1. Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT

2. Low-energy neutrino physics Belén Gavela Universidad Autónoma de Madrid and IFT and leptogenesis

3. What are the main physics goals in physics? To determine the absolute scale of masses To determine whether they are Dirac or Majorana * To discover Leptonic CP-violation in neutrino oscillations

4. What are the main physics goals in physics? To determine the absolute scale of masses To determine whether they are Dirac or Majorana * To discover Leptonic CP-violation in neutrino oscillations What is the relation of those putative discoveries to the matter-antimatter asymmetry of the universe? Can leptogenesis be “proved”?

5. The short, and rather accurate answer, is NO Nevertheless, a positive discovery of both 2 last points, that is: To establish the Majorana character (neutrinoless  decay) Leptonic CP-violation in neutrino oscillations (at   - e oscillations at superbeams, betabeams…. neutrino factory) would constitute a very compelling argument in favour of leptogenesis plus

6. The short, and rather accurate answer, is NO Nevertheless, a positive discovery of both 2 last points, that is: To establish the Majorana character (neutrinoless  decay) Leptonic CP-violation in neutrino oscillations (at   - e oscillations at superbeams, betabeams…. neutrino factory) would constitute a very compelling argument in favour of leptogenesis Go for those discoveries! plus

7.  masses ----> Beyond SM scale  * What is the prize for  TeV  without unnatural fine-tunings? * What observable observable effects could we then expect? …..This talk deals much with the Majorana character

8. No  masses in the SM because the SM accidentally preserves B-L ……only left-handed neutrinos and ……only scalar doublets (Higgs)

9. No  masses in the SM because the SM accidentally preserves B-L right-handed R → Would require Y ~10 -12 !!! Why s are so light??? Why R does not acquire large Majorana mass? i.e. Adding singlet neutrino fields N R  L  M (  R  R  OK with gauge invariance NRNR + NRNR + NRNR NRNR YY YY L -

10. No  masses in the SM because the SM accidentally preserves B-L right-handed R → Would require Y  ~10 -12 !!! Why s are so light??? Why R does not acquire large Majorana mass? i.e. Adding singlet neutrino fields N R  L  M (  R  R  OK with gauge invariance NRNR + NRNR + NRNR YY NRNR L -

11. No  masses in the SM because the SM accidentally preserves B-L right-handed R → Would require Y  ~10 -12 !!! Why s are so light??? Why R does not acquire large Majorana mass? i.e. Adding singlet neutrino fields N R  L  M (  R  R  OK with gauge invariance NRNR + NRNR + NRNR Seesaw model YY NRNR Which allows Y N ~1 --> M~M Gut L -

12. No  masses in the SM because the SM accidentally preserves B-L right-handed R → Would require Y  ~10 -12 !!! Why s are so light??? Why R does not acquire large Majorana mass? i.e. Adding singlet neutrino fields N R  L  M (  R  R  OK with gauge invariance NRNR + NRNR + NRNR Seesaw model YY NRNR Which allows Y N ~1 --> M~M Gut L - Y N ~10 -6 --> M~TeV

13. masses beyond the SM Favorite options: new physics at higher scale M Heavy fields manifest in the low energy effective theory (SM) via higher dimensional operators Dimension 5 operator: It’s unique → very special role of  masses: lowest-order effect of higher energy physics →  /M (L L H H)  v /M (  2 c O d=5 L=L= c i O i

14. masses beyond the SM Favorite options: new physics at higher scale M Heavy fields manifest in the low energy effective theory (SM) via higher dimensional operators Dimension 5 operator: This mass term violates lepton number (B-L) → Majorana neutrinos It’s unique → very special role of  masses: lowest-order effect of higher energy physics →  /M (L L H H)  v /M (  2 O d=5 L=L= c i O i

15. masses beyond the SM Favorite options: new physics at higher scale M Heavy fields manifest in the low energy effective theory (SM) via higher dimensional operators Dimension 5 operator: This mass term violates lepton number (B-L) → Majorana neutrinos It’s unique → very special role of  masses: lowest-order effect of higher energy physics →  /M (L L H H)  v /M (  2 is common to all models of Majorana s  O d=5 L=L= c i O i O

16. Dimension 6 operators, O discriminate among models. d=6 Which are the d=6 operators characteristic of Seesaw models? (A. Abada, C. Biggio, F.Bonnet, T. Hambye +MBG )

17. masses beyond the SM : tree level m ~ v 2 c d=5 = v 2 Y N Y N /M N T Fermionic Singlet Seesaw ( or type I) 2 x 2 = 1 + 3

18. masses beyond the SM : tree level Fermionic Singlet Seesaw ( or type I) 2 x 2 = 1 + 3 L H L H ++ LEPTOGENESIS: NR’NR’ NR’NR’ NRNR (Fukugita, Yanagida) (Flanz, Paschos, Sarkar,Covi, Roulet,Vissani, Pilaftsis)

19. masses beyond the SM : tree level Fermionic Triplet Seesaw ( or type III) m ~ v 2 c d=5 = v 2 Y  Y  /M  T 2 x 2 = 1 + 3

20. masses beyond the SM : tree level Fermionic Triplet Seesaw ( or type III) T L H ++  + RR RR R’R’ RR R’R’ LEPTOGENESIS: 2 x 2 = 1 + 3 (Hambye, Li, Papucci, Notari, Strumia))

21. masses beyond the SM : tree level 2 x 2 = 1 + 3 Scalar Triplet Seesaw ( or type II) m ~ v 2 c d=5 = v 2   Y  /M  2

22. masses beyond the SM : tree level 2 x 2 = 1 + 3 Scalar Triplet Seesaw ( or type II) T + +  ’’ LEPTOGENESIS: LL (Ma, Sarkar, Hambye)

23. L L NRNR Or hybrid models, i.e Fermionic Singlet + Scalar Triplet H H  ( O'Donnell, Sarkar, Hambye, Senjanovic; Antusch, King )

24. Heavy fermion singlet N R (Type I See-Saw) Minkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic masses beyond the SM : tree level  Heavy  scalar triplet  Magg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle Heavy fermion triplet  R Ma, Roy, Senjanovic, Hambye et al., …

25. Minimal see-saw (fermionic singlet) Integrate out N R d=5 operator it gives mass to d=6 operator it renormalises kinetic energy Broncano, Gavela, Jenkins 02 L = L SM + i N R d N R - Y  L H N R - M N R N R __ MM 2 Y N Y N /M ( L L H H) T Y N Y N /M 2 ( L H) (H L) +

26. Minimal see-saw (fermionic singlet) Integrate out N R d=5 operator it gives mass to d=6 operator it renormalises kinetic energy Kaluza-Klein model: De Gouvea, Giudice, Strumia, Tobe L = L SM + i N R d N R - Y  L H N R - M N R N R __ MM 2 Y N Y N /M ( L L H H) T Y N Y N /M 2 ( L H) (H L) +

27. c d=6 ~ (c d=5 ) 2 For Y´s ~ O(1), and the smallness of neutrino masses would preclude in practice observable effects from c d=6 with m ~ v 2 c d=5 = v 2 Y N Y N /M N T while c d=6 = Y  Y  /M 2 + How to evade this without ad-hoc cancelations of Yukawas?

28. Fermionic triplet seesaw Integrate out N R d=5 operator it gives mass to d=6 operator it renormalises kinetic energy+… L = L SM + i  R D  R - Y  L .H  R - M  R  R __ MM 2 Y  Y  /M ( L L H H) T Y  Y  /M 2 ( L  H) D (H  L) + _

29. Scalar triplet see-saw L = L SM + D  D   -  + M 2  + Y  L .  L +   H .  H + V(H, , i )  Y    /M 2 ( L L H H) d=5 d=6 Y  Y  /M 2 ( L L) (L L) + __   /M 4 (H + H) 3 i   /M 4 (H  H) D  D  (H  H) 2 2

31. Y Y M + 2

32. Y Y M + Notice that the combination also is crucial to the LEPTOGENESIS CP-asymmetries i.e., in Type I: L H ++ NR’NR’ NR’NR’ NRNR + YNTYNT YNYN in addition to the m  combination ~ Y N T Y N v 2 /M 2

33. Indeed, in Type I (fermionic seesaw) the individual CP asymmetries: vanish for degenerate c d=5 (that is, m ) eigenvalues or degenerate c d=6 eigenvalues ( Broncano, Gavela, Jenkins )

34. Y Y M + 2 Can M be close to EW scale, say ~ TeV?

35. M~1 TeV is suggested by electroweak hierarchy problem N H H H   L L (Vissani, Casas et al., Schmaltz)

36. M~1 TeV actively searched for in colliders -> m  > 136 GeV by CDF Atlas groups studying searches of Triplet Seesaws (scalar and fermionic) (Ma……….Bajc, Senjanovic) i.e. Scalar Triplet          l+l+ l+l+ Same sign dileptons….~ no SM background

37. Is it possible to have M ~ 1 TeV with large Yukawas (even O(1) ) ? It requires to decouple the coefficient c d=5 of O d=5 from c d=6 of O d=6

38. Notice that all d=6 operators preserve B-L, in contrast to the d=5 operator. This suggests that, from the point of view of symmetries, it may be natural to have large c d=6, while having small c d=5.

39. Light Majorana m should vanish: - inversely proportional to a Majorana scale ( c d=5 ~ 1/M ) - or directly proportional to it

40. Light Majorana m should vanish: - inversely proportional to a Majorana scale ( c d=5 ~ 1/M ) - or directly proportional to it Ansatz: When the breaking of L is proportional to a small scale  << M, while M ~ O(TeV), c d=5 is suppressed while c d=6 is large: c d=5 ~    c d=6 ~    1

41. Light Majorana m should vanish: - inversely proportional to a Majorana scale ( c d=5 ~ 1/M ) - or directly proportional to it Ansatz: When the breaking of L is proportional to a small scale  << M, while M ~ O(TeV), c d=5 is suppressed while c d=6 is large: c d=5 ~    c d=6 ~ f(Y)    Y +

42. Y Y M + 2

43. Y Y M + 2 M2M2 Y

44. * The minimal scalar triplet model obeys that ansatz:    Y    Y + * Singlet fermion seesaws with M~1 TeV also obey it !!! : i.e. INVERSE SEESAW H H LL c d=6 ~ c d=5 ~ In fact, any Scalar mediated Seesaw will give 1/(D 2 -M 2 ) ~ -1/M 2 - D 2 /M 4 + …… m ~ v 2 c d=5 ~ 1/M 2

45. * Singlet fermion seesaws with M~1 TeV also obey it !!! : i.e. INVERSE SEESAW What about fermionic-mediated Seesaws?

46. INVERSE SEESAW texture L N 1 N 2 L N1N1 N2N2 * Toy: 1 light  Mohapatra, Valle, Glez- Garcia

47. INVERSE SEESAW texture L N 1 N 2 L N1N1 N2N2 * Toy: 1 light 

48. INVERSE SEESAW texture L N 1 N 2 L N1N1 N2N2 * 3 generation Inverse Seesaw: e, , , N 1, N 2, N 3 * Toy: 1 light  Abada et al., Kersten+Smirnov

49. Were M ~ TeV and Y’s ~ 1, is LEPTOGENESIS possible? Not easily It would require resonant leptogenesis NRNR with rather degenerate heavy states M-M’ <<M Yes, but not easy

50. Were M ~ TeV and Y’s ~ 1, is LEPTOGENESIS possible? Not easily It would require resonant leptogenesis NRNR with rather degenerate heavy states M-M’ <<M Very interesting for FERMIONIC inverse seesaws, as they are naturally resonant ( have 2 NR or 2 SR degenerate) Yes, but not easy

51. Were M ~ TeV and Y’s ~ 1, is LEPTOGENESIS possible? Not easily It would require resonant leptogenesis NRNR with rather degenerate heavy states M-M’ <<M * Difficult in Triplet Seesaws (fermionic or scalar) because the extra gauge scattering processes push towards thermal equilibrium. Needs M-M’ ~  Very interesting for FERMIONIC inverse seesaws, as they are naturally resonant ( have 2 NR or 2 SR degenerate) Yes, but not easy

52. d=6 operator is crucial for leptog.: if observed at E~TeV ---> at least one N (or  or  ) at low scale --------> only resonant leptogenesis is possible

53. c d=6 ~    Y + Experimental information on from: --- 4 fermion operators (Scalar triplet seesaw) M W, W decays… --- Unitarity corrections (Fermionic seesaws)

54. Scalar triplet seesaw Bounds on c d=6

55. Scalar triplet seesaw Combined bounds on c d=6

56. Fermionic seesaws ---> Non unitarity

57. i.e, a neutrino mass matrix larger than 3x3 3 x 3 The complete theory of  masses is unitary. Low-energy non- unitarity may result from new physics contributing to neutrino propagation. Unitarity violations arise in models for masses with heavy fermions

58. → YES deviations from unitarity Fermion singlet N R (Type I See-Saw)  Scalar triplet  Fermion triplet  R → NO deviations from unitarity → YES deviations from unitarity Broncano, Gavela, Jenkins 02

59. A general statement… We have unitarity violation whenever we integrate out heavy fermions : There’s a   : it connects fermions with the same chirality → correction to the kinetic terms It connects fermions with opposite chirality → mass term Y  Y  /M 2 ( L  H) D (H  L) Y N Y N /M 2 ( L H) (H L) Fermionic seesaws: I II A flavour dependent rescaling is needed, which is NOT a unitary transformation

60. In all fermionic Seesaws, the departures from unitarity give directly | c d=6 | i.e. Fermion singlet Seesaws N U PMNS --------> N (non-unitary)

61. Antusch, Biggio, Fernández-Martínez, López-Pavón, M.B.G. 06 → Worthwhile to analyze neutrino data relaxing the hypothesis of unitarity of the mixing matrix

62. The general idea… The general idea……… U= W - i ll e ii ii e 1

63. KamLAND+CHOOZ+K2K SNO UNITARITY Atmospheric + K2K This affects  oscillation probabilities …

64. KamLAND+CHOOZ+K2K SNO UNITARITY Atmospheric + K2K This affects  oscillation probabilities …....  raw of N remains unconstrained

65. Unitarity constraints on (NN ) from : + * Near detectors… MINOS, NOMAD, BUGEY, KARMEN * Weak decays… * W decays * Invisible Z width * Universality tests * Rare lepton decays

66. Unitarity constraints on (NN ) from : + * Near detectors… MINOS, NOMAD, BUGEY, KARMEN * Weak decays… * W decays * Invisible Z width * Universality tests * Rare lepton decays |N| is unitary at the % level

67. All in all, as of today, for the Singlet-fermion Seesaws : (NN + -1)  

68. New CP-violation signals even in the two-family approximation i.e. P (  --->  ) = P (  --->  ) __ Increased sensitivity to the moduli |N| in future Neutrino Factories E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G.

69. Fermion-triplet seesaws: similar - although richer! - analysis

70. Singlet and triplet Seesaws differ in the the pattern of the Z couplings

71. @ tree level in Type III (not in Type I) Bounds on Yukawas type III  → eee  → eee  →  ee  →  e  →  Z→  e Z→  e Z→   → e   → e   →  Ma, Roy 02 Bajc, Nemevsek, Senjanovic 07 Production @ colliders For M ≈ TeV → |Y| < 10 -2 + W decays Invisible Z width Universality tests

72. For the Triplet-fermion Seesaws (type III): (NN + -1)  

73. In summary, for all scalar and fermionic Seesaw models, present bounds: or stronger

74. Conclusions * d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models.

75. Conclusions * d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models. * While the d=5 operator violates B-L, all d=6 ops. conserve it --> natural ansatz: c d=5 ~  /M 2, allowing M~TeV and large Yukawa couplings (even O(1)).

76. Conclusions * d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models. * While the d=5 operator violates B-L, all d=6 ops. conserve it --> natural ansatz: c d=5 ~  /M 2, allowing M~TeV and large Yukawa couplings (even O(1)). d=6 operator crucial: if observed at low energies, only resonant leptogenesis is possible

77. Conclusions * d= 6 operators discriminate among models of Majorana s. - we have determined them for the 3 families of Seesaw models. * While the d=5 operator violates B-L, all d=6 ops. conserve it --> natural ansatz: c d=5 ~  /M 2, allowing M~TeV and large Yukawa couplings (even O(1)). d=6 operator crucial: if observed at low energies, only resonant leptogenesis is possible * c d=6 ~Y + Y/M 2 bounded from 4-  interactions + unitarity deviations     CP-asymmetry may be a clean probe of the new phases of seesaw scenarios. -> Keep tracking these deviations in the future. They are excellent signals of new physics.

78. Back-up slides

79. Low-energy effective theory After EWSB, in the flavour basis: M  → diagonalized → unitary transformation K  → diagonalized and normalized → unitary transf. + rescaling N non-unitary In the mass basis:

80. A general statement… We have unitarity violation whenever we integrate out heavy fermions : scalar field The propagator of a scalar field does not contain   → if it generates neutrino mass, it cannot correct the kinetic term 1/(D 2 -M 2 ) ~ -1/M 2 - D 2 /M 4 + ……. There’s a   : it connects fermions with the same chirality → correction to the kinetic terms It connects fermions with opposite chirality → mass term

81. Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions. Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...) They add 4-fermion exotic operators to production or detection or propagation in matter  __

82. 3 generation Inverse Seesaw and also similar extensions of the fermionic triplet Seesaw e, , , N 1, N 2, N 3 Abada et al. Kersten+Smirnov

83. M (inimal) U (nitarity) V (iolation) : with only 3 light  W - i Z i j

84. N elements from oscillations & decays with unitarity OSCILLATIONS without unitarity OSCILLATIONS +DECAYS 33.79 -.88.47 -.61 <.20 |U| =.19 -.52.42 -.73.58 -.82.20 -.53.44 -.74.56 -.81 M. C. Gonzalez Garcia hep-ph/0410030.75 -.89.45 -.65 <.20 |N| =.19 -.55.42 -.74.57 -.82.13 -.56.36 -.75.54 -.82 MUV Antusch, Biggio, Fernández-Martínez, López-Pavón, M.B.G. 06

85. If we parametrize with If L/E small Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G. + )) (1 +  )   v 2  c d=6    4

86. If we parametrize with If L/E small Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G. + )) (1 +  )   v 2  c d=6     Im (    -     4

87. If we parametrize with If L/E small Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G. + )) (1 +  )   v 2  c d=6    SM  Im (    - 4    

88. If we parametrize with If L/E small Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G. + )) (1 +  )   v 2  c d=6    SM Zero dist. effect  Im (    -     4

89. If we parametrize with If L/E small Can we measure the phases of N ? E. Fdez-Martinez, J.Lopez, O. Yasuda, M.B.G. + )) (1 +  )   v 2  c d=6    SM CP violating interference Zero dist. effect  Im (    -     4

90. Measuring non-unitary phases Present bound from  →   Sensitivity to |   | Sensitivity to       For non-trivial   , one order of magnitude improvement for |N| 

91. The CP phase   can be measured At a Neutrino Factory of 50 GeV with L = 130 Km In P  there is no or suppression:      

92. New CP-violation signals even in the two-family approximation i.e. P (  --->  ) = P (  --->  ) __

93. New CP-violation signals even in the two-family approximation i.e. P (  --->  ) = P (  --->  ) __

94. The effects of non-unitarity… … appear in the interactions This affects weak decays… W - i Z i j      … and oscillation probabilities… NN + =

95. This affects weak decays…

96. … and oscillation probabilities… Zero-distance effect at near detectors:

97. This affects weak decays… … and oscillation probabilities… Zero-distance effect at near detectors: W - Matter  e e e  u d N N N N N + + + Non-Unitary Mixing Matrix

98. W - Matter  e e e  u d N N N N N + + + Zero-distance effect at near detectors: In matter

99. Number of events Exceptions: measured flux leptonic production mechanism detection via NC produced and detected in CC

100. N elements from oscillations:  -row 1.Degeneracy 2. cannot be disentangled Atmospheric + K2K: Δ 12 ≈0 UNITARITY

101. N elements from oscillations: e-row KamLAND: SNO: → all | N ei | 2 determined KamLAND+CHOOZ+K2K SNO CHOOZ

102. N elements from oscillations only with unitarity OSCILLATIONS without unitarity OSCILLATIONS 33.79 -.89.47 -.61 <.20 |U| =.19 -.52.42 -.73.58 -.82.20 -.53.44 -.74.56 -.81 M. C. Gonzalez Garcia hep-ph/0410030.75 -.89.45 -.66 <.34 |N| = [( |N | +|N | ) 1/2 = 0.57-0.86 ].57-.86 ? ? ? 11 22 22 MUV

103. Unitarity constraints on (NN ) from : + * Near detectors… KARMEN: (NN † )  e  0.05 NOMAD: (NN † )   0.09 (NN † ) e   0.013 MINOS: (NN † )   1±0.05 BUGEY: (NN † ) ee  1±0.04 * Weak decays…

104. |N| is unitary at the % level At 90% CL

105. In the future… MEASUREMENT OF MATRIX ELEMENTS |N e3 | 2,  -row → MINOS, T2K, Super-Beams, Factories…  -row → high energies: Factories phases → appearance experiments: Super-Beams, Factories,  -beams TESTS OF UNITARITY (90%CL) OPERAlike

107. Measuring unitarity deviations The bounds on Also apply to   The constraints on  e   from  → e  are very strong We will study the sensitivity to the CP violating terms  e  and   in P e  and P 

108. Measuring unitarity deviations In P e  the CP violating term is supressed by or appart from The zero distance term in |  e  | 2 dominates No sensitivity to the CP phase  e 

109. W - Matter Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions.  e e e  u d Standard Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)

110. Matter  e e e  u d Exotic production Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions. Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)

111. W - Matter  e e  u d e Exotic propagation Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions. Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)

112. W - Matter  e e e  u d Exotic detection Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions. Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...)

113. W - Matter  e e e  u d Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions. Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...) W - Matter  e e e  u d

114. W - Matter  e e e  u d N N N N N + + + Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions. Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...) W - Matter  e e e  u d Non-Unitary Mixing Matrix

115. Matter  e e e  u d Non-Unitary Mixing Matrix Our analysis will also apply to ``non-standard” or ``exotic” neutrino interactions. Grossman, Gonzalez-Garcia et al., Huber et al., Kitazawa et al., Davidson et al. Blennow et al...) W - Matter  e e e  u d

116. masses beyond the SM radiative mechanisms: ex.) 1 loop: Other realizations SUSY models with R-parity violation Models with large extra dimensions: i.e., R are Kaluza-Klein replicas … SM Dirac mass suppressed by (2  R) d/2 Frigerio

117. Quarks are detected in the final state → we can directly measure |V ab | ex: |V us | from K 0 →  - e + e → Measurements of V CKM elements relies on U PMNS unitarity Unitarity in the quark sector With V ab we check unitarity conditions: ex: |V ud | 2 +|V us | 2 +|V ub | 2 -1 = -0.0008±0.0011 decays → only (NN † ) and (N † N) N elements → we need oscillations to study the unitarity of N : no assumptions on V CKM With leptons: K0K0  - dd W+W+ V us * e e+e+ U ei → ∑ i |U ei | 2 =1 if U unitary