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``Mesonium and antimesonium’’

Right time. B. Pontecorvo. ``Mesonium and antimesonium’’. Zh. Eksp.Teor. Fiz. 33, 549 (1957) [Sov. Phys. JETP 6, 429 (1957)] translation . First paper where a possibility of neutrino mixing and oscillations was mentioned. 50 years!. Right place. III International Pontecorvo

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``Mesonium and antimesonium’’

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  1. Right time B. Pontecorvo ``Mesonium and antimesonium’’ Zh. Eksp.Teor. Fiz. 33, 549 (1957) [Sov. Phys. JETP 6, 429 (1957)] translation First paper where a possibility of neutrino mixing and oscillations was mentioned 50 years! Right place S.P.Mikheyev INR RAS

  2. III International Pontecorvo Neutrino Physics School Neutrinos in Matter S.P. Mikheyev INR RAS

  3. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Propagation of massive neutrino 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

  4. Neutrinos in Matter III International Pontecorvo Neutrino Physics School "Standard model of neutrino" A. Yu. Smirnov hep-ph/0702061 • There are only three types of light neutrinos • Their interactions are described by the Standard electroweak theory • Masses and mixing are generated in vacuum S.P.Mikheyev INR RAS

  5. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Introduction • How neutrino looks (neutrino “image”) • How neutrino oscillations look (graphic representation) S.P.Mikheyev INR RAS

  6. Neutrinos in Matter |nf= Ufi|ni i III International Pontecorvo Neutrino Physics School Neutrino sates correspond to certain charged leptons certain neutrino flavors (interact in pairs) n1 m1 ne e n2 m nm m2 nt t n3 m3 Eigenstates of the CC weak interactions mixing Mass eigenstates S.P.Mikheyev INR RAS

  7. Neutrinos in Matter ( ) 2U = cosq sinq -sinq cosq ne nm n2 n2 n1 n1 III International Pontecorvo Neutrino Physics School Neutrino sates 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 n1 ne wave packets n2 n1 nm n2 n2 n1 Neutrino “images”: S.P.Mikheyev INR RAS

  8. Neutrinos in Matter ne n2 n1 III International Pontecorvo Neutrino Physics School Neutrino propagation in vacuum Due to difference of masses 1 and 2 have different phase velocities Oscillation depth: Oscillation length: S.P.Mikheyev INR RAS

  9. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Neutrino propagation in vacuum Oscillation probability: 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

  10. Neutrinos in Matter B  III International Pontecorvo Neutrino Physics School Graphic representation z (P-1/2) Evolution equation:  Analogy to equation for the electron spin precession in magnetic field 2 x (Re e+) y (Im e+) P(e e) = e+e= ½(1 + cosZ) S.P.Mikheyev INR RAS

  11. Neutrinos in Matter z x y III International Pontecorvo Neutrino Physics School Graphic representation S.P.Mikheyev INR RAS

  12. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Matter effect • Matter potential • Evolution equation in matter • Resonance • Adiabatic conversion • Adiabaticity violation • Survival probability • Parametric enhancement of oscillations S.P.Mikheyev INR RAS

  13. Neutrinos in Matter e- e e, e, + Z0 W+ e e- e- e- Potential: V = Ve- V III International Pontecorvo Neutrino Physics School Matter potential • At low energy elastic forward scattering • (real part of amplitude) dominate. • Effect of elastic forward scattering is • describer by potential • Only difference of e and  is important Elastic forward scattering S.P.Mikheyev INR RAS

  14. Neutrinos in Matter - neutrino velocity - vector of polarization III International Pontecorvo Neutrino Physics School Matter potential  - the wave function of the system neutrino - medium Hint – Hamiltonian of the weak interaction at low energy (CC interaction with electrons) (gV = -gA = 1) Unpolarized and isotropic medium: S.P.Mikheyev INR RAS

  15. Neutrinos in Matter ~ 10-20 inside the Earth < 10-18 inside in the Sun ~ 10-6 inside neutron star III International Pontecorvo Neutrino Physics School Matter potential V ~ 10-13 eV inside the Earth at E = 10 MeV Refraction index: Refraction length: S.P.Mikheyev INR RAS

  16. Neutrinos in Matter vacuum part matter part III International Pontecorvo Neutrino Physics School Evolution equation in matter total Hamiltonian S.P.Mikheyev INR RAS

  17. Neutrinos in Matter Hvac Hvac + V • Effective Hamiltonian 1, 2 1m, 2m • Eigenstates e 1 m12/2E, m22/2E 1m H1m, H2m 2m • Eigenvalue  2 m  III International Pontecorvo Neutrino Physics School Evolution equation in matter vacuum vs. matter Depend on ne, E Mixing angle determines flavors of eigenstatea (i) (f)  (f) (im) m S.P.Mikheyev INR RAS

  18. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Evolution equation in matter Diagonalizationof the Hamiltonian: • Mixing • Differenceof theeigenvalues At resonance: • Resonance condition differenceof theeigenvalues is minimal mixing is maximal level crossing S.P.Mikheyev INR RAS

  19. Neutrinos in Matter n n III International Pontecorvo Neutrino Physics School Resonance At sin2 2qm = 1 sin2 2qm Resonance half width: sin2 2q= 0.08 sin2 2q= 0.825 Resonance energy: Resonance density: Resonance layer: S.P.Mikheyev INR RAS

  20. Neutrinos in Matter sin2 2q = 0.08 (small mixing) ne n2m nm n1m III International Pontecorvo Neutrino Physics School Resonance H sin2 2q = 0.825 (large mixing) Level crossing: ne n2m Dependence of the neutrino eigenvalues on the matter potential (density) nm n1m V. Rubakov, private comm. N. Cabibbo, Savonlinna 1985 H. Bethe, PRL 57 (1986) 1271 H • Crossing point - resonance • the level split is minimal • the oscillation length is maximal For maximal mixing: nR = 0 S.P.Mikheyev INR RAS

  21. Neutrinos in Matter matter dominated vacuum dominated III International Pontecorvo Neutrino Physics School Resonance Oscillation length in matter: Lm E S.P.Mikheyev INR RAS

  22. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter 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

  23. Neutrinos in Matter ne n2 n1 III International Pontecorvo Neutrino Physics School Oscillations in matter Constant density • Flavors of the eigenstates do not change • Admixtures of matter eigenstates do not • change: no 1m2m transitions Oscillations as in vacuum • Monotonous increaseof the phase • difference between eigenstates Δm n2 n1 Dfm= 0 Dfm= (H2 - H1) L sin22qm, Lm Parameters of oscillations (depth and length) are determined by mixing in matter and by effective energy split in matter instead of sin22q, Ln S.P.Mikheyev INR RAS

  24. Neutrinos in Matter ne ne  F0(E) F(E) Layer of matter with constant density, length L Detector Source thick layer L = 10L0/p thin layer L = L0/p F (E) F0(E) ~E/ER ~E/ER III International Pontecorvo Neutrino Physics School Oscillations in matter Constant density: Resonance enhancement of oscillations sin2 2q = 0.08 sin2 2q = 0.824 S.P.Mikheyev INR RAS

  25. Neutrinos in Matter ne ne  F0(E) F(E) Detector Source z x y III International Pontecorvo Neutrino Physics School Oscillations in matter Instantaneous density change n1 n2 m = 1 m = 2 S.P.Mikheyev INR RAS

  26. Neutrinos in Matter ne ne  F0(E) F(E) Detector Source z x y III International Pontecorvo Neutrino Physics School Oscillations in matter Instantaneous density change n1 n2 m = 1 m = 2 S.P.Mikheyev INR RAS

  27. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Instantaneous density change:parametric resonance m = 1 1 1 1 n1 n2  1 2 3 4 2 5 6 2 7 8 2 m = 2 B2 B1 1 = 2 =  . Enhancement associated to certain conditions for the phase of oscillations. . 1 2 . 3 . 4 Another way to get strong transition. No large vacuum mixing and no matterenhancement of mixing or resonance conversion . 5 . 6 . . 7 8 S.P.Mikheyev INR RAS

  28. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Instantaneous density change:parametric resonance n1 n2 m = 2m m = 1m  1 2 Resonance condition: Simplest realization: 1 = 2 =  In general, certain correlation between phases and mixing angles S.P.Mikheyev INR RAS

  29. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density 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

  30. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density:Adiabaticity One can neglect of 1m 2m transitions if the density changes slowly enough Adiabaticity condition: Adiabaticity parameter: S.P.Mikheyev INR RAS

  31. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density:Adiabaticity 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

  32. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density: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

  33. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density:Adiabatic conversion Resonance  • Flavors of eigenstates change • according to the density change • determined by m • fixed by mixing in the production point • Admixtures of the eigenstates, • 1m 2m, do not change • Phase difference increases • according to the level split which changes with density Effect is related to the change of flavors of the neutrino eigenstates in matter with varying density S.P.Mikheyev INR RAS

  34. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density:Adiabatic conversion S.P.Mikheyev INR RAS

  35. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density: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

  36. Oscillations of Natural Neutrinos 13th Lomonosov Conference on Elementary Particle Physics Oscillations in matter Non-uniform density: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

  37. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density:Adiabaticity violation Fast density change n0 >> nR n2m n1m n2 n1 ne Resonance • Transitions1m2moccur, admixtures of the eigenstateschange • Flavors of the eigenstatesfollow the density change • Phase difference of the eigenstateschanges, leading to oscillations = (H1-H2) t S.P.Mikheyev INR RAS

  38. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations in matter Non-uniform density:Adiabaticity violation S.P.Mikheyev INR RAS

  39. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations versus 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

  40. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Oscillations versus conversion Adiabatic conversion Spatial picture survival probability Oscillations distance survival probability distance S.P.Mikheyev INR RAS

  41. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Matter potential Unpolarizedrelativistic medium:   e   e polarized isotropic medium: if S.P.Mikheyev INR RAS

  42. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Neutrino propagation in real media • The Sun • The Earth • Supernovae S.P.Mikheyev INR RAS

  43. Neutrinos in Matter III International Pontecorvo Neutrino Physics School The Sun 4p + 2e- 4He + 2ne + 26.73 MeV electron neutrinos are produced Adiabatic conversion in matter of the Sun r : (150 0) g/cc J.N. Bahcall Oscillations in vacuum n Oscillations in matter of the Earth e Adiabaticity parameter  ~ 104 S.P.Mikheyev INR RAS

  44. Neutrinos in Matter III International Pontecorvo Neutrino Physics School The Sun Borexino Collaboration arXiv:0708.2251 S.P.Mikheyev INR RAS

  45. Neutrinos in Matter III International Pontecorvo Neutrino Physics School The Sun 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

  46. Neutrinos in Matter III International Pontecorvo Neutrino Physics School The Earth Density Profile (PREM model) core mantle mantle S.P.Mikheyev INR RAS

  47. Neutrinos in Matter III International Pontecorvo Neutrino Physics School The Earth S.P.Mikheyev INR RAS

  48. Neutrinos in Matter III International Pontecorvo Neutrino Physics School The Earth Liu, Smirnov, 1998; Petcov, 1998; E.Akhmedov 1998 Akhmedov, Maltoni & Smirnov, 2005 S.P.Mikheyev INR RAS

  49. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Supernovae Supernova Neutrino Fluxes H.-T. Janka & W. Hillebrand, Astron. Astrophys. 224 (1989) 49 G.G. Rafelt, “Star as laboratories for fundamental physics” (1996) S.P.Mikheyev INR RAS

  50. Neutrinos in Matter III International Pontecorvo Neutrino Physics School Supernovae Matter effect in Supernova Inverted Hierarchy Normal Hierarchy Dighe & Smirnov, astro-ph/9907423 S.P.Mikheyev INR RAS

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