Weiss, Phys. Rev. D53 (996) 53] [Giunti, Kim, Phys. Rev. D 58 (998) 0730] [Giunti, Kim, Found. Phys. Lett. 4 (00) 3], [Beuthe, Phys. Rept. 375 (003) 05], [Giunti, Found. Phys. Lett. 7 (004) 03] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 6

7 Two-Neutrino Mixing cos ϑ sin ϑ k =, = U = sin ϑ cos ϑ m m m m ( ) m Transition Probability (α β): P να ν β (L, E) = sin ϑ sin L 4E Survival Probability (α = β): P να ν α (L, E) = P να ν β (L, E) Averaged Transition Probability: P να ν β = sin ϑ m = 0 3 ev sin ϑ = E = GeV E = 0. GeV Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 7

8 Solar Neutrinos [J.N. Bahcall, jnb] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 8

9 Main Characteristics of Solar ν Data!#" $ %!'& ( )* +, , :; <= > :; <? DC C E E F FG : H? G I H G FG FG ; K L G ; M N G ; : O P. 3.4 Q,R -. S S T U 89 K : VW > K : YX DC C S - 5 : H? G I H G FG FG ; K L G ; M N G ; : O - P E 4 E [ U \ Q P 3 - S. P ] ^_ ` \ 5.4 Q ba [ c > 5 P Q 0 - ed f` \ 5 Q 4 - E 89 g > F 9 F C C Q. I H E 4 R h i N kj 9 g > F 9 l 9 R C m ^fc e \ S S > g > F 9 F C C Q. P 4 R L = VW kj 9 g > F 9 l 9 R C - 0 ] nec ] \. 4 S > 3 SE 4 3 Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 9

10 SNO Φ SNO CC Φ SNO NC Φ SNO ν e Φ SNO ν µ,ν τ =.76 ± cm s = 5.09 ± cm s =.76 ± cm s = 5.4 ± cm s SNO SOLVED SOLAR NEUTRINO PROBLEM NEUTRINO PHYSICS (April 00) [SNO, Phys. Rev. Lett. 89 (00) 030, nucl-ex004008] ν e ν µ, ν τ oscillations Large Mixing Angle solution m ev tan ϑ %, 95%, 99%, 99.73% (3σ) C.L. [Fogli, Lisi, Marrone, Montanino, Palazzo, PRD 66 (00) 05300] see also [SNO, PRL 89 (00) 030] [Barger, Marfatia, Whisnant, Wood, PLB 537 (00) 79] [Bahcall, Gonzalez-Garcia, Peña-Garay, JHEP 07 (00) 054] [SK, PLB 539 (00) 79] [de Holanda, Smirnov, PRD66 (00) 3005] [Aliani et al., PRD 67 (003) 03006] [Bandyopadhyay et al., PLB 540 (00) 4] [Creminelli, Signorelli, Strumia, hep-ph0034] [Maltoni, Schwetz, Tortóla, Valle, PRD 67 (003) 030] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 0

11 KamLAND spectacular confirmation of LMA (December 00) NobsNexp ILL Savannah River Bugey Rovno Goesgen Krasnoyarsk Palo Verde Chooz KamLAND Distance to Reactor (m) Shade: 95% C.L. LMA m = ev Curve: sin ϑ = 0.83 ) (ev m Rate excluded Rate+Shape allowed LMA Palo Verde excluded Chooz excluded sin 95% C.L. θ [KamLAND, Phys. Rev. Lett. 90 (003) 080, hep-ex00] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004

12 KamLAND: Evidence of Spectral Distortion hep-ex , June 004 Events 0.45 MeV no-oscillation best-fit oscillation accidentals KamLAND data Ratio MeV prompt analysis threshold KamLAND data best-fit oscillation best-fit decay best-fit decoherence E (MeV) Fri Jun :43: prompt L 0 E νe (kmmev) L 0 = 80 km The confidence level for reactor ν e disappearance is now %. The observed energy spectrum disagrees with the expected spectral shape in the absence of neutrino oscillation at the 99.9% confidence level but agrees with the distortion expected from ν e oscillation effects. Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004

13 Combined Fit of Solar + Reactor Neutrino Data [KamLAND, hep-ex ] ) (ev m ) (ev m Solar 95% C.L. 99% C.L % C.L. solar best fit tan θ KamLAND 95% C.L. 99% C.L % C.L. KamLAND best fit tan θ KamLAND+Solar fluxes 95% C.L. 99% C.L % C.L. global best fit Best Fit: m = ev tan ϑ = Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 3

14 Atmospheric Neutrinos N(ν µ + ν µ ) N(ν e + ν e ) at E GeV uncertainty on ratios: 5% uncertainty on absolute fluxes: 30% R ratio of ratios [ N(νµ + ν µ )N(ν e + ν e ) ] data [ N(νµ + ν µ )N(ν e + ν e ) ] MC R K sub-gev = 0.60 ± 0.07 ± 0.05 [Kamiokande, Phys. Lett. B 80 (99) 46] R K multi-gev = 0.57 ± 0.08 ± 0.07 [Kamiokande, Phys. Lett. B 335 (994) 37] R SK sub-gev = 0.6 ± 0.03 ± 0.05 [Super-Kamiokande, Phys. Lett. B 433 (998) 9, hep-ex ] R SK multi-gev = 0.66 ± 0.06 ± 0.08 [Super-Kamiokande, Phys. Lett. B 436 (998) 33, hep-ex ] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 4

15 Super-Kamiokande Up-Down Asymmetry Plane tangent to S ν µ entering S any ν entering the sphere S later exits it ν µ exiting S steady state Φ in (S) = Φ out (S) Sample ν µ path Detector Earth S E ν GeV isotropic flux of cosmic rays homogeneity Φ in (s) = Φ out (s), s S D S Φ up (D) = Φ down (D), [B. Kayser, Review of Particle Properties, PRD 66 (00) 0000] A up-down ν µ (SK) = N up ν µ N up ν µ N down ν µ + N down ν µ = 0.96 ± ± 0.0 (December 998) [Super-Kamiokande, Phys. Rev. Lett. 8 (998) 56, hep-ex ] 6σ MODEL INDEPENDENT EVIDENCE OF ν µ DISAPPEARANCE! Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 5

16 Super-Kamiokande Evidence of Oscillations hep-ex , April 004 Number of events LE (kmgev) Number of events as a function of LE for the data (points) and the atmospheric neutrino MC events without oscillations (histogram). DataPrediction (null osc.) LE (kmgev) Ratio of the data to the MC events without neutrino oscillation (points) as a function of LE together with the best-fit expectations for ν µ ν τ oscillations (solid line), neutrino decay (dashed line) and neutrino decoherence (dotted line). Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 6

17 ν µ ν τ Fit of Super-Kamiokande Atmospheric Data 0 - m (ev ) Best Fit: m = ev sin θ =.0 99% C.L. 90% C.L. 68% C.L. [Super-Kamiokande, hep-ex ] sin θ Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 7

18 Soudan- & MACRO 0 - m (ev ) SOUDAN MACRO SK sin (θ) [Giacomelli, Giorgini, Spurio, hep-ex0003] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 8

19 KK confirmation of atmospheric allowed region (June 00) Events 0 8 m (ev ) E ν rec 0-4 [KK, Phys. Rev. Lett. 90 (003) 0480] sin θ Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 9

20 KK: Evidence of Spectral Distortion June 004 KK energy spectrum (data points), compared to the scaled KEK beam spectrum (black histogram) and the best-fit expected spectrum taking into account neutrino oscillations (red histogram). 90% confidence regions for ν µ ν τ oscillation from KK (green) and Super-Kamiokande atmospheric neutrinos (black). Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 0

21 Experimental Evidences of Neutrino Oscillations Solar ν e ν µ, ν τ Homestake, Kamiokande, GALLEX, SAGE, GNO, Super-Kamiokande, SNO Reactor ν e disappearance (KamLAND) = m best fit SUN = < m SUN < [ ] ev (3σ) [Bahcall, Gonzalez-Garcia, Pena-Garay, hep-ph040694] Atmospheric ν µ ν τ Kamiokande, IMB, Super-Kamiokande, MACRO, SOUDAN Accelerator ν µ disappearance (KK) = m best fit ATM = < m ATM < [ ] ev (3σ) [Fogli, Lisi, Marrone, Montanino, PRD 67 (003) ] Three-Neutrino Mixing flavor fields ν α, α = e, µ, τ ν αl = 3 U αk ν kl k= massive fields ν k m k m SUN = m m ATM m 3 m 3 Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004

22 Allowed Three-Neutrino Schemes normal inverted absolute scale is not determined by neutrino oscillation data Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004

23 δm (ev ) Analysis A ν e ν x 90% CL Kamiokande (multi-gev) m m % CL Kamiokande (sub+multi-gev) CHOOZ: m = CHOOZ m = 3 m ATM sin ϑ CHOOZ = 4 U e3 ( U e3 ) U e3 < 5 0 (99.73% C.L.) % CL [Fogli et al., PRD 66 (00) ] 90% CL SOLAR AND ATMOSPHERIC ν OSCILLATIONS ARE PRACTICALLY DECOUPLED! sin (θ) [CHOOZ, PLB 466 (999) 45] see also [Palo Verde, PRD 64 (00) 00] TWO-NEUTRINO SOLAR and ATMOSPHERIC ν OSCILLATIONS ARE OK! sin ϑ SUN = U e U e3 U e sin ϑ ATM = U µ3 [Bilenky, Giunti, PLB 444 (998) 379] [Guo, Xing, PRD 67 (003) 05300] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 3

24 Standard Parameterization of Mixing Matrix U = R 3 W 3 R 0 0 c 3 0 s 3 e iδ 3 c s 0 = 0 c 3 s s c 0 0 s 3 c 3 s 3 e iδ 3 0 c ϑ 3 ϑ ATM ϑ 3 = ϑ CHOOZ ϑ = ϑ SUN = c c 3 s c 3 s 3 e iδ 3 s c 3 c s 3 s 3 e iδ 3 c c 3 s s 3 s 3 e iδ 3 s 3 c 3 s s 3 c c 3 s 3 e iδ 3 c s 3 s c 3 s 3 e iδ 3 c 3 c 3 sin ϑ CHOOZ = U e3 = sin ϑ 3 sin ϑ SUN = U e U e3 = s c 3 s 3 = sin ϑ sin ϑ ATM = U µ3 = s 3 c 3 sin ϑ 3 Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 4

25 U e3 U Bilarge Mixing c ϑs s ϑs 0 s ϑs c ϑa c ϑs c ϑa s ϑa s ϑs s ϑa c ϑs s ϑa c ϑa ν e = c ϑs ν + s ϑs ν ν (S) a = s ϑs ν + c ϑs ν = c ϑa ν µ s ϑa ν τ c ϑs s ϑs 0 sin ϑ A ϑ A π 4 U s ϑs c ϑs s ϑs c ϑs ( ) Solar ν e ν (S) a νµ ν τ Φ SNO CC Φ SSM νe 3 = Φ ν e Φ νµ Φ ντ for E 6 MeV LMA tan ϑ S 0.4 ϑ S π 6 U Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 5

26 Global Fit of Oscillation Data Bilarge Mixing [Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, hep-ph ] m bf ev m (3σ) m bf ev m (3σ) sin ϑ bf sin ϑ 0.37 (3σ) sin ϑ bf sin ϑ (3σ) sin ϑ bf ATM sin ϑ ATM 0.86 (3σ) [Fogli, Lisi, Marrone, Montanino, PRD 67 (003) ] sin ϑ ATM = U µ3 = sin ϑ 3 cos ϑ U bf U Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 6

27 Open Questions on Neutrino Masses Value of U e3, J CP? ν Oscillations Sterile Neutrinos? ν Oscillations LSND indication = wait MiniBooNE Absolute Scale of Neutrino Masses? β Decay, Cosmology, ββ 0ν Decay Pattern of Neutrino Masses? ν Osc., β Dec., Cosmology, ββ 0ν Dec. Are Neutrinos Majorana? ββ 0ν Decay Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 7

28 Oscillations are Insensitive to Absolute Scale of Neutrino Masses oscillations are due to the interference of different massive components of a flavor ν oscillations can be sensitive only to mass differences In Neutrino Oscillations Dirac = Majorana dν α dt = E ( UM U + EV ) αβ ν β M = diag(m, m, m 3 ) Dirac: U U D Majorana: U U M = U D D U D = c c 3 s c 3 s 3 e iδ s c 3 c s 3 s 3 e iδ c c 3 s s 3 s 3 e iδ s 3 c 3 s s 3 c c 3 s 3 e iδ c s 3 s c 3 s 3 e iδ c 3 c 3 D = diag(, e iλ, e iλ 3 ) Majorana phases U M M U M = U DDM D U D = U DM U D [Bilenky, Hosek, Petcov, PLB 94 (980) 495] [Doi, Kotani, Nishiura, Okuda, Takasugi, PLB 0 (98) 33] [Langacker, Petcov, Steigman, Toshev, NPB 8 (987) 589] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 8

29 6 6 "! & ' ( # $ % Absolute Scale of Neutrino Masses normal scheme inverted scheme m = m + m = m + m SUN m 3 = m + m 3 = m + m ATM Quasi Degenerate for m m m3 mν m = m 3 m 3 = m 3 + m ATM m = m + m m 3 + m ATM m ATM 5 0 ev Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October ), : 6 7 9, 6 79 * : B >;?C D? EB <; =>?@ A> ), 6 7 9, * ) + ) * A > I> > F G C H ; 6 78

30 Tritium β Decay 3 H 3 He + e + ν e dγ dt = (cosϑ CG F ) π 3 Kurie plot: K(T) = F(E) pe (Q T) Q = M3 H M3 He m e = 8.58 kev [ dγdt = (Q T) (cosϑ C G F ) π 3 F(E) pe (Q T) m ν e (Q T) m νe ] m νe <. ev (95% C.L.) Mainz & Troitsk [Weinheimer, hep-ex00050] m νe <.8 ev (95% C.L.) Mainz + Troitsk [Fogli et al., hep-ph ] future: KATRIN [hep-ex009033] [hep-ex ] sensitivity: m νe ev Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

31 Neutrino Mixing = K(T) = (Q T) U ek (Q T) m k k "!! analysis of data is different from the no-mixing case N parameters = N masses + N mixing matrix elements U ek = k Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 3

32 if experiment is not sensitive to masses (m k Q T) = effective mass m β = U ek m k k [McKellar, PLB 97 (980) 93] [Shrock, PLB 96 (980) 59] [Kobzarev, Martemyanov, Okun, Shchepkin, SJNP 3 (980) 83] [Holzschuh, RPP 55 (99) 035] [Weinheimer et al., PLB 460 (999) 9] [Vissani, NPB PS 00 (00) 73 (NOW 000)] [Farzan, Smirnov, PLB 557 (003) 4] K = (Q T) k (Q T) k (Q T) U ek (Q T) m k = (Q T) k U ek m β m k (Q T) = (Q T) (Q T) = (Q T) (Q T) m β U ek m β (Q T) m νe <. ev (95% C.L.) = m β <. ev (95% C.L.) m k (Q T) Three-Neutrino Mixing = m β = c c 3 m + s c 3 m + s 3 m 3 Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 3

33 e ; e N KLM JIH QRST ; m = m + m = m + m SUN m = m 3 m 3 = m 3 + m ATM m 3 = m + m 3 = m + m ATM m = m + m m 3 + m ATM m β m + U e m SUN + U e3 m ATM m β m 3 + ( Ue + Ue ) m ATM Quasi Degenerate: m m m3 mν = m β m ν Uek = m ν FUTURE: IF mβ 4 0 ev = NORMAL HIERARCHY k Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October "$# % & 9 < [$\ ] ^ f h i e f h < e f6h : e f6h ; e f4g 65 f6h < 9 < 65 e f6h : 9 ; ')( *, : 65 _)` a,b.c0d e f6h ; 83 e f8g! OP WR V XYZ O >=?@ C e f e f

34 Cosmological Bound on Neutrino Masses neutrinos are in equilibrium in the primeval plasma through weak interaction reactions ν ν e + e ( ) νe ( ) νe ( ) νn ( ) νn ν e n pe ν e p ne + n pe ν e weak interactions freeze out Γ weak = Nσv G F T5 T M P G N T 4 G N ρ H = T dec MeV neutrino decoupling Relic Neutrinos: T ν = number density: n f = 3 4 ( ) 4 3 Tγ.945 K = k T ν ev (T γ =.75±0.00 K) ζ(3) π g f T 3 f = n νk, ν k 0.87 T 3 ν cm 3 density contribution: Ω k = n ν k, ν k m k ρ c h m k 94.4 ev = Ω ν h = h 0.7, Ω ν = k m k 94.4 ev ( ) ρ c = 3H 8πG N [Gershtein, Zeldovich, JETP Lett. 4 (966) 0] [Cowsik, McClelland, PRL 9 (97) 669] m k 46 ev k Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

35 Power Spectrum of Density Fluctuations hot dark matter prevents early galaxy formation small scale suppression P(k) P(k) 8 Ω ( ) ( ) ν k m k Ω m ev Ω m h for k k nr 0.06 mν ev Ωm h Mpc [Hu, Eisenstein, Tegmark, PRL 80 (998) 555] [SDSS, astro-ph03075] Reviews: [Dolgov, Phys. Rept. 370 (00) 33], [Kainulainen, Olive, hep-ph00663], [Sarkar, hep-ph03075], [Hannestad, NJP 6 (004) 08] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

36 WMAP, AJ SS 48 (003) 75 CMB (WMAP, CBI, ACBAR) + LSS (dfgrs) + Lyα + HST + SN-Ia T 0 = 3.7 ± 0. Gyr h = ΛCDM:, Ω tot =.0 ± 0.0 Ω b h = 0.04 ± Ω m h = Ω ν h < (95% confidence) = m k < 0.7 ev Hannestad, JCAP 0305 (003) 004 k m k <.0 ev (95% confidence) WMAP+CBI+dFGRS+HST+SN-Ia k m k <.0 ev (95% confidence) WMAP+CBI+dFGRS k m k <. ev (95% confidence) WMAP+dFGRS Elgaroy and Lahav, JCAP 04 (003) 004 k m k <. ev (95% confidence) WMAP+dFGRS+HST k Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

37 SDSS, PRD 69 (004) 0350 CMB(WMAP)+LSS(SDSS)+SN-Ia h = Ω 0.03 m = 0.30 ± 0.04 k m k <.7 ev SDSS, astro-ph (95% confidence) CMB(WMAP)+LSS(SDSS)+bias(SDSS) Ω m = 0.5 ± 0.03 k m k < 0.54 ev P g (k) = b P m (k) (95% confidence) SDSS, astro-ph CMB(WMAP)+LSS(SDSS)+bias(SDSS)+Lyα(SDSS)+SN-Ia Ω Λ = 0.7 ± 0.0 k m k < 0.4 ev (95% confidence) Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, hep-ph k m k <.4 ev (σ) CMB+LSS+HST+SN-Ia k m k < 0.47 ev (σ) CMB+LSS+HST+SN-Ia+Lyα(SDSS) Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

38 ( S ( S : : H F F I JK L M )-, ( )-, ( )-, ( )+* T-V I S T-V G S T-V H )-, F I ( )-, S T-V G!#"%$'& ( )., N O#P%Q'R F G S T.V H D EF E ; < >=?@ A?@ A B C ; ; < >=?@ A A ; ( )+* S T+U Approximate Estimate mk ev ( σ) CMB+LSS+HST+SN-Ia k k mk 0.5 ev ( σ) CMB+LSS+HST+SN-Ia+Lyα FUTURE: IF k mk 8 0 ev = NORMAL HIERARCHY Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October T-V I S T+U

39 Majorana Neutrino Mass? known natural explanations of smallness of ν masses: See-Saw Mechanism 5-D Non-Renormalizable Effective Operator both imply Majorana ν masses L = ββ 0ν decay see-saw type relation m ν new high energy scale EW Majorana neutrino masses provide the most accessible window on New Physics Beyond the Standard Model Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

40 Two-Neutrino Double-β Decay: L = 0 (A, Z) (A, Z + ) + e + e + νe + νe (T ν ) = G ν ν second order weak interaction process in the Standard Model Neutrinoless Double-β Decay: L = (A, Z) (A, Z + ) + e + e (T 0ν ) = G 0ν 0ν m ββ effective Majorana mass m ββ = U ek m k k Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

41 Majorana Neutrino Mass ββ 0ν Decay [Schechter, Valle, PRD 5 (98) 95] [Takasugi, PLB 49 (984) 37] Majorana Mass Term: M el = m ( ν c el ν ) el + ν el ν c el = m ( ν T el ν el + ν el ν el ) two conditions: u, d, e are massive standard left-handed weak interaction exists cancellations with other diagrams are very unlikely (unstable under perturbations) Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 4

42 The Problem of Calculation of Nuclear Matrix Elements (T 0ν ) = G 0ν 0ν m ββ m ββ = U ek m k k [Cremonesi, NPB PS 8 (003) 87] traditional estimated range for 0ν : about one order of magnitude about factor of 3 range for 0ν and m ββ Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 4

43 76 Ge 0ν m ββ [ev] Method Reference.35.4 QRPA with np pairing Pantis et al. (999) Large-scale shell model Caurier et al. (996) QRPA Bobyk et al. (00) Full RQRPA Simkovic et al. (997) RQRPA with forbidden Rodin et al. (003) RQRPA Stoica and Klapdor-K. (00) QRPA with forbidden Rodin et al. (003) QRPA Stoica and Klapdor-K. (00) Full RQRPA Stoica and Klapdor-K. (00) RQRPA Bobyk et al. (00) RQRPA with forbidden Simkovic et al. (999) QRPA Suhonen et al. (99) QRPA Pantis et al. (996) Number-projected QRPA Suhonen et al. (99) Second QRPA Stoica and Klapdor-K. (00) QRPA Barbero et al. (999) RQRPA Faessler and Simkovic (998) QRPA Civitarese and Suhonen (003) RQRPA Simkovic et al. (999) QRPA Muto et al. (989), Staudt et al. (990) QRPA Tomoda (99) QRPA Aunola and Suhonen (998) [Elliott, Engel, J. Phys. G 30 (004) R83] (T 0ν ) = G 0ν 0ν m ββ G 0ν = y ev unrealistic calculations excluded.35 0ν 4. about factor of 3 range for 0ν and m ββ other estimates [Bahcall et al, PRD 70 (004) 0330] [Fogli et al, hep-ph ] [Deppisch, Paes, Suhonen, hep-ph ] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

44 Indication of ββ 0ν Decay at Quasi Degenerate Mass Scale [Klapdor-Kleingrothaus, Dietz, Harney, Krivosheina, Mod. Phys. Lett. A6 (00) 409] [Klapdor-Kleingrothaus, Dietz, Krivosheina, Found. Phys. 3 (00) 8] [Klapdor-Kleingrothaus, Dietz, Chkvorez, Krivosheina, NIMA 5 (004) 37] [Klapdor-Kleingrothaus, Krivosheina, Dietz, Chkvorets, PLB 586 (004) 98] 0ν bf T = y T 0ν = ( ) 05 y (3σ) 4.σ evidence SSE nb Rosen Primakov Approximation CountskeV 3 Counts kev Q=039 kev Energy, kev Energy,keV pulse-shape selected spectrum 3.8σ evidence [PLB 586 (004) 98] the indication must be checked by other experiments.35 0ν 4. = 0. ev m ββ.6 ev if confirmed very exciting (Majorana ν and large mass scale) Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

45 Best limits for ββ 0ν Decay Heidelberg-Moscow 76 Ge [EPJA (00) 47] T 0ν >.9 05 y (90% C.L.) = m ββ ev (90% C.L.) IGEX 76 Ge [PRD 65 (00) 09007] T 0ν > y (90% C.L.) = m ββ ev (90% C.L.) FUTURE EXPERIMENTS NEMO3, CUORICINO, COBRA, XMASS, CAMEO, CANDLES EXO, MOON, Super-NEMO, CUORE, Majorana, GEM, GERDA m ββ few 0 ev m ββ few 0 ev see [Zdesenko, RMP 74 (00) 663], [Elliott,Vogel, Ann. Rev. Nucl. Part. Sci. 5 (00) 5], [Elliott, Engel, J. Phys. G 30 (004) R83] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

46 Neutrino Oscillations Bounds for ββ 0ν Decay m ββ = U ek m k k complex U ek possible cancellations Im[m ββ ] m ββ U e3 e iα 3 m3 m ββ = U e m + U e e iλ m + U e3 e i(λ 3 δ) m 3 = U e m + U e e iα m + U e3 e iα 3 m 3 U e m U e e iα m Re[m ββ ] conserved CP = δ = 0 λ kj = α kj = 0, π = e iλ kj = e iα kj = ± δ 0 = calling Majorana phases λ kj or α kj is a convention c c 3 s c 3 s 3 e iδ s 3 c 3 0 e iλ 0 = c 3 c e iλ 3 c c 3 s c 3 s s 3 c 3 e iδ 0 e iα c 3 c 3 e iδ 0 0 e iα 3 Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

47 m ββ = Normal Hierarchy m m m 3 U ek m k U e m + U e3 m 3 = U e m + U e3 e i(α 3 α ) m 3 U e m + U e3 m 3 k m m m SUN m 3 m 3 m ATM U e m U e3 m ν contribution U e m may be dominant! (no cancellation = lower limit for m ββ ) [Giunti, PRD 6 (000) 03600] overlap of allowed ranges for U e m and U e3 m 3 = strong cancellation is possible in any case: m ββ ev [Vissani, JHEP 06 (999) 0] [Bilenky et al, PLB 465 (999) 93] the difference α 3 α of the two Majorana phases is potentially measurable m ββ U e 4 m SUN + U e3 4 m ATM + U e U e3 m m cos(α SUN ATM 3 α ) [Bilenky, Pascoli, Petcov, PRD 64 (00) 05300] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

48 CP Conservation: Normal Scheme λ = α = 0 λ 3 = α 3 = λ = α = π λ 3 = α 3 = π mββ [ev] H-M & IGEX m 3 m m mββ [ev] H-M & IGEX m 3 m m m ββ U e m + U e e iα m + m SUN + U e3 e iα 3 m + m ATM m 0 [ev] λ = α = 0 λ 3 = α 3 = π λ = α = π 0 m 0 [ev] λ 3 = α 3 = m SUN ( ) 0 5 ev m ATM (.8 3.) 0 3 ev mββ [ev] 0 0 H-M & IGEX m 3 m mββ [ev] 0 0 H-M & IGEX m 3 m U e U e U e m 0 3 m m [ev] m [ev] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

49 Inverted Hierarchy m m m 3 m ββ = U ek m k U e m + U e m k U e + U e m ATM = U e + U e e iα m ATM 0.59 U e U e 0.37 no overlap of allowed ranges for U e and U e = complete cancellation is not possible! m ββ m ATM the Majorana phase α is potentially measurable [Bilenky et al, PRD 54 (996) 443] m ββ m ATM U e 4 + U e 4 + U e U e cos α Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

50 CP Conservation: Inverted Scheme λ = α = 0 λ 3 = α 3 = λ = α = π λ 3 = α 3 = π mββ [ev] H-M & IGEX m m m 3 mββ [ev] H-M & IGEX m m m 3 m ββ ( ) U e + U e e iα m 3 + m ATM U e3 e iα 3m m 3 [ev] λ = α = 0 λ 3 = α 3 = π λ = α = π m 3 [ev] λ 3 = α 3 = 0 m ATM (.8 3.) 0 3 ev U e mββ [ev] 0 0 H-M & IGEX m m mββ [ev] 0 0 H-M & IGEX m m U e U e m m m 3 [ev] m 3 [ev] Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

51 General Neutrino Oscillations Bounds for ββ 0ν Decay [Vissani, JHEP 06 (999) 0] [Pascoli et al, PLB 549 (00) 77] [Czakon et al, PRD65 (00) ] [Elliott, Vogel, ARNPS 5 (00) 5] [Joaquim, PRD68 (003) 03309] [Giunti, Laveder, hep-ph03038] [Feruglio et al, NPB659 (003) 359] [Pascoli, Petcov, PLB 580 (004) 80] [Bilenky et al, PRD70 (004) ] [Bahcall et al, PRD 70 (004) 0330] [Petcov, NJP 6 (004) 09] 0 NORMAL SCHEME 0 INVERTED SCHEME mββ [ev] 0 0 H-M & IGEX CP violation mββ [ev] 0 0 H-M & IGEX CP violation m [ev] Quasi Degenerate: m m m 3 m ν = m ββ U e + U e e iα + U e3 e iα 3 m ν m 3 [ev] FUTURE: IF m ββ 0 ev = NORMAL HIERARCHY Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 5

52 Indication of ββ 0ν Decay at Quasi Degenerate Mass Scale 0. ev m ββ.6 ev (3σ range) 0 CMB+LSS OSC. CMB+LSS+Lyα mββ [ev] 0 0 3σ range 0 0 m ν [ev] [Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, hep-ph ] tension among oscillation data, CMB+LSS+Lyα and ββ 0ν signal Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October 004 5

53 Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October [Fogli, Lisi, Marrone, Melchiorri, Palazzo, Serra, Silk, hep-ph ]

54 Summary ν e ν µ, ν τ with m SUN ev (solar ν, KamLAND) ν µ ν τ with m ATM ev (atmospheric ν, KK) Bilarge 3ν-Mixing with U e3 β Decay, Cosmology, ββ 0ν Decay = m ν ev FUTURE Theory: Why m ν m e? Why only U e3? Exp.: Measure U e3 > 0 normal or inverted scheme and CP violation in ν osc. Check ββ 0ν signal at Quasi Degenerate mass scale Improve bounds from β Decay, Cosmology, ββ 0ν Decay Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October

55 Conclusions Neutrino Physics is a very active and interesting field of research next years will hopefully bring new interesting results Open Fundamental Questions Absolute Scale of Neutrino Masses? Nature of Neutrinos (Dirac or Majorana)? Are There Sterile Neutrinos? Short-Baseline ν µ ν e (LSND)? = MiniBooNE Electromagnetic Properties of Neutrinos? Neutrino Unbound Carlo Giunti & Marco Laveder Carlo Giunti Status of Neutrino Masses and Mixing POSTECH, Pohang, Korea, October