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Neutrino Oscillations Theory and Experiments

Neutrino Oscillations Theory and Experiments. S.P.Mikheyev (INR RAS). Introduction. Vacuum oscillations. Oscillations in matter. Adiabatic conversion. Graphical representation of oscillations Conclusion. n 1. n e. n m. n 2. n t. n 3. mixing. | n f  =  U fi | n i . i.

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Neutrino Oscillations Theory and Experiments

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  1. Neutrino Oscillations Theory and Experiments S.P.Mikheyev (INR RAS)

  2. Introduction. • Vacuum oscillations. • Oscillations in matter. • Adiabatic conversion. • Graphical representation of oscillations • Conclusion S.P.Mikheyev (INR RAS)

  3. n1 ne nm n2 nt n3 mixing |nf= Ufi|ni i Standard neutrino scenario • There are only 3 types of light neutrinos: 3 flavors and 3 mass states. • Their interactions are described by the Standard electroweak theory • Neutrino are massive. Neutrino masses are in the sub-eV range - much smaller than masses of charge leptons and quarks. • Neutrinos mix. There are two large mixings • and one small or zero mixing. Pattern of lepton • mixing strongly differs from that of quarks. • Masses and mixing are generated in vacuum A. Yu. Smirnov hep-ph/0702061 S.P.Mikheyev (INR RAS)

  4. с12 s12 0 -s12 c12 0 0 0 1 с13 0 s13 ei 0 1 0 -s13 e-i 0 c13 1 0 0 0 с23s23 0 -s23 c23              U =        Mixing matrix Mixing matrix U can be parameterized with 3 mixing angles(12,23,13) Phase of CP violation () сij = cosij sij = sinij Pontecorvo – Maki – Nakagava -Sakata S.P.Mikheyev (INR RAS)

  5. ( ) 2U = cosq sinq -sinq cosq ne = cosq n1 + sinq n2 n2 = sinq ne + cosq nm nm = - sinq n1 + cosq n2 n1 = cosq ne - sinq nm coherent mixtures of mass eigenstates flavor composition of the mass eigenstates wave packets n1 ne n2 n1 nm n2 n2 n1 Neutrino “images”: ne nm n2 n2 n1 n1 Neutrino states S.P.Mikheyev (INR RAS)

  6. Due to difference of masses 1 and 2 have different phase velocities Oscillation depth: ne n2 Oscillation length: n1 Propagation in vacuum Oscillation probability: S.P.Mikheyev (INR RAS)

  7. Periodic (in time and distance) process of transformation (partial or complete) of one neutrino species into another one Oscillations: I. Oscillations  effect of the phase difference increase between mass eigenstates II. Admixtures of the mass eigenstates i in a given neutrino state do not change during propagation III. Flavors (flavor composition) of the eigenstates are fixed by the vacuum mixing angle S.P.Mikheyev (INR RAS)

  8. Evolution equation Schroedinger’s equation M is the mass matrix Mixing matrix in vacuum S.P.Mikheyev (INR RAS)

  9. Experiments • Disappearance experiments: Atmospheric neutrinos; LBL: K2K, MINOS; reactor neutrinos: KamLAND Probability as a function of distance (atmospheric neutrinos) energy (K2K, MINOS) L/E (atmospheric neutrinos, KamLAND) • Appearence experiment: LBL: MINOS, OPERA, T2K S.P.Mikheyev (INR RAS)

  10. Atmospheric neutrinos Jennifer Raaf Talk at Neutrino’2008 S.P.Mikheyev (INR RAS)

  11. Erec (GeV)  Long Baseline Neutrinos K2K Hugh Gallagher Talk at Neutrino’2008 MINOS S.P.Mikheyev (INR RAS)

  12. Reactor Neutrinos KamLAND Patrick Decowski Talk at Neutrino’2008 S.P.Mikheyev (INR RAS)

  13. Propagation in matter Neutrino interactions with matter affect neutrino properties as well as medium itself Incoherent interactions Coherent interactions • CC & NC inelastic scattering • CC quasielastic scattering • NC elastic scattering with energy loss • CC & NC elastic forward scattering • Potentials • Neutrino absorption (CC) • Neutrino energy loss (NC) • Neutrino regeneration (CC) S.P.Mikheyev (INR RAS)

  14. e- e e, e, + Z0 W+ Elastic forward scattering e e- e- e- Potential: V = Ve- V Unpolarized and isotropic medium: Potential • At low energy elastic forward scattering • (real part of amplitude) dominates. • Effect of elastic forward scattering is • describer by potential • Only difference of e and  is important S.P.Mikheyev (INR RAS)

  15. Refraction index: ~ 10-20 inside the Earth < 10-18 inside in the Sun ~ 10-6 inside neutron star Refraction length: Potential V ~ 10-13 eV inside the Earth at E = 10 MeV S.P.Mikheyev (INR RAS)

  16. Evolution equation in matter Diagonalizationof the Hamiltonian: • Mixing • Differenceof theeigenvalues • Resonance condition At resonance: S.P.Mikheyev (INR RAS)

  17. sin2 2qm n n sin2 2q= 0.08 Resonance half width: Resonance energy: Resonance layer: sin2 2q= 0.825 Resonance density: Resonance At sin2 2qm = 1 S.P.Mikheyev (INR RAS)

  18. F (E) F0(E) F (E) F0(E) vacuum matter ~E/ER ~E/ER Oscillations in matter (Constant density) Pictures of neutrino oscillations in media with constant density and vacuum are identical In uniform matter (constant density) mixing is constant qm(E, n) = constant As in vacuum oscillations are due to change of the phase difference between neutrino eigenstates S.P.Mikheyev (INR RAS)

  19. Oscillations in matter (Non-uniformdensity) In matter with varying density the Hamiltonian depends on time: Htot = Htot(ne(t)) Its eigenstates, m, do not split the equations of motion θm= θm(ne(t)) The Hamiltonian is non-diagonal no split of equations Transitions1m2m S.P.Mikheyev (INR RAS)

  20. Oscillations in matter Varying density vs. constant density Pictures of neutrino oscillations in media with constant density and variable density are different In uniform matter (constant density) mixing is constant qm(E, n) = constant As in vacuum oscillations are due to change of the phase difference between neutrino eigenstates MSW effect In varying density matter mixing is function of distance (time) qm(E, n) = F(x) Transformation of one neutrino type to another is due to change of mixing or flavor of the neutrino eigenstates S.P.Mikheyev (INR RAS)

  21. Adiabatic conversion One can neglect of 1m 2m transitions if the density changes slowly enough External conditions (density) change slowly so the system has time to adjust itself Adiabaticity condition: Transitions between the neutrino eigenstates can be neglected The eigenstates propagate independently LR = L/sin2 is the oscillation length in resonance Crucial in the resonance layer: - the mixing angle changes fast - level splitting is minimal is the width of the resonance layer S.P.Mikheyev (INR RAS)

  22. Adiabatic conversion Initial state: Adiabatic conversion to zero density: 1m(0)  1 2m(0)  2 Final state: Probability to find e averaged over oscillations: S.P.Mikheyev (INR RAS)

  23. Adiabatic conversion Dependence on initial condition The picture of adiabatic conversion is universal in terms of variable: resonance layer There is no explicit dependence on oscillation parameters, density distribution, etc. Only initial value of y0 is important. production pointy0 = - 5 oscillation band Non-oscillatory conversion y0 < -1 survival probability Interplay of conversion and oscillations y0 = -11 averaged probability resonance Oscillations with small matter effect y0 > 1 y (distance) S.P.Mikheyev (INR RAS)

  24. Adiabatic conversion Survive probability (avergedover oscillations) sin22 = 0.8 Vacuum oscillations P = 1 – 0.5sin22 Non - adiabatic conversion (0) = e = 2m  2 Adiabatic edge Adiabatic conversion P =|<e|2>|2 = sin2 200 0.2 2 20 E (MeV) (m2 = 810-5 eV2) S.P.Mikheyev (INR RAS)

  25. Oscillations vs. conversion Both require mixing, conversion is usually accompanyingby oscillations Adiabatic conversion Oscillation • Vacuum or uniform mediumwith constant parameters • Non-uniform medium or/and medium with varying in time parameters • Change of mixing in medium = change of flavor of the eigenstates • Phase difference increasebetween the eigenstates θm  In non-uniform medium: interplay of both processes S.P.Mikheyev (INR RAS)

  26. Oscillations vs. conversion Adiabatic conversion Spatial picture survival probability Oscillations distance survival probability distance S.P.Mikheyev (INR RAS)

  27. 4p + 2e- 4He + 2ne + 26.73 MeV electron neutrinos are produced Adiabatic conversion in matter of the Sun r : (150 0) g/cc e Adiabaticity parameter  ~ 104 Solar neutrinos J.N. Bahcall n S.P.Mikheyev (INR RAS)

  28. Solar neutrinos SNO Hamish Robertson Talk at Neutrino’2008 S.P.Mikheyev (INR RAS)

  29. Solar neutrinos Cl-Ar data Cristano Galbiati Talk at Neutrino’2008 S.P.Mikheyev (INR RAS)

  30. Solar neutrinos Solar neutrinos vs. KamLAND Adiabatic conversion (MSW) Vacuum oscillations Matter effect dominates (at least in the HE part) Matter effect is very small Non-oscillatory transition, or averaging of oscillationsthe oscillation phase is irrelevant Oscillation phase is crucialfor observed effect Adiabatic conversionformula Vacuum oscillations formula Coincidence of these parameters determined from the solar neutrino data and from KamLANDresults testifies for the correctness of the theory (phase of oscillations, matter potential, etc..) S.P.Mikheyev (INR RAS)

  31. Solar neutrinos m2(5.410-59.510-5) eV2 Sin22 (0.710.95) m21 12 с12 s12 0 -s12 c12 0 0 0 1 с13 0 s13 ei 0 1 0 -s13 e-i 0 c13 1 0 0 0 с23s23 0 -s23 c23              U =        Atmosphericneutrinos m2 (1.310-3 3.010-3) eV2 Sin22> 0.9 m32 23 Oscillation parameters Knownparameters S.P.Mikheyev (INR RAS)

  32. Mixing matrix Unknownparameters sin2213  0.2  - CP phase Mass hierarchy Sin213 = 0.0160.010 O. Mena and S. Parke, hep-ph/0312131 G.L. Fogli, E. Lisi, A. Marrone, A. Palazzo, A.M. RotunnoarXiv:0806.2649 S.P.Mikheyev (INR RAS)

  33. Neutrino polarization vectors Polarization vector: ( - Pauli matrices) Evolution equation: d Y d t Differentiating P and using equation of motion Coincides with equation for the electron spin precession in the magnetic field S.P.Mikheyev (INR RAS)

  34. z (P-1/2)  B 2 x (Re e+x)  y (Im e+x) Graphic representation S.P.Mikheyev (INR RAS)

  35. Graphic representation Non-uniform density:Adiabatic conversion S.P.Mikheyev (INR RAS)

  36. Graphic representation Non-uniform density:Adiabaticity violation S.P.Mikheyev (INR RAS)

  37. ne ne ne nb Z0 Z0 nb nb nb ne ne (p) t-channel nb nb (q) ne ne (p) u-channel ne nb (q) nb Non-linear effects Collective effects related to neutrino self-interactions ( - scattering) Momentum exchange  flavor exchange  flavor mixing elastic forward scattering Collective flavor transformations J. Pantaleone can lead to the coherent effect S.P.Mikheyev (INR RAS)

  38. Conclusion “Standard neutrino scenario” gives complete description of neutrino oscillation phenomena. But it tells us nothing what physics is behind of neutrino masses and mixing. New experiments will allow us to measure the 1-3 mixing, deviation of 2-3 mixing from maximal, and CP-phases, as well as hopefully to establish type of neutrino hierarchy, nature of neutrino and neutrino mass. S.P.Mikheyev (INR RAS)

  39. Conclusion “Standard neutrino scenario” gives complete description of neutrino oscillation phenomena. But it tells us nothing what physics is behind of neutrino masses and mixing. New experiments will allow us to measure the 1-3 mixing, deviation of 2-3 mixing from maximal, and CP-phases, as well as hopefully to establish type of neutrino hierarchy, nature of neutrino and neutrino mass. However neutrinos gave us many puzzles in past and one can expect more in future!!! S.P.Mikheyev (INR RAS)

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