PLAN. Lecture I: Lecture II: Neutrino oscillations and the discovery of neutrino masses and mixings. Lecture III: The quest for leptonic CP violation

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1 PLAN Lecture I: Neutrinos in the SM Neutrino masses and mixing: Majorana vs Dirac Lecture II: Neutrino oscillations and the discovery of neutrino masses and mixings Lecture III: The quest for leptonic CP violation A neutrino look at BSM and the history of the Universe

2 For the discovery of neutrino oscillations, which shows that neutrinos have mass

3 Stars shine neutrinos 1939 Bethe Stablishes the theory of stelar nucleosynthesis Nobel 1967

4 How many neutrinos from the Sun? Bahcall

5 The hero of the caves 1966 he detects for the first time solar neutrinos in a tank of liters 1280m underground (Homestake mine) R. Davis Nobel 2002 Did not convince because he saw 0.4 of the expected. Problem in detector? In solar model? In neutrinos?

6 Neutrino masses & lepton mixing (Dirac) Couplings to the Higgs give rise to fermion masses and connect families! In the mass eigenbasis

7 Neutrino masses & lepton mixing (Dirac) Couplings to the Higgs give rise to fermion masses and connect families! In the mass eigenbasis Three massive neutrinos and three massive leptons

8 Neutrino masses & lepton mixing (Dirac) In the new basis: Pontecorvo-Maki-Nakagawa-Sakata Matrix unitary matrix analogous to CKM

9 Lepton mixing ν e e + ν µ W + W + The neutrino flavour basis: ν e e + ν µ µ + ν τ W + W + W + e + ν µ µ + ν τ τ + States produced in a CC interaction W + in combination with e, m, t µ + W + τ + Eigenstates of the free Hamiltonian ν τ

an interferometer in flavour space, because neutrinos are so

10 Neutrino oscillations Neutrinos are produced and detected via weak interactions as flavour states: A neutrino experiment is an interferometer in flavour space, because neutrinos are so weakly interacting that can keep coherence over very long distances! L

11 Classical analogy I: no flavour mixing A n e is produced and stays a n e n e

12 The probability to find a to find a is zero. n m n e at any time is the same, but the probability

13 n m No flavour mixing n m A is produced and stays a n m

14 The probability to find a to find a is zero. n e n m at any time is the same, but the probability

15 Classical analogy II: Maximal flavour mixing n e n m

16 The probability to find a n e oscillates with time and so does that of n m

17 Mass eigenstates=normal modes

18 The probability to find a n e o n m does not change with time

19 Classical analogy III: small flavour mixing

20 The probability to find a n e oscillates with time and so does that of n m

21 Neutrino oscillations in vacuum We start at time t 0 with a neutrino state of flavour a: We want to know the probability that at time t a measurement reveals that the state is one with flavour b:

22 Neutrino oscillations in vacuum

23 Neutrino Oscillation: 2n Only one oscillation frequency, (appearance probability) (disappearance or survival probability)

24 Optimal experiment: Oscillation suppressed Fast oscillation regime Equivalent to incoherent propagation: sensitivity to mass splitting is lost

$accelerator experiments, Sun for solar neutrinos) Wolfenstein Index of refraction (coherent forward scattering) different for electron and m/t$

25 Neutrino Oscillations in matter Many neutrino oscillation experiments involve neutrinos propagating in matter (Earth for atmospheric neutrinos or accelerator experiments, Sun for solar neutrinos) Wolfenstein Index of refraction (coherent forward scattering) different for electron and m/t neutrinos

26 Neutrino propagation in matter +: neutrinos, -: antineutrinos In the flavour basis: Earth: Sun:

27 Effective masses in matter Solar neutrinos are produced in the center of the sun and as the exit they encounter a decaying matter density: q=0 2

28 q 0 2 MSW resonance Mikheyev, Smirnov 85 MSW Resonance: -Only for n or n, not both -Only for one sign of Dm 2 cos2q

29 Neutrinos in variable matter If the variation is slow enough: adiabatic approximation (if a state is at r=0 in an eigenstate it remains in the i-th eigenstate until it exits the sun) e m m e

30 Solar neutrinos MSW resonance energy

31 Solar neutrinos and MSW P 3n² ee! pp (all solar)! 7 Be (BX)! pep (BX)! 8 B (SNO + SK)! 8 B (SNO LETA + BX)! Energy [kev]! FIG. 84. Electron neut rino survival probability Borexino as a function of neutrino energy according t o MSW LMA model. T he band is the same as in Fig. 83, calculat ed for the production region in some cases, The central measurement o measurement s were made as neutrinos, the the flux of CN surement of th lat ter measure low backgroun the first two e t ion capability genic backgrou from an extens sources that pr In this pape ground and th published solar the first time, 7

32 Classical analogy IV:MSW resonance

33 Classical analogy IV:MSW resonance As we cross the resonance (when the two lengths are the same), there is a maximal flavour conversion: what was mostly is now mostly n e n m

34 Underground cathedrals of light Superkamiokande Koshiba (Nobel 2002) Allows to reconstruct velocity and direction, e/m particle identification

35 Neutrinography of the sun SuperKamiokande (22.5 kton!) SNO e - n

36 Flavour of solar neutrinos -1 Can be tested in the Earth with Reines&Cowen experiment!

37 KamLAND: solar oscillation Reines&Cowan experiment ½ century later at 170 km from Japenese reactors Large mixing

38 Atmospheric Neutrinos

39 Atmospheric Neutrinos Produced in the atmosphere when primary cosmic rays collide with it, producing p, K

40 Atmospheric Neutrinos

41 Atmospheric Neutrinos

42 Atmospheric Neutrinos

43 Atmospheric Oscillation Large mixing -1 Reines&Cowan experiment at 1km! Lederman&co experiment at 1000km!

44 Lederman&co neutrinos oscillate with the atmospheric wave length Pulsed neutrino beams to 700 km baselines MINOS OPERA

45 Reactor neutrinos oscillate with atmospheric wave length Double Chooz, Daya Bay, RENO 10%

46 Using the SuperKamiokande detector!

47 Standard 3n scenario Solar and atmospheric osc. decouple as 2x2 mixing phenomena: hierarchy small

48 SM+3 massive neutrinos: Global Fits

Solar spectrum. Nuclear burning in the sun produce Heat, Luminosity and Neutrinos. pp neutrinos < 0.4 MeV

Solar spectrum. Nuclear burning in the sun produce Heat, Luminosity and Neutrinos. pp neutrinos < 0.4 MeV SOLAR NEUTRINOS Solar spectrum Nuclear burning in the sun produce Heat, Luminosity and Neutrinos pp neutrinos < 0.4 MeV Beryllium neutrinos 0.86 MeV Monochromatic since 2 body decay 2 kev width due to