Neutrino Physics. Carlo Giunti

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1 Neutrino Physics Carlo Giunti INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Università di Torino Neutrino Unbound: CERN, May 2009 C. Giunti and C.W. Kim Fundamentals of Neutrino Physics and Astrophysics Oxford University Press 15 March pages C. Giunti Neutrino Physics CERN, May

2 Part I: Theory of Neutrino Masses and Mixing Dirac Neutrino Masses and Mixing Majorana Neutrino Masses and Mixing Dirac-Majorana Mass Term C. Giunti Neutrino Physics CERN, May

3 Part II: Neutrino Oscillations in Vacuum and in Matter Neutrino Oscillations in Vacuum CPT, CP and T Symmetries Two-Neutrino Mixing and Oscillations Neutrino Oscillations in Matter C. Giunti Neutrino Physics CERN, May

4 Part III: Phenomenology of Three-Neutrino Mixing Solar Neutrinos and KamLAND Atmospheric Neutrinos and LBL Three-Neutrino Mixing Absolute Scale of Neutrino Masses Experimental Neutrino Anomalies Conclusions C. Giunti Neutrino Physics CERN, May

5 Part I Theory of Neutrino Masses and Mixing C. Giunti Neutrino Physics CERN, May

6 Fermion Mass Spectrum t m [ev] d u e c s µ ν µ b τ ν τ ν e C. Giunti Neutrino Physics CERN, May

7 Dirac Neutrino Masses and Mixing Majorana Neutrino C. Giunti Masses Neutrino andphysics Mixing CERN, May Dirac Neutrino Masses and Mixing Dirac Mass Higgs Mechanism in SM Dirac Lepton Masses Three-Generations Dirac Neutrino Masses Massive Chiral Lepton Fields Massive Dirac Lepton Fields Mixing Flavor Lepton Numbers Mixing Matrix Standard Parameterization of Mixing Matrix CP Violation Jarlskog Rephasing Invariant Maximal CP Violation Lepton Numbers Violating Processes

8 Dirac Mass Dirac Equation: (i / m) (x) = 0 (/ ) Dirac Lagrangian: L (x) = (x)(i / m) (x) Chiral decomposition: L P L R P R = L + R P L P R P 2 L = P 2 R = 1 P L P R = P R P L = 0 L = L i / L + R i / R m ( L R + R L ) In SM only L =µ no Dirac mass Oscillation experiments have shown that neutrinos are massive Simplest extension of the SM: add R C. Giunti Neutrino Physics CERN, May

9 Higgs Doublet: Φ(x) = + (x) 0 (x) Higgs Mechanism in SM Φ 2 = Φ Ý Φ = + Ý + + Ý 0 0 Higgs Lagrangian: L Higgs = (D Φ) Ý (D Φ) V (Φ 2 ) Higgs Potential: V (Φ 2 ) = 2 Φ 2 + Φ and 0 =µ V (Φ 2 ) = Vacuum: V min for Φ 2 = v2 2 Φ 2 2, Õ v2 2 with v 1 =µ Φ = Ô 0 2 v 2 Spontaneous Symmetry Breaking: SU(2) L U(1) Y U(1) Q Unitary Gauge: Φ(x) = Ô v + H(x) C. Giunti Neutrino Physics CERN, May

10 H φ + φ 0 C. Giunti Neutrino Physics CERN, May

11 Dirac Lepton Masses L L L R L Lepton-Higgs Yukawa Lagrangian R L HL = y L L Φ R y L L Φ R + H.c. Φ(x) = 1 Ô 2 0 v + H(x) Unitary Gauge Φ = i 2 Φ = 1 Ô v + H(x) 2 0 L HL = y Ô 0 L L 2 v + H(x) R y Ô L 2 L v + H(x) 0 R + H.c. C. Giunti Neutrino Physics CERN, May

12 L HL = y v Ô2 L R y v Ô 2 L R y Ô 2 L R H y Ô 2 L R H + H.c. m = y v Ô2 m = y v Ô 2 g H = y Ô 2 = m v g H = y Ô 2 = m v C. Giunti Neutrino Physics CERN, May

13 Three-Generations Dirac Neutrino Masses L el el el e L ½ L L L L L ½ L L L L L er e R R R R R er R R ½ L HL = Lepton-Higgs Yukawa Lagrangian «=e Y «L «L Φ R + Y «L «L Φ R + H.c. Φ(x) = Ô v + H(x) Unitary Gauge ½ Φ = i2 Φ = 1 Ô 2 C. Giunti Neutrino Physics CERN, May v + H(x) 0 ½

14 L HL = l L v + H Ô 2 L HL = e L L L ½ Y Y ee Y e Ye «=e Y ««L R + Y ««L R + H.c. v + H Ô l L Y l R + νl Y νr + H.c. 2 l R Y e Y Y e R R R Y e Y Y ½ ½ ν L el L L ½ Y Y ee Y e Ye ν R Y e Y Y er R R Y e Y Y ½ ½ M = v Ô 2 Y M = v Ô 2 Y C. Giunti Neutrino Physics CERN, May

15 L HL = v + H Ô l L Y l R + ν L Y νr + H.c. 2 Diagonalization of Y and Y with unitary V L, V R, V L, V R l L = V L l L l R = V R l R ν L = V L n L ν R = V R n R Kinetic terms are invariant under unitary transformations of the fields L HL = v + H Ô l L V Ý L Y VR l R + ν L V Ý L Y VR ν R + H.c. 2 V Ý L Y V R = Y Y «= y «Æ «(«= e ) V Ý L Y V R = Y Y kj = y k Æ kj (kj = 123) Real and Positive y «, y k C. Giunti Neutrino Physics CERN, May

16 Massive Chiral Lepton Fields l L = V Ý L l L n L = V Ý L ν L e L L L 1L 2L 3L ½ ½ l R = V Ý R l R n R = V Ý R ν R e R R R 1R 2R 3R ½ ½ L HL = = v + H Ô 2 v + H Ô 2 l L Y l R + n L Y n R + H.c. «=e y ««L «R + 3 k=1 y k kl kr + H.c. C. Giunti Neutrino Physics CERN, May

17 Massive Dirac Lepton Fields ««L + «R («= e ) L HL = «=e «=e k = kl + kr y «v Ô 2 ««3 k=1 y«ô 3 ««H 2 k=1 (k = 123) y k v Ô 2 k k Mass Terms y k Ô 2 k k H Lepton-Higgs Couplings Charged Lepton and Neutrino Masses m «= y «v Ô 2 («= e ) m k = y k v Ô 2 (k = 123) Lepton-Higgs coupling» Lepton Mass C. Giunti Neutrino Physics CERN, May

18 Mixing j W L = Charged-Current Weak Interaction Lagrangian L (CC) I Weak Charged Current: «=e = g 2 Ô 2 j W W + H.c. j W = j W L + j W Q Leptonic Weak Charged Current «1 5 «= 2 «=e «L «L = 2ν L l L l L = V L l L ν L = V L n L j W L = 2n L V Ý L V L l L = 2n L V Ý L V L l L = 2n L U Ý l L Mixing Matrix U Ý = V Ý L V L U = V Ý L V L C. Giunti Neutrino Physics CERN, May

19 Definition: Left-Handed Flavor Neutrino Fields ν L = U n L = V Ý L ν L = el L They allow us to write the Leptonic Weak Charged Current as in the SM: j W L = 2ν L l L = 2 «L «L «=e Each left-handed flavor neutrino field is associated with the corresponding charged lepton field which describes a massive charged lepton: L ½ j W L = 2( el e L + L L + L L ) C. Giunti Neutrino Physics CERN, May

20 Flavor Lepton Numbers Flavor Neutrino Fields are useful for defining Flavor Lepton Numbers as in the SM L e L L ( e e ) ( ) ( ) L e L L ( c e e+ ) c ( c + ) L = L e + L + L Standard Model: Lepton numbers are conserved C. Giunti Neutrino Physics CERN, May

21 ½ m Lmass D ee D m D e m D e = el L L me D m D m D me D m D m D er R + H.c. R ½ L e, L, L are not conserved L is conserved: L( «R ) = L( L ) µ L = 0 C. Giunti Neutrino Physics CERN, May

22 Mixing Matrix Leptonic Weak Charged Current: j W L = 2n L U Ý l L ½ U = V Ý L V L = U 11 U 12 U 13 U 21 U 22 U 23 U e1 U e2 U e3 U 1 U 2 U 3 U 31 U 32 U 33 U 1 U 2 U 3 Unitary N N matrix depends on N 2 independent real parameters N = 3 =µ Not all phases are physical observables ½ N (N 1) = 3 2 Mixing Angles N (N + 1) = 6 2 Phases Only physical effect of mixing matrix occurs through its presence in the Leptonic Weak Charged Current C. Giunti Neutrino Physics CERN, May

23 Weak Charged Current: j W L = 2 3 k=1 «=e kl U «k «L Apart from the Weak Charged Current, the Lagrangian is invariant under the global phase transformations (6 arbitrary phases) k e i ³ k k (k = 123) «e i ³««(«= e ) Performing this transformation, the Charged Current becomes j W L j W L = 2 3 = 2 e i(³1 ³e) ßÞ Ð 1 k=1 «=e 3 k=1 «=e kl e i ³ k U «k e i ³««L kl e i(³ k ³ 1) ßÞ Ð U «k 2 ³e) ei(³«ßþ Ð «L 2 There are 5 arbitrary phases of the fields that can be chosen to eliminate 5 of the 6 phases of the mixing matrix 5 and not 6 phases of the mixing matrix can be eliminated because a common rephasing of all the fields leaves the Charged Current invariant. C. Giunti Neutrino Physics CERN, May

24 The mixing matrix contains 1 Physical Phase. It is convenient to express the 3 3 unitary mixing matrix only in terms of the four physical parameters: 3 Mixing Angles and 1 Phase C. Giunti Neutrino Physics CERN, May

25 Standard Parameterization of Mixing Matrix el L = U e1 U e2 U e3 U 1 U 2 U 3 U 1 U 2 U 3 L ½ U = c 23 s 23 0 s 23 c 23 = ½ ½ c 13 0 s 13 e i Æ s 13 e i Æ13 0 c 13 1L 2L 3L ½ ½ c 12 s 12 0 s 12 c c 12c 13 s 12c 13 s 13e i Æ 13 s 12c 23 c 12s 23s 13e i Æ 13 c 12c 23 s 12s 23s 13e i Æ 13 s 23c 13 s 12s 23 c 12c 23s 13e i Æ 13 c 12s 23 s 12c 23s 13e i Æ 13 c 23c 13 ½ ½ c ab cos ab s ab sin ab 0 ab 2 0 Æ Mixing Angles 12, 23, 13 and 1 Phase Æ 13 C. Giunti Neutrino Physics CERN, May

26 U = c 23 s 23 0 s 23 c 23 Standard Parameterization ½ c 13 0 s 13 e i Æ s 13 e i Æ13 0 c 13 ½ Example of Different Phase Convention U = c 23 s 23 e i Æ23 0 s 23 e i Æ13 c 23 ½ c 13 0 s s 13 0 c 13 c 12 s 12 0 s 12 c ½ Example of Different Parameterization 12 0 U = c 12 s12 e i Æ s12 ei Æ 12 c ½ c23 s23 0 s23 c23 c 12 s 12 0 s 12 c ½ c 13 0 s s13 0 c13 ½ ½ ½ C. Giunti Neutrino Physics CERN, May

27 CP Violation U = U =µ CP Violation Jarlskog Rephasing Invariant J = m U e2 U e3 U 2 U 3 [C. Jarlskog, Phys. Rev. Lett. 55 (1985) 1039, Z. Phys. C 29 (1985) 491] [O. W. Greenberg, Phys. Rev. D 32 (1985) 1841] [I. Dunietz, O. W. Greenberg, Dan-di Wu, Phys. Rev. Lett. 55 (1985) 2935] C. Giunti Neutrino Physics CERN, May

28 Jarlskog Rephasing Invariant Simplest rephasing invariants: U «k = U «k U «k U «k U «ju ku j m U «k U «ju ku j = J J = m U e2 U e3 U 2 U 3 In standard parameterization: = m Æ ½ Æ J = c 12 s 12 c 23 s 23 c 2 13 s 13 sin Æ 13 = 1 8 sin2 12 sin2 23 cos 13 sin2 13 sin Æ 13 Jarlskog invariant is useful for quantifying CP violation in a parameterization-independent way All measurable CP-violation effects depend on J. C. Giunti Neutrino Physics CERN, May

29 Maximal CP Violation Maximal CP violation is defined as the case in which J has its maximum possible value J max = 1 6 Ô 3 In the standard parameterization it is obtained for 12 = 23 = 4 s 13 = 1 Ô 3 sin Æ 13 = 1 This case is called Trimaximal Mixing. All the Ô absolute values of the elements of the mixing matrix are equal to 1 3: U = Ô1 Ô3 1 3 Ô i 3 1 i 2 2 Ô 1 i Ô 1Ô i 2 2 Ô 1 i Ô 1Ô 3 3 ½ = 1 Ô i e i 6 e i 6 1 e i 6 e i 6 1 ½ C. Giunti Neutrino Physics CERN, May

30 Lepton Numbers Violating Processes Dirac mass term allows L e, L, L violating processes Example: e + e + e + + e e + U k U ek = 0 =µ only part of k propagator» m k contributes k Γ = G Fm 5 3« U k U m 2 2 k ek m 2 k W ßÞ Ð BR Suppression factor: U µk W γ W µ ν k e U ek m k m W for m k 1eV (BR) the (BR) exp C. Giunti Neutrino Physics CERN, May

31 Majorana Neutrino Masses and Mixing Dirac Neutrino Masses and Mixing Majorana Neutrino Masses and Mixing Two-Component Theory of a Massless Neutrino Majorana Equation Majorana Lagrangian Lepton Number No Majorana Neutrino Mass in the SM Effective Majorana Mass Mixing of Three Majorana Neutrinos Mixing Matrix Dirac-Majorana Mass Term C. Giunti Neutrino Physics CERN, May

32 Two-Component Theory of a Massless Neutrino [L. Landau, Nucl. Phys. 3 (1957) 127], [T.D. Lee, C.N. Yang, Phys. Rev. 105 (1957) 1671], [A. Salam, Nuovo Cim. 5 (1957) 299] Dirac Equation: (i m) = 0 Chiral decomposition of a Fermion Field: = L + R Equations for the Chiral components are coupled by mass: i L = m R i R = m L They are decoupled for a massless fermion: Weyl Equations (1929) i L = 0 i R = 0 A massless fermion can be described by a single chiral field L or R (Weyl Spinor). C. Giunti Neutrino Physics CERN, May

33 L and R have only two independent components: in the chiral representation ½ ½ 0 0 R1 L = 0 L L1 L2 R R = 0 R2 The possibility to describe a physical particle with a Weyl spinor was rejected by Pauli in 1933 because it leads to parity violation ( L P µ R ) The discovery of parity violation in invalidated Pauli s reasoning, opening the possibility to describe massless particles with Weyl spinor fields =µ Two-component Theory of a Massless Neutrino (1957) 0 0 V A Charged-Current Weak Interactions =µ L In the 1960s, the Two-component Theory of a Massless Neutrino was incorporated in the SM through the assumption of the absence of R C. Giunti Neutrino Physics CERN, May

34 Majorana Equation Can a two-component spinor describe a massive fermion? Yes! (E. Majorana, 1937) Trick: R and L are not independent: R = L T L T is right-handed: Majorana Equation: PR L T = L T i L = m L T ( T 1 = ) Majorana Field: = L + R = L + L T Majorana Condition: = T = C i Only two independent components: = 2 L = L C. Giunti Neutrino Physics CERN, May L2 L1 L1 L2 ½

35 = C implies the equality of particle and antiparticle Only neutral fermions can be Majorana particles For a Majorana field, the electromagnetic current vanishes identically: = C C = T Ý T = T Ý = = 0 C. Giunti Neutrino Physics CERN, May

36 Majorana Lagrangian Dirac Lagrangian L D = (i / m) = L i / L + R i / R m ( R L + L R ) R C L = L T 1 2 L D L i / L m 2 L M = L i / L m 2 Majorana Lagrangian = L i / L m 2 T L Ý L + L L T L T Ý L + L T L C L L + L C L C. Giunti Neutrino Physics CERN, May

37 Lepton Number L = +1 = C L = 1 L =µ L = +1 L C =µ L = 1 L M = L i / L m 2 C L L + L C L Total Lepton Number is not conserved: L = 2 Best process to find violation of Total Lepton Number: Neutrinoless Double- Decay Æ(AZ) Æ(AZ + 2) + 2e + 2 e ( 0 ) Æ(AZ) Æ(AZ 2) + 2e e ( + ) 0 C. Giunti Neutrino Physics CERN, May

38 No Majorana Neutrino Mass in the SM Majorana Mass Term» T L Ý L L L T involves only the neutrino left-handed chiral field L, which is present in the SM (one for each lepton generation) Eigenvalues of the weak isospin I, of its third component I 3, of the hypercharge Y and of the charge Q of the lepton and Higgs multiplets: lepton doublet L L = L L ½ I I 3 Y Q = I 3 + Y lepton singlet R Higgs doublet Φ(x) = +(x) (x) 12 T L Ý L has I 3 = 1 and Y = 2 =µ needed Higgs triplet with Y = 2 ½ C. Giunti Neutrino Physics CERN, May

39 Effective Majorana Mass Dimensional analysis: Fermion Field [E] 32 Boson Field [E] Dimensionless action: I = d 4 x L (x) =µ L (x) [E] 4 Kinetic terms: i / [E] 4, ( ) Ý [E] 4 Mass terms: m [E] 4, m 2 Ý [E] 4 CC weak interaction: g ν L l L W [E] 4 Yukawa couplings: y L L Φ R [E] 4 Product of fields O d with energy dimension d dim-d operator L (Od ) = C (Od )O d =µ C (Od ) [E] 4 d O d4 are not renormalizable C. Giunti Neutrino Physics CERN, May

40 SM Lagrangian includes all O d4 invariant under SU(2) L U(1) Y SM cannot be considered as the final theory of everything SM is an effective low-energy theory It is likely that SM is the low-energy product of the symmetry breaking of a high-energy unified theory It is plausible that at low-energy there are effective non-renormalizable O d4 [S. Weinberg, Phys. Rev. Lett. 43 (1979) 1566] All O d must respect SU(2) L U(1) Y, because they are generated by the high-energy theory which must include the gauge symmetries of the SM in order to be effectively reduced to the SM at low energies C. Giunti Neutrino Physics CERN, May

41 O d4 is suppressed by a coefficient Å 4 d, where Å is a heavy mass characteristic of the symmetry breaking scale of the high-energy unified theory: Analogy with L = L SM + g 5 Å O 5 + g 6 Å 2 O 6 + L (CC) eff O 6 ( el e L )(e L el ) +» G F ( el e L ) (e L el ) + g 6 Å 2 G F Ô 2 = g2 8m 2 W Å 4 d is a strong suppression factor which limits the observability of the low-energy effects of the new physics beyond the SM The difficulty to observe the effects of the effective low-energy non-renormalizable operators increase rapidly with their dimensionality O 5 =µ Majorana neutrino masses (Lepton number violation) O 6 =µ Baryon number violation (proton decay) C. Giunti Neutrino Physics CERN, May

42 Only one dim-5 operator: O 5 = (L T L 2 Φ) Ý (Φ T 2 L L ) + H.c. = 1 2 (LT L Ý 2 L L ) (Φ T 2 Φ) + H.c. L 5 = g 5 2Å (LT L Ý 2 L L ) (Φ T 2 Φ) + H.c. Electroweak Symmetry Breaking: Φ = + 0 Symmetry Breaking 0 Ô v 2 L 5 Symmetry Breaking L M mass = 1 2 g 5 v 2 Å T L Ý L + H.c. =µ m = g 5 v 2 Å C. Giunti Neutrino Physics CERN, May

43 The study of Majorana neutrino masses provides the most accessible low-energy window on new physics beyond the SM m» v2 Å» m2 D Å natural explanation of smallness of neutrino masses (special case: See-Saw Mechanism) Example: m D v 10 2 GeV and Å GeV =µ m 10 2 ev C. Giunti Neutrino Physics CERN, May

44 Mixing of Three Majorana Neutrinos ν L el L L ½ L M mass = 1 2 νt L Ý M L ν L + H.c. = 1 2 «=e T «L Ý M L «L + H.c. In general, the matrix M L is a complex symmetric matrix ««L T Ý M L «L = L T M L «( Ý ) T «L «= «L T Ý M L ««L = «L T Ý M L «L «M L «= M L «µ M L = M LT C. Giunti Neutrino Physics CERN, May

45 L M mass = 1 2 νt L Ý M L ν L + H.c. ν L = V L n L =µ L M mass = 1 2 νt L (V L )T Ý M L V L ν L + H.c. (VL ) T M L VL = M M kj = m k Æ kj (kj = 123) Left-handed chiral fields with definite mass: n L = VL Ý νl = 1L 2L L M mass = 1 2 = 1 2 n T L Ý M n L n L M n T L 3 m k kl T Ý kl kl kl T k=1 Majorana fields of massive neutrinos: k = kl + C kl n = ½ =µ L M = k=1 3L ½ C k = k k (i / m k ) k = 1 n(i / M)n 2 C. Giunti Neutrino Physics CERN, May

46 Mixing Matrix Leptonic Weak Charged Current: j W L = 2n L U Ý l L with U = V Ý L V L Definition of the left-handed flavor neutrino fields: ν L = U n L = V Ý L ν L = el L L Leptonic Weak Charged Current has the SM form j W L = 2ν L l L = 2 «L «L «=e Important difference with respect to Dirac case: Two additional CP-violating phases: Majorana phases ½ C. Giunti Neutrino Physics CERN, May

47 3 Majorana Mass Term Lmass M = 1 m k kl T Ý kl + H.c. is not invariant 2 k=1 under the global U(1) gauge transformations kl e i ³ k kl (k = 123) Left-handed massive neutrino fields cannot be rephased in order to eliminate two Majorana phases factorized on the right of ½mixing matrix: U = U D D M D M = e i e i 3 U D is analogous to a Dirac mixing matrix, with one Dirac phase Standard parameterization: U = c 12c 13 s 12c 13 s 13e i Æ 13 s 12c 23 c 12s 23s 13e i Æ 13 c 12c 23 s 12s 23s 13e i Æ 13 s 23c 13 s 12s 23 c 12c 23s 13e i Æ 13 c 12s 23 s 12c 23s 13e i Æ 13 c 23c 13 ½ e i e i 3 ½ Jarlskog rephasing invariant: J = c 12 s 12 c 23 s 23 c 2 13 s 13 sin Æ 13 C. Giunti Neutrino Physics CERN, May

48 Dirac-Majorana Mass Term Dirac Neutrino Masses and Mixing Majorana Neutrino Masses and Mixing Dirac-Majorana Mass Term One Generation See-Saw Mechanism Majorana Neutrino Mass? Number of Massive Neutrinos? C. Giunti Neutrino Physics CERN, May

49 One Generation If R exists, the most general mass term is the Dirac-Majorana Mass Term L D+M mass = L D mass + L L mass + L R mass L D mass = m D R L + H.c. Dirac Mass Term L L mass = 1 2 m L T L Ý L + H.c. Majorana Mass Term L R mass = 1 2 m R T R Ý R + H.c. New Majorana Mass Term! C. Giunti Neutrino Physics CERN, May

50 Column matrix of left-handed chiral fields: N L = L L D+M mass = 1 2 NT L Ý M N L + H.c. M = R C ml m D L = T R m D m R The Dirac-Majorana Mass Term has the structure of a Majorana Mass Term for two chiral neutrino fields coupled by the Dirac mass Diagonalization: n L = U Ý 1L N L = 2L L D+M mass = 1 2 U T M U = k=12 m1 0 0 m 2 m k T kl Ý kl + H.c. = 1 2 k = kl + C kl Real m k 0 k=12 m k k k Massive neutrinos are Majorana! k = C k C. Giunti Neutrino Physics CERN, May

51 See-Saw Mechanism [Minkowski, PLB 67 (1977) 42; Yanagida (1979); Gell-Mann, Ramond, Slansky (1979); Mohapatra, Senjanovic, PRL 44 (1980) 912] m L = 0 m D m R L L mass is forbidden by SM symmetries =µ m L = 0 m D v 100GeV is generated by SM Higgs Mechanism (protected by SM symmetries) m R is not protected by SM symmetries =µ m R Å GUT v m 1 ³ m2 D m R m 2 ³ m R ν 2 ν 1 Natural explanation of smallness of neutrino masses Mixing angle is very small: tan2 = 2 m D m R 1 1 is composed mainly of active L : 1L ³ L 2 is composed mainly of sterile R : 2L ³ C R C. Giunti Neutrino Physics CERN, May

52 Majorana Neutrino Mass? ¾ Ù Ø ½ ½ ½ ½ ¾ ½ ½ ½ ½ ½ ½ ¾ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½½ ½ ½¾ Ñ Î 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 = 2 µ 0 decay see-saw type relation m Å2 EW Å Majorana neutrino masses provide the most accessible window on New Physics Beyond the Standard Model C. Giunti Neutrino Physics CERN, May

53 Number of Massive Neutrinos? Z µ e active flavor neutrinos N mixing µ «L = k=1 U «k kl «= e Mass Basis: Flavor Basis: e s1 s2 ACTIVE STERILE N 3 no upper limit! STERILE NEUTRINOS singlets of SM =µ no interactions! active sterile transitions are possible if 4, are light (no see-saw) disappearance of active neutrinos C. Giunti Neutrino Physics CERN, May

54 Part II Neutrino Oscillations in Vacuum and in Matter C. Giunti Neutrino Physics CERN, May

55 Neutrino Oscillations in Vacuum Neutrino Oscillations in Vacuum Neutrino Oscillations Neutrinos and Antineutrinos CPT, CP and T Symmetries Two-Neutrino Mixing and Oscillations Neutrino Oscillations in Matter C. Giunti Neutrino Physics CERN, May

56 Neutrino Oscillations [Eliezer, Swift, NPB 105 (1976) 45] [Fritzsch, Minkowski, PLB 62 (1976) 72] [Bilenky, Pontecorvo, SJNP 24 (1976) 316] Ä CC W ( el e L + L L + L L ) Fields «= k U «k k =µ «= k U «k k States initial flavor: «= e or or k (t x) = e iekt+ipkx k µ «(t x) = k k = U k µ «(t x) = =e =e U «k e iekt+ipkx k U «k e iekt+ipkx U k k ßÞ Ð «(tx) «(0 0) = k U «ku k = Æ ««(t 0 x 0) = Æ «C. Giunti Neutrino Physics CERN, May

57 P «(tx) = «(tx) 2 = 2 U «k e ie kt+ip k x U k ultra-relativistic neutrinos =µ t ³ x = L source-detector distance E k t p k x ³ (E k p k ) L = E2 k p 2 k E k + p k L = P «(LE) = = kj 2 U «k e im2 k L2E U k k U «ku k U «j U j exp k m2 k E k + p k L ³ m2 k 2E L i m2 kj L 2E m 2 kj m 2 k m 2 j C. Giunti Neutrino Physics CERN, May

58 Neutrinos and Antineutrinos Right-handed antineutrinos are described by CP-conjugated fields: CP = 0 T = C =µ Particle Antiparticle P =µ Left-Handed Right-Handed Fields: «L = k U «k kl CP CP «L = k U «k CP kl States: «= k U «k k CP «= k U «k k NEUTRINOS U U ANTINEUTRINOS P «(LE) = U «k U ku «j U j exp i m2 kj L 2E kj P «(LE) = U «k U ku «ju j exp i m2 kj L 2E kj C. Giunti Neutrino Physics CERN, May

59 CPT, CP and T Symmetries Neutrino Oscillations in Vacuum CPT, CP and T Symmetries CPT Symmetry CP Symmetry T Symmetry Two-Neutrino Mixing and Oscillations Neutrino Oscillations in Matter C. Giunti Neutrino Physics CERN, May

60 CPT Symmetry P «CPT P «CPT Asymmetries: A CPT «= P «P «Local Quantum Field Theory =µ A CPT «= 0 CPT Symmetry P «(LE) = U «k U ku «j U j exp i m2 kj L 2E kj is invariant under CPT: U U «P «= P «P ««= P ««(solar e, reactor e, accelerator ) C. Giunti Neutrino Physics CERN, May

61 CP Symmetry P «CP P «CP Asymmetries: A CP = P ««P «CPT µ A CP = «ACP «A«(LE) CP = 4 Im U «ku k U «j U j sin kj m 2 kj L 2E Jarlskog rephasing invariant: Im U «ku k U «j U j = J J = c 12 s 12 c 23 s 23 c 2 13 s 13 sin Æ 13 violation of CP in neutrino oscillations is proportional to U e3 = sin 13 and sin Æ 13 C. Giunti Neutrino Physics CERN, May

62 T Symmetry P «T P «T Asymmetries: A T «= P «P «CPT =µ 0 = A CPT = P ««P «= P «P «+ P «P «= A T + «ACP = «AT «A CP «=µ A T = «ACP «A T «(LE) = 4 kj Im U «ku k U «j U j sin m 2 kj L 2E Jarlskog rephasing invariant: Im U «ku k U «j U j = J C. Giunti Neutrino Physics CERN, May

63 Two-Neutrino Mixing and Oscillations «= 2 k=1 cos U = sin U «k k («= e ) sin cos ν µ ν 2 ϑ ν e ν 1 e = cos 1 + sin 2 = sin 1 + cos 2 m 2 m 2 21 m 2 2 m 2 1 Transition Probability: P e = P e = sin 2 2sin 2 m 2 L 4E Survival Probabilities: P e e = P = 1 P e C. Giunti Neutrino Physics CERN, May

64 Two-Neutrino Mixing Types of Experiments P «(L E) = sin 2 2 sin 2 m 2 L 4E observable if m 2 L 4E 1 SBL LE 10eV 2 µ m 2 01eV 2 Reactor: L 10m E 1MeV Accelerator: L 1km E 01GeV ATM & LBL LE 10 4 ev 2 m ev 2 Reactor: L 1km E 1MeV CHOOZ, PALO VERDE Accelerator: L 10 3 km E 1GeV K2K, MINOS, CNGS Atmospheric: L km E GeV Kamiokande, IMB, Super-Kamiokande, Soudan, MACRO, MINOS SUN L 10 8 km E 01 10MeV L E 1011 ev 2 µ m ev 2 Homestake, Kamiokande, GALLEX, SAGE, Super-Kamiokande, GNO, SNO, Borexino Matter Effect (MSW) µ10 4 sin ev 2 m ev 2 VLBL LE 10 5 ev 2 µ m ev 2 C. Giunti Neutrino Physics CERN, May Reactor: L 10 2 km E 1MeV KamLAND

65 Neutrino Oscillations in Matter Neutrino Oscillations in Vacuum CPT, CP and T Symmetries Two-Neutrino Mixing and Oscillations Neutrino Oscillations in Matter Effective Potentials in Matter Evolution of Flavor Transition Amplitudes Two-Neutrino Mixing Constant Matter Density MSW Effect (Resonant Transitions in Matter) Phenomenology of Solar Neutrinos In Neutrino Oscillations Dirac = Majorana C. Giunti Neutrino Physics CERN, May

66 Effective Potentials in Matter Ï Ô Ò Ô Ò V CC = Ô 2G F N e V (e ) NC = V (p) NC µ V NC = V (n) NC = Ô 2 2 G FN n V e = V CC + V NC only V CC = V e V = V e V V = V = V NC is important for flavor transitions antineutrinos: V CC = V CC V NC = V NC C. Giunti Neutrino Physics CERN, May

67 Evolution of Flavor Transition Amplitudes Ψ «= e i d dx Ψ «= 1 U M 2 U Ý + A Ψ «2E M 2 = m m m3 2 A = ACC A CC = 2EV CC = 2 Ô 2EG F N e effective mass-squared matrix in vacuum M 2 VAC = U M 2 U Ý matter U M 2 U Ý + 2E V = M 2 MAT potential due to coherent forward elastic scattering effective mass-squared matrix in matter C. Giunti Neutrino Physics CERN, May

68 Two-Neutrino Mixing i d e = 1 dx 4E m 2 cos2 + 2A CC m 2 sin2 initial e =µ e (0) = (0) m 2 sin2 m 2 cos2 1 0 e P e (x) = (x) 2 P e e (x) = e (x) 2 = 1 P e (x) C. Giunti Neutrino Physics CERN, May

69 Constant Matter Density i d e = 1 dx 4E m 2 cos2 + 2A CC m 2 sin2 m 2 sin2 m 2 cos2 e da CC dx = 0 Diagonalization of Effective Hamiltonian e d i dx 1 2 cosm sin = M 1 sin M cos M 2 = 1 m 2 M 0 1 4E 0 mm 2 2 C. Giunti Neutrino Physics CERN, May

70 Effective Mixing Angle in Matter tan2 M = 1 tan2 A CC m 2 cos 2 Effective Squared-Mass Difference m 2 M = Õ( m 2 cos 2 A CC ) 2 + ( m 2 sin2) 2 Resonance ( M = 4) A R CC = m2 cos 2 =µ N R e = m2 cos 2 2 Ô 2EG F C. Giunti Neutrino Physics CERN, May

71 e = d i dx cos M sinm e =µ 1 2 sinm = 1 m 2 M 0 1 4E 0 mm 2 1 cosm e (0) (0) 2 = µ (x) = cos M exp 2 (x) = sin M exp 1 2 =µ 2 cos M sinm = sinm cosm 1 (0) cosm 2 (0) sin M i m2 M x 4E i m2 M x 4E P e (x) = (x) 2 = sin M 1 (x) + cos M 2 (x) 2 P e (x) = sin 2 2 M sin 2 m 2 M x 4E e C. Giunti Neutrino Physics CERN, May

72 MSW Effect (Resonant Transitions in Matter) ϑm m 2 M1, m2 M2 (10 6 ev 2 ) Ne R/NA ν e ν 2 ν µ ν ϑ = ν e ν 1 ν µ ν N e/n A (cm 3 ) Ne R/NA ν 2 ν µ ν µ ν 1 ν e ν e ν N e/n A (cm 3 ) ν 1 m 2 = ev 2, ϑ = 10 3 e = cos M 1 + sin M 2 = sin M 1 + cos M 2 tan2 M = m 2 M = tan2 1 A CC m 2 cos 2 m 2 cos2 A CC 2 + m 2 sin C. Giunti Neutrino Physics CERN, May

73 Phenomenology of Solar Neutrinos LMA (Large Mixing Angle): m ev 2 tan 2 08 LOW (LOW m 2 ): m ev 2 tan 2 06 SMA (Small Mixing Angle): m ev 2 tan QVO (Quasi-Vacuum Oscillations): m ev 2 tan 2 1 VAC (VACuum oscillations): m ev 2 tan SMA LMA 2 2 m (ev ) LOW VAC tan 2 θ [de Gouvea, Friedland, Murayama, PLB 490 (2000) 125] [Bahcall, Krastev, Smirnov, JHEP 05 (2001) 015] C. Giunti Neutrino Physics CERN, May

74 In Neutrino Oscillations Dirac = Majorana Evolution of Amplitudes: M 2 = difference: D() = m m m 2 N d «dt = 1 2E Dirac: U (D) Majorana: e i e i N1 UM 2 U Ý + 2EV U (M) = U (D) D() ½ µ D Ý = D 1 «½ =µ DM2 = M 2 D =µ DM 2 D Ý = M 2 U (M) M 2 (U (M) ) Ý = U (D) DM 2 D Ý (U (D) ) Ý = U (D) M 2 (U (D) ) Ý C. Giunti Neutrino Physics CERN, May

75 Part III Phenomenology of Three-Neutrino Mixing C. Giunti Neutrino Physics CERN, May

76 Solar Neutrinos and KamLAND Nobs/Nexp ILL Savannah River Bugey Rovno Goesgen Krasnoyarsk Palo Verde Chooz KamLAND Distance to Reactor (m) C. Giunti Neutrino Physics CERN, May

77 KamLAND Reactor e e confirmation of LMA (December 2002) 53 nuclear power reactors in Japan and Korea Kamioka Mine L ³ 180km E ³ 4MeV Survival Probability Data - BG - Geo ν e Expectation based on osci. parameters determined by KamLAND L 0 /E νe (km/mev) [KamLAND, PRL 100 (2008) ] C. Giunti Neutrino Physics CERN, May

78 6σ 5σ 4 σ 3 1 2σ σ σ 2 χ σ 3σ 2σ 1σ KamLAND 95% C.L. 99% C.L % C.L. best fit m 2 21 ) 2 (ev Solar 95% C.L. 99% C.L % C.L. best fit tan 2 θ 12 [KamLAND, PRL 100 (2008) ] χ C. Giunti Neutrino Physics CERN, May

79 Atmospheric Neutrinos and LBL p π + π µ + µ e e + νµ νµ νe νµ νµ νe C. Giunti Neutrino Physics CERN, May

80 Super-Kamiokande Up-Down Asymmetry A θ AB z E 1GeV µ isotropic flux of cosmic rays ν α B (A) «( AB z ) = (B) «(A) «( z AB ) (A) «( AB z ( z ) = (A) «( 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) 1562, hep-ex/ ] 6 MODEL INDEPENDENT EVIDENCE OF DISAPPEARANCE! C. Giunti Neutrino Physics CERN, May

81 Fit of Super-Kamiokande Atmospheric Data 10-2 Measure of CC Int. is Difficult: E th = 35 GeV =µ 20eventsyr -Decay =µ Many Final States m 2 (ev 2 ) 10-3 Best Fit: 99% C.L. 90% C.L. 68% C.L sin 2 2θ m 2 = ev 2 sin 2 2 = live-days (Apr 1996 Jul 2001) [Super-Kamiokande, PRD 71 (2005) , hep-ex/ ] -Enriched Sample N the = 78 m 2 = ev 2 N exp = N 24 [Super-Kamiokande, PRL 97(2006) , hep-ex/ ] Check: OPERA ( ) CERN to Gran Sasso (CNGS) L ³ 732 km E ³ 18 GeV [NJP 8 (2006) 303, hep-ex/ ] C. Giunti Neutrino Physics CERN, May

82 Solar e Reactor e disappearance Atmospheric Accelerator disappearance Homestake Kamiokande GALLEX/GNO & SAGE Super-Kamiokande SNO BOREXino (KamLAND) Kamiokande IMB Super-Kamiokande MACRO Soudan-2 (K2K & MINOS) ½ ½ m 2 SOL ³ (76 02) 10 5 ev 2 tan 2 SOL ³ m 2 ATM ³ (24 01) 10 3 ev 2 sin 2 ATM ³ Two scales of m 2 : m 2 ATM ³ 30 m 2 SOL Large mixings: ATM ³ 45 Æ SOL ³ 34 Æ C. Giunti Neutrino Physics CERN, May

83 Three-Neutrino Mixing «L = 3 k=1 U «k kl («= e ) three flavor fields: e,, three massive fields: 1, 2, 3 m m m 2 13 = m 2 2 m m 2 3 m m 2 1 m 2 3 = 0 m 2 SOL = m2 21 ³ (76 02) 10 5 ev 2 m 2 ATM ³ m 2 31 ³ m 2 32 ³ (24 01) 10 3 ev 2 C. Giunti Neutrino Physics CERN, May

84 Allowed Three-Neutrino Schemes m 2 m 2 ν 3 ν 2 m 2 SOL ν 1 m 2 ATM m 2 ATM ν 2 m 2 SOL ν 1 ν 3 normal inverted different signs of m 2 31 ³ m 2 32 absolute scale is not determined by neutrino oscillation data C. Giunti Neutrino Physics CERN, May

85 Mixing Matrix SOL U e1 U e2 U e3 δm 2 (ev 2 ) 1 Analysis A ν e ν x 90% CL Kamiokande (multi-gev) m 2 21 m2 31 U = U µ1 U µ2 U τ1 U τ2 U µ3 U τ % CL Kamiokande (sub+multi-gev) ATM 10-2 CHOOZ: m 2 CHOOZ = m 2 31 = m2 ATM sin 2 2 CHOOZ = 4U e3 2 (1 U e3 2 ) U e % CL 95% CL SOLAR AND ATMOSPHERIC OSCILLATIONS ARE PRACTICALLY DECOUPLED! sin 2 (2θ) [CHOOZ, PLB 466 (1999) 415] [Palo Verde, PRD 64 (2001) ] U e1 2 ³ cos 2 SOL U 3 2 ³ sin 2 ATM U e2 2 ³ sin 2 SOL U 3 2 ³ cos 2 ATM C. Giunti Neutrino Physics CERN, May

86 U = c 23 s 23 0 s 23 c 23 = 23 ³ ATM ½ Bilarge Mixing c 13 0 s 13 e i Æ s 13 e i Æ13 0 c ³ CHOOZ ½ c 12 s 12 0 s 12 c ³ SOL c 12c 13 s 12c 13 s 13e i Æ 13 s 12c 23 c 12s 23s 13e i Æ 13 c 12c 23 s 12s 23s 13e i Æ 13 s 23c 13 s 12s 23 c 12c 23s 13e i Æ 13 c 12s 23 s 12c 23s 13e i Æ 13 c 23c 13 ½ ½ e i e i e i e i 3 sin 2 12 = sin 2 23 = sin (90% C.L.) [Schwetz, Tortola, Valle, New J. Phys. 10 (2008) ] Hint of [Fogli, Lisi, Marrone, Palazzo, Rotunno, NO-VE, April 2008] [Balantekin, Yilmaz, JPG 35 (2008) ] ½ ½ sin 2 13 = [Fogli, Lisi, Marrone, Palazzo, Rotunno, PRL 101 (2008) ] C. Giunti Neutrino Physics CERN, May

87 The Hunt for 13 sin 2 2Θ 13 discovery reach3σ MINOS CNGS DCHOOZ T2K NOA ReactorII NOAFPD Conventional beams Reactor experiments Superbeams CHOOZSolar excluded sin 2 2Θ 13 discovery reach3σ MINOS CNGS DCHOOZ T2K NOA ReactorII NOAFPD 2 nd GenPDExp NuFact SuperbeamsReactor exps Conv. beams Superbeam upgrades Νfactories Branching point CHOOZSolar excluded Year 3 sensitivities. Bands reflect dependence of sensitivity on the CP violating phase Æ Year Branching point refers to the decision between an upgraded superbeam and/or detector and a neutrino factory program. Neutrino factory is assumed to switch polarity after 2.5 years. [Physics at a Fermilab Proton Driver, Albrow et al, hep-ex/ ] C. Giunti Neutrino Physics CERN, May

88 Absolute Scale of Neutrino Masses Solar Neutrinos and KamLAND Atmospheric Neutrinos and LBL Three-Neutrino Mixing Absolute Scale of Neutrino Masses Mass Hierarchy or Degeneracy? Tritium Beta-Decay Neutrinoless Double-Beta Decay Cosmological Bound on Neutrino Masses Experimental Neutrino Anomalies Conclusions C. Giunti Neutrino Physics CERN, May

89 Mass Hierarchy or Degeneracy? normal scheme inverted scheme 10 0 QUASI DEGENERATE 10 0 QUASI DEGENERATE 10 1 m m2 m1 m [ev ] 10 2 m2 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 2 2 = m m 2 21 = m m 2 SOL m 2 3 = m m 2 31 = m m 2 ATM m 2 1 = m 2 3 m 2 31 = m m 2 ATM m 2 2 = m m 2 21 ³ m m 2 ATM Quasi-Degenerate for m 1 ³ m 2 ³ m 3 ³ m Ô m 2 ATM ³ ev C. Giunti Neutrino Physics CERN, May

90 Tritium Beta-Decay 3 H 3 He + e + e K(T) = ÚÙ Ù Ø Õ dγ dt = (coscgf)2 Å 2 F(E)pE (Q T) (Q T) 2 m e Q = M3 H M3 He m e = 1858keV 2 3 Kurie plot dγdt = (coscg F) 2 Å 2 F(E)pE (Q T) Õ 12 (Q T) 2 m 2 e K(T) m νe = m νe = 100 ev T Q m νe Q m e 22eV (95% C.L.) Mainz & Troitsk [Weinheimer, hep-ex/ ] future: KATRIN (start 2012) [arxiv: ] sensitivity: m e ³ 02eV (3y) C. Giunti Neutrino Physics CERN, May

91 Neutrino Mixing =µ K(T) = (Q T) k U ek 2 Õ(Q T) 2 m 2 k 12 Ã Ì µ º¾ º½ º½ º ½º ½º ½º ½º ½º É Ñ ¾ Í ½ ¾ Í ¾ ¾ Ì Ñ½ ½ ΠѾ ½ Î É Ñ ½ analysis of data is different from the no-mixing case: 2N 1 parameters k U ek 2 = 1 if experiment is not sensitive to masses (m k Q T) effective mass: m 2 = k U ek 2 m 2 k K 2 = (Q T) 2 U ek 2 m 1 k 2 ³ (Q T) (Q 2 T)2 U ek mk 2 2 (Q T) 2 k k Õ = (Q T) m 2 ³ (Q T) (Q T) 2 m 2 2 (Q T) 2 C. Giunti Neutrino Physics CERN, May

92 m 2 = U e1 2 m U e2 2 m U e3 2 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,m2 KATRIN 10 2 m m1 m Lightest Mass: m 1 [ev ] Lightest Mass: m 3 [ev ] Quasi-Degenerate: m 1 ³ m 2 ³ m 3 ³ m =µ m 2 ³ m 2 k U ek 2 = m 2 FUTURE: IF m ev =µ NORMAL HIERARCHY C. Giunti Neutrino Physics CERN, May

93 Neutrinoless Double-Beta Decay 2 + β As 0 + β 76 32Ge β β 0 + Effective Majorana Neutrino Mass: m = k 76 34Se U 2 ek m k C. Giunti Neutrino Physics CERN, May

94 Two-Neutrino Double- Decay: L = 0 Æ(A Z) Æ(A Z + 2) + e + e + e + e Ï Ù (T 2 12 ) 1 = G 2 Å 2 2 second order weak interaction process in the Standard Model Ï Ù Neutrinoless Double- Decay: L = 2 Æ(AZ) Æ(AZ + 2) + e + e (T 0 12 ) 1 = G 0 Å 0 2 m 2 Ï Í Ù effective Majorana mass m = k U 2 ek m k Ñ Í Ï Ù C. Giunti Neutrino Physics CERN, May

95 Effective Majorana Neutrino Mass m = k U 2 ek m k complex U ek µ possible cancellations m = U e1 2 m 1 + U e2 2 e i «2 m 2 + U e3 2 e i «3 m 3 «2 = 2 2 «3 = 2( 3 Æ 13 ) Im[m ββ ] Im[m ββ ] m ββ U e1 2 m 1 α 2 U e3 2 e iα3 m 3 α 3 U e2 2 e iα2 m 2 Re[m ββ ] m ββ U e3 2 e iα3 m 3 α 2 α 3 U e2 2 e iα2 m 2 U e1 2 m 1 Re[mββ ] C. Giunti Neutrino Physics CERN, May

96 Experimental Bounds T y T y T y CUORICINO ( 130 Te) [PRC 78 (2008) ] (90% C.L.) =µ m eV Heidelberg-Moscow ( 76 Ge) [EPJA 12 (2001) 147] T y (90% C.L.) =µ m eV IGEX ( 76 Ge) [PRD 65 (2002) ] (90% C.L.) =µ m eV NEMO 3 ( 100 Mo) [PRL 95 (2005) ] (90% C.L.) =µ m 07 28eV FUTURE EXPERIMENTS COBRA, XMASS, CAMEO, CANDLES m few10 1 ev EXO, MOON, Super-NEMO, CUORE, Majorana, GEM, GERDA m few10 2 ev C. Giunti Neutrino Physics CERN, May

97 Bounds from Neutrino Oscillations m = U e1 2 m 1 + U e2 2 e i «21 m 2 + U e3 2 e i «31 m NORMAL SCHEME 10 1 INVERTED SCHEME mββ [ev] EXP CP violation mββ [ev] EXP CP violation m1 [ev] m3 [ev] FUTURE: IF m 10 2 ev =µ NORMAL HIERARCHY C. Giunti Neutrino Physics CERN, May

98 Experimental Positive Indication [Klapdor et al., MPLA 16 (2001) 2409] T 0 12 = ( ) 1025 y 65 evidence [MPLA 21 (2006) 1547] Counts / kev SSE 2n2b Rosen Primakov Approximation Q=2039 kev Energy,keV [PLB 586 (2004) 198] [MPLA 21 (2006) 1547] the indication must be checked by other experiments m = eV [MPLA 21 (2006) 1547] if confirmed, very exciting (Majorana and large mass scale) C. Giunti Neutrino Physics CERN, May

99 Cosmological Bound on Neutrino Masses 44 High-Z SN Search Team 42 Supernova Cosmology Project m-m (mag) W M =0.3, W L =0.7 W M =0.3, W L =0.0 W M =1.0, W L =0.0 [WMAP, D(m-M) (mag) z [Springel, Frenk, White, Nature 440 (2006) 1137] [ C. Giunti Neutrino Physics CERN, May

100 Relic Neutrinos neutrinos are in equilibrium in primeval plasma through weak interaction reactions e + ( ) e e ( ) ( ) e N ( ) N e n pe e p ne + n pe e weak interactions freeze out Γ weak = Nv G 2 F T 5 T 2 M P Ô G N T 4 Ô G N H =µ T dec 1 MeV Relic Neutrinos: T = neutrino decoupling 3 T ³ 1945 K =µ k T ³ ev (T = K) number density: n f = 3 (3) 4 2 g f Tf 3 =µ n k k ³ T 3 ³ 112 cm 3 density contribution: Ω k = c= 3H2 8G N n k k m k c ³ 1 h 2 m k 9414 ev =µ Ω h 2 = È k m k 9414 ev [Gershtein, Zeldovich, JETP Lett. 4 (1966) 120] [Cowsik, McClelland, PRL 29 (1972) 669] h 07, Ω 03 =µ k m k 14 ev C. Giunti Neutrino Physics CERN, May

101 Power Spectrum of Density Fluctuations hot dark matter prevents early galaxy formation [Tegmark, hep-ph/ ] Solid Curve: flat ΛCDM model Dashed Curve: (Ω 0 M = 028 h = 072 Ω0 B Ω0 M = 016) 3 k=1 m k = 1 ev Æ(x 1 )Æ(x 2 ) = P(k) P(k) Æ(x) (x) d 3 k (2) 3 ei k x P( k) small scale suppression 8 Ω 08 Ω m for È k m k 1 ev 01 Ω m h 2 k k nr 0026Ö m Ô Ωm h Mpc 1 1 ev [Hu, Eisenstein, Tegmark, PRL 80 (1998) 5255] C. Giunti Neutrino Physics CERN, May

102 WMAP (First Year), AJ SS 148 (2003) 175, astro-ph/ CMB (WMAP,...) + LSS (2dFGRS) + HST + SN-Ia =µ Flat ΛCDM T 0 = Gyr h = Ω 0 = Ω b = Ω m = Ω h (95% conf.) =µ 3 k=1 m k 071eV WMAP (Five Years), AJS 180 (2009) 330, astro-ph/ CMB + HST + SN-Ia + BAO T 0 = Gyr Ω Ω b = k=1 h = (95% C.L.) Ω m = m k 067eV (95% C.L.) N eff = C. Giunti Neutrino Physics CERN, May

103 Fogli, Lisi, Marrone, Melchiorri, Palazzo, Rotunno, Serra, Silk, Slosar [PRD 78 (2008) , hep-ph/ ] Flat ΛCDM Case Cosmological data set Σ (at 2) 1 CMB 119 ev 2 CMB + LSS 071 ev 3 CMB + HST + SN-Ia 075 ev 4 CMB + HST + SN-Ia + BAO 060 ev 5 CMB + HST + SN-Ia + BAO + Ly«019 ev 2 (95% C.L.) constraints on the sum of masses Σ. C. Giunti Neutrino Physics CERN, May

104 3 3 k=1 k=1 m k 06eV ( 2) CMB + HST + SN-Ia + BAO m k 02eV ( 2) CMB + HST + SN-Ia + BAO + Ly«NORMAL SCHEME INVERTED SCHEME CMB+HST+SN-Ia+BAO CMB+HST+SN-Ia+BAO m [ev ] 10 1 k mk m 3 CMB+HST+SN-Ia+BAO+Lyα m [ev ] 10 1 k mk m 2 m 1 CMB+HST+SN-Ia+BAO+Lyα 10 2 m m FUTURE: IF Lightest Mass: m 1 [ev ] m Lightest Mass: m 3 [ev ] 3 m k ev =µ NORMAL HIERARCHY k=1 C. Giunti Neutrino Physics CERN, May

105 Indication of 0 Decay: 022eV m 16eV ( 3 range) CMB+LSS+SNIa+BAO CMB+LSS+SNIa+BAO+Lyα OSC. CMB+LSS+SNIa+BAO CMB+LSS+SNIa+BAO+Lyα OSC mββ [ev] ββ0ν mββ [ev] ββ0ν NORMAL SCHEME INVERTED SCHEME LightestMass: m 1 [ev] LightestMass: m 3 [ev] 10 1 tension among oscillation data, CMB+LSS+BAO(+Ly«) and 0 signal C. Giunti Neutrino Physics CERN, May

106 Experimental Neutrino Anomalies Solar Neutrinos and KamLAND Atmospheric Neutrinos and LBL Three-Neutrino Mixing Absolute Scale of Neutrino Masses Experimental Neutrino Anomalies LSND MiniBooNE Gallium Radioactive Source Experiments Conclusions C. Giunti Neutrino Physics CERN, May

107 LSND [PRL 75 (1995) 2650; PRC 54 (1996) 2685; PRL 77 (1996) 3082; PRD 64 (2001) ] e L ³ 30m 20MeV E 200MeV Beam Excess Beam Excess p(ν _ µ ν_ e,e+ )n p(ν _ e,e+ )n other L/E ν (meters/mev) m 2 (ev 2 /c 4 ) Karmen Bugey 90% (L max -L < 2.3) 99% (L max -L < 4.6) CCFR NOMAD sin 2 2θ m 2 LSND 02eV2 ( m 2 ATM m 2 SOL ) C. Giunti Neutrino Physics CERN, May

108 MiniBooNE [PRL 98 (2007) ] e L ³ 541m 475MeV E 3GeV Events / MeV Data ν e from µ + ν e from K 0 ν e from K π 0 misid Nγ dirt other Total Background QE E ν (GeV) Excess Events / MeV 0.8 data - expected background best-fit ν µ ν e sin 2θ=0.004, m =1.0eV sin 2θ=0.2, m =0.1eV QE E ν (GeV) [arxiv: ] Low-Energy Anomaly! [arxiv: ] C. Giunti Neutrino Physics CERN, May

109 Gallium Radioactive Source Experiments tests of solar neutrino detectors GALLEX [PLB 342 (1995) 440; PLB 420 (1998) 114] SAGE [PRL 77 (1996) 4708; PRC 59 (1999) 2246; PRC 73 (2006) ; arxiv: ] Sources: e + 51 Cr 51 V + e e + 37 Ar 37 Cl + e Detector: e + 71 Ga 71 Ge + e 1.1 GALLEX Cr1 SAGE Cr p(measured)/p(predicted) GALLEX Cr2 SAGE Ar R Ga = [SAGE, arxiv: ] [SAGE, PRC 73 (2006) ] C. Giunti Neutrino Physics CERN, May

110 Conclusions e with m 2 SOL ³ ev 2 (SOL, KamLAND) with m 2 ATM ³ ev 2 (ATM, K2K, MINOS) Bilarge 3-Mixing with U e3 2 1 (CHOOZ) & 0 Decay and Cosmology =µ m 1eV FUTURE Theory: Why lepton mixing = quark mixing? (Due to Majorana nature of s?) Why only U e3 2 1? Explain experimental neutrino anomalies (sterile s?). Exp.: Measure U e3 0 µ CP viol., matter effects, mass hierarchy. Check experimental neutrino anomalies. Check 0 signal at Quasi-Degenerate mass scale. Improve & 0 Decay and Cosmology measurements. C. Giunti Neutrino Physics CERN, May

111 Hint of 13 0 [Fogli, Lisi, Marrone, Palazzo, Rotunno, NO-VE, April 2008] [Balantekin, Yilmaz, JPG 35 (2008) ] P ( ) e ( ) e ³ sin 2 13 = [Fogli, Lisi, Marrone, Palazzo, Rotunno, PRL 101 (2008) ] 1 sin sin 2 12 SOL low-energy & KamLAND 1 sin sin 2 12 SOL high-energy (matter effect) C. Giunti Neutrino Physics CERN, May

112 0 Decay Majorana Neutrino Mass d d u e ββ 0ν =µ e u d d ββ 0ν u u e e W + W + ν e ν e(h = 1) ν e ν e(h = +1) [Schechter, Valle, PRD 25 (1982) 2951] [Takasugi, PLB 149 (1984) 372] Majorana Mass Term Ä Å el = 1 2 m ee el c el + el el c C. Giunti Neutrino Physics CERN, May

113 Lyman-alpha Forest [Springel, Frenk, White, astro-ph/ ] Rest-frame Lyman «,, wavelengths: 0 «= Å, 0 = Å, 0 = Å Lyman-«forest: The region in which only Ly«photons can be absorbed: [(1 + z q) 0 (1 + zq)0 «] C. Giunti Neutrino Physics CERN, May