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NEUTRINO OSCILLATIONS AND THE MSW EFFECT

NEUTRINO OSCILLATIONS AND THE MSW EFFECT. S. P. Mikheyev INR RAS Moscow. LEP: Number of light, active neutrinos  3. 35. 25.  (nb). 15. 5. 90. 92. 94. 96. 88.  s = E cm (GeV).

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NEUTRINO OSCILLATIONS AND THE MSW EFFECT

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  1. NEUTRINO OSCILLATIONS AND THE MSW EFFECT S. P. Mikheyev INR RAS Moscow

  2. LEP: Number of light, active neutrinos  3 35 25 (nb) 15 5 90 92 94 96 88 s = Ecm (GeV) Erice 9 July 2004

  3. Non-zero neutrino masses introduce lepton mixing matrix,U, which, in general, is not expected to be diagonal. The matrix connects the flavor eigenstates (ne,nm,nt,…)with the mass eigenstates (n1,n2,n3,…). Neutrino Oscillations B. Pontecorvo (1957), Z. Maki, M. Nakagawa, S. Sakata (1962) Erice 9 July 2004

  4. Flavors, Masses & Mixing ne nm i n3 n1 n2 nt 2 ) U = ( cosq sinq - sinq cosq Flavor Neutrino States Mass Eigetstates m1 m2 m3 m t e • Correspond to certain charged lepton Mixing • Interact in pairs na= SUaini • Eigenstates of the CC Weak Interactions Erice 9 July 2004

  5. Neutrino Oscillations n2 n1 ne n2 nm n1 n2 = sinq ne + cosq nm ne = cosq n1 + sinq n2 inversely n1 = cosq ne - sinq nm nm = - sinq n1 + cosq n2 coherent mixtures of mass eigenstates flavor composition of the mass eigenstates n2 n2 ne n1 wave packets n1 n2 inserting nm n1 Flavors of eigenstates The relative phases of the mass states in ne and nm are opposite Interference of the parts of wave packets with the same flavor depends on the phase difference Df between n1 and n2 Erice 9 July 2004

  6. Neutrino Oscillations Dm2 2E Dvphase = Dm2 = m22 - m12 Propagation in vacuum: Flavors of mass eigenstates do not change Determined by q Admixtures of mass eigenstates do not change: no n1 <-> n2 transitions n2 ne n1 Df = Dvphase t Df = 0 Due to difference of masses n1 and n2 have different phase velocities: Oscillation length: oscillations: ln = 2p/Dvphase= 4pE/Dm2 effects of the phase difference increase which changes the interference pattern Amplitude (depth) of oscillations: A = sin22q Erice 9 July 2004

  7. d i (ni)= Mdiag(ni) dt d i (na)= UMdiagU*(na) dt nanbt=SUaiUbie-iE t i * i <nanbt2= SUaiUbiUajUbje-i(E – E )t j i * * i,j (ni)= U*(na) Erice 9 July 2004

  8. 2- Oscillations in Vacuum 1.0 0.8 Probability 0.6 0.4 0.2 102 103 104 L/E (km/GeV) P(ee ) =1 - sin22q sin2 (1.27m2(eV2)L(km)/E(GeV)) (L/E) = 0.1 (L/E) = 0.25 (L/E) = 0.5 Erice 9 July 2004

  9. Oscillation Measurements • Disappearence experiment: P( ) • Appearence experiment: P( ) P( ) = 1 - P( ) <P> = P( ) Erice 9 July 2004

  10. Matter Effect L. Wolfenstein, 1978 ne e Elastic forward scattering Potentials Ve, Vm W V ~ 10-13 eV inside the Earth for E = 10 MeV ne e Difference of potentials is important for ne nm : Ve- Vm = 2 GFne Refraction index: n - 1 = V / p Refraction length: l0 = 2p / (Ve - Vm) ~ 10-20 inside the Earth < 10-18 inside the Sun n - 1 = 2 p/GFne ~ 10-6 inside the neutron star Erice 9 July 2004

  11. ne n1 n2m n1m q n2 nm qm Neutrino eigenstates in matter in vacuum: in matter: Effective Hamiltonean H = H0 + V H0 V = Ve - Vm n1m, n2m n1, n2 Eigenstates depend on ne, E m1m, m2m m1, m2 Eigenvalues m12/2E, m22/2E H1m, H2m Mixing in matter is determined with respect to eigenstates in matter qm is the mixing angle in matter Erice 9 July 2004

  12. Oscillations in matter In uniform matter (constant density) qm(E, n) = constant mixing is constant Flavors of the eigenstates do not change Admixtures of matter eigenstates do not change: no n1m <-> n2mtransitions Oscillations Monotonous increase of the phase difference between the eigenstates Dfm as in vacuum n2m ne n1m Dfm= (H2 - H1) L Dfm= 0 Parameters of oscillations (depth and length) are determined by mixing in matter and by effective energy split in matter sin22qm, lm sin22q, ln Erice 9 July 2004

  13. Resonance In resonance: sin2 2qm sin2 2qm = 1 n n Mixing in matter is maximal Level split is minimal sin2 2q= 0.08 sin2 2q= 0.825 ln = l0 cos 2q ~ Refraction length Vacuum oscillation length ~ For large mixing: cos 2q = 0.4 - 0.5 the equality is broken the case of strongly coupled system shift of frequencies ln / l0 ~ n E Resonance width:DnR = 2nR tan2q Resonance layer: n = nR + DnR Erice 9 July 2004

  14. Two effects Adiabatic (partially adiabatic) neutrino conversion Resonance enhancement of neutrino oscillations Density profiles: Variable density Constant density Change of mixing, or flavor of the neutrino eigenstates Change of the phase difference between neutrino eigenstates Degrees of freedom: In general: Interplay of oscillations and adiabatic conversion MSW Erice 9 July 2004

  15. Resonance enhancement n ne ne F0(E) F(E) Source Layer of matter with constant density, length L Detector k = p L/ l0 thin layer thick layer k = 1 k = 10 F (E) F0(E) sin2 2q = 0.824 sin2 2q = 0.824 E/ER E/ER Erice 9 July 2004

  16. Resonance enhancement n ne ne F0(E) F(E) Source Layer of matter with constant density, length L Detector thick layer thin layer k = 1 k = 10 F (E) F0(E) sin2 2q = 0.08 sin2 2q = 0.08 E/ER E/ER Erice 9 July 2004

  17. Resonance enhancement resonance layer Continuity: neutrino and antineutrino semiplanes normal and inverted hierarchy P Oscillations (amplitude of oscillations) are enhanced in the resonance layer ln / l0 E = (ER - DER) -- (ER + DER) DER = ERtan 2q = ER0sin 2q ER0= Dm2 / 2V P With increase of mixing: q -> p/4 ER-> 0 ln / l0 DER-> ER0 Erice 9 July 2004

  18. MSW: adiabatic conversion H = H(t) depends on time Non-uniform matter density changes on the way of neutrinos: n1m n2m are no more the eigenstates of propagation -> n1m <-> n2m transitions qm = qm(ne(t)) mixing changes in the course of propagation ne = ne(t) However if the density changes slowly enough (adiabaticity condition) n1m <->n2m transitions can be neglected Flavors of eigenstates change according to the density change determined by qm Admixtures of the eigenstates, n1m n2m, do not change fixed by mixing in the production point Phase difference increases according to the level split which changes with density MSW Effect is related to the change of flavors of the neutrino eigenstates in matter with varying density Erice 9 July 2004

  19. Adiabaticity External conditions (density) change slowly so the system has time to adjust itself dqm dt Adiabaticity condition << 1 H2 - H1 The eigenstates propagate independently transitions between the neutrino eigenstates can be neglected n1m <--> n2m Crucial in the resonance layer: - the mixing angle changes fast - level splitting is minimal if vacuum mixing is small DrR > lR lR = ln/sin2q is the oscillation width in resonance DrR = nR / (dn/dx)Rtan2q is the width of the resonance layer If vacuum mixing is large the point of maximal adiabaticity violation is shifted to larger densities n(a.v.) -> nR0 > nR nR0 = Dm 2/ 2 2 GF E Erice 9 July 2004

  20. Adiabatic conversion and initial condition The picture of conversion depends on how far from the resonance layer in the density scale the neutrino is produced n0 < nR n0 > nR n0 ~ nR nR - n0 >> DnR n0 - nR >> DnR Interplay of conversion and oscillations Oscillations with small matter effect Non-oscillatory conversion nR ~ 1/ E All three possibilities are realized for the solar neutrinos in different energy ranges Erice 9 July 2004

  21. Adiabatic conversion n1m <-->n2m P = sin2q n0 >> nR Non-oscillatory transition n2m n1m n2 n1 interference suppressed Resonance Mixing suppressed n0 > nR Adiabatic conversion + oscillations n2m n1m n2 n1 n0 < nR Small matter corrections n2m n1m n2 n1 ne Erice 9 July 2004

  22. Adiabaticity violation n2m n1m Fast density change n0 >> nR n2m n1m n2 n1 ne Resonance Admixture of n1m increases Erice 9 July 2004

  23. The MSW effect The picture of adiabatic conversion is universal in terms of variable y = (nR - n ) / DnR (no explicit dependence on oscillation parameters density distribution, etc.) Only initial value y0 matters. resonance layer production point y0 = - 5 resonance survival probability For zero final density: y = 1/tan 2q oscillation band averaged probability LMA y = (nR - n) / DnR (distance) Erice 9 July 2004

  24. Solar neutrinos Adiabatic conversion in matter of the Sun r : (150 0) g/cc Oscillations in vacuum n Oscillations in matter of the Earth Erice 9 July 2004

  25. Conversion inside the Sun tan2q = 0.41, Dm2 = 7.3 10-5 eV2 survival probability survival probability sin2q E = 14 MeV resonance E = 10 MeV core y y distance surface survival probability survival probability E = 6 MeV E = 2 MeV y y Erice 9 July 2004

  26. Conversion inside the Sun tan2q = 0.41, Dm2 = 7.3 10-5 eV2 Low energy part of the spectrum: vacuum oscillations with small matter corrections E = 0.4 MeV E = 0.86 MeV survival probability survival probability y y distance distance Dashed lines: for pure vacuum oscillations Erice 9 July 2004

  27. Atmospheric Neutrinos: Flux Features p, He, … A N E3dF/dE N p± (K ±) E(GeV) m± nm ne e± nm (nm + ) nm R = = 2 (ne+ ) ne E(GeV) Erice 9 July 2004

  28. Atmospheric Neutrinos: Flux Features cos = 0.8 L = 20km 104 Path length (km) L = 500km cos = 0 103 L = 10 000km 102 -1 -.6 -.2 .2 .6 1 Cos cos = -0.8 up horizontal down L/E values from 0.1 (10 km/1000 GeV) to 104 (104 km/1 GeV) can be explored to study neutrino oscillations. Flux is up/down symmetric but isn’t isotropic Fn~ 1/CosQ Erice 9 July 2004

  29. Atmospheric Neutrino Detection K.Nishikawa’s talk Erice 9 July 2004

  30. Atmospheric Neutrino Detection Super-Kamiokande Erice 9 July 2004

  31. Atmospheric Neutrino Events m Partially contained 1/10t/year Acceptance 4p nm m e Fully contained Ed Kearns for the SK Collaboration Neutrino2004, June 15, Paris 0.8 0.6 Events/day 0.4 ne nm 0.2 100 103 101 102 Neutrino energy (GeV) Erice 9 July 2004

  32. Atmospheric Neutrino Events Upward through-going m 1/10m2/year Acceptance 2p Ed Kearns for the SK Collaboration Neutrino2004, June 15, Paris 0.18 Upwardstopping 0.14 m 0.10 Events/day 0.06 nm nm 0.02 100 103 101 102 Neutrino energy (GeV) Erice 9 July 2004

  33. Atmospheric Neutrinos Zenith Angle Distributions Sub-GeV Evis < 1.3 GeV Ed Kearns for the SK Collaboration Neutrino2004, June 15, Paris Multi-GeV Evis > 1.3 GeV Erice 9 July 2004

  34. Atmospheric Neutrinos  oscillations Ed Kearns for the SK Collaboration Neutrino2004, June 15, Paris Erice 9 July 2004

  35. Atmospheric Neutrinos  oscillations L/E analysis Ed Kearns for the SK Collaboration Neutrino2004, June 15, Paris Oscillation deep @ L/E  500 km/GeV Erice 9 July 2004

  36. K2K is the first accelerator-based long-baseline neutrino oscillation experiment to investigate the neutrino oscillation observed in atmospheric neutrinos. K2K experiment Super-Kamiokande KEK- 12GeV PS L=250 km Erice 9 July 2004

  37. K2K experiment Neutrino Beam Production p+Al  p+  m+ +nm e+ + ne (1.3%)+ nm (0.5%) Near Detector Far Detector  - disappearance Erice 9 July 2004

  38. Erec (GeV)  K2K experiment Shape of energy spectrum CC – quasielastic reactions Erice 9 July 2004

  39. K2K experiment Both  disappearance and energy spectrum distortion have the consistent result Erice 9 July 2004

  40. Solar Neutrinos G.Fogli et al. hep-ph/0106247 Erice 9 July 2004

  41. Solar Neutrinos All solar neutrino data Erice 9 July 2004

  42. Experiment KamLAND Erice 9 July 2004

  43. Experiment KamLAND Erice 9 July 2004

  44. Experiment KamLAND Erice 9 July 2004

  45. Experiment KamLAND Erice 9 July 2004

  46. Experiment KamLAND Erice 9 July 2004

  47. 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 =        Atmospheric neutrinos m2 (1.310-3 3.010-3) eV2 Sin22> 0.9 m32 23 3 – neutrino mixing 3 mixing angles(12,23,13) &phase of CP violation () сij = cosij sij = sinij Erice 9 July 2004

  48. m21 m31 2 2 Known parameters ( ,, sin2212, sin2223) … and limit forsin2213 Erice 9 July 2004

  49. normal inverted 3 2 1 2 Sign ofm31 2 1 3 Unknownparameters sin2213  0.2  - phase of CP violation  Mass hiererchy Erice 9 July 2004

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