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Neutrino Mass and

Neutrino Mass and. New Physics. A. Yu. Smirnov. International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia. Part I: Reconstructing neutrino spectrum. Part II: Towards Underlying physics. On mechanisms of mass generation.

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Neutrino Mass and

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  1. Neutrino Mass and New Physics A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Institute for Nuclear Research, RAS, Moscow, Russia Part I: Reconstructing neutrino spectrum Part II: Towards Underlying physics On mechanisms of mass generation Masses and mixing Oscillations and the MSW effect Analyzing experimental results Neutrino symmetry? Quarks and leptons

  2. Neutrino mass is considered as the first manifestation of physics beyond the standard model , as window to new physics. What is this New Physics? What do we see in the window? How far beyond?

  3. Remark : Quark and lepton mass hierarchies as well as the structure of CKM mixing have no explanation in the SM. And in a sense they are also manifestations of Physics Beyond SM New physics Quark Mass and mixing Some New physics may be in common New physics Neutrino Mass and mixing At the same time Neutrinos may require something more

  4. Two zeros Weak interactions – particular role in Nature Neutrality be a Majorana particle (Majorana mass term) Qg = 0 Qc = 0 mix with singlets of the SM symmetry group have large Majorana masses M R >> VEW Properties of mass spectrum and mixing Right handed components, if exists, are singlet of SU(3) x SU(2) xU(1) propagate in extra dimensions Unprotected by this symmetry

  5. Window to hidden world? Theoretical setup A S Standard Model A nl nR S l ... L lR ... H M s A Yu Smirnov

  6. Part I. Reconstructing Mass and Flavor Spectrum

  7. 1. Masses and mixing

  8. Flavors, Masses, Mixing Flavor states: Mixing: = Flavor states Mass eigenstate ne nm nt Eigenstates of the CC weak interactions m3 n3 ? ns Sterile neutrinos no weak interactions mass m2 n2 Mass eigenstates: m1 n1 n1 n2 n3 m1 m2 m3 Neutrino mass and flavor spectrum A Yu Smirnov

  9. Mixing angles ne nm nt |Ue3|2 |Um 3|2 |Ut 3|2 n3 tan2q12 =|Ue2|2 / |Ue1|2 sin2q13 = |Ue3|2 Dm2atm mass |Ue2|2 n2 tan2q23 = |Um 3|2 / |Ut 3|2 n1 Dm2sun |Ue1|2 Normal mass hierarchy nf = UPMNSnmass Dm2atm = Dm232 = m23 - m22 UPMNS = U23 Id U13 U12 Dm2sun = Dm221 = m22 - m21 Id = diag (1, 1, e-id)

  10. ``Portrait'' of the flavor state n2 = sinq ne + cosq nm n1 = cosq ne - sinq nm vacuum mixing angle ne = cosq n1 + sinq n2 coherent mixture of mass eigenstates n1 ne Portrait of the electron neutrino n2 wave packets Phases and phase difference Interference of the parts of wave packets with the same flavor depends on the phase difference Df between n1 and n2

  11. 2. Two effects

  12. Determining the oscillation parameters Effects involved Source of info Parameters Adiabatic conversion Solar neutrinos Dm212, q12 Averaged oscillations KamLAND Vacuum oscillations Atmospheric neutrinos, K2K Dm223, q23 Vacuum oscillations CHOOZ, Atmospheric neutrinos + … q13 Vacuum oscillations

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

  14. Oscillation probability A p 2 2pL ln pL ln P(nm) = 1 - cos =sin22q sin2 Dm2 L 4 E =sin22q sin2 L/E dependence Observable effects - oscillatory dependence of the probability on L for a given E E for fixed distance L/E in general A Yu Smirnov

  15. Refraction 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 for ne nm : Difference of potentials is important 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 focusing of neutrinos fluxes by stars complete internal reflection, etc Neutrino optics

  16. Eigenstates and mixing in matter in vacuum: in matter: Effective Hamiltonian H = H0 + V H0 n1, n2 n1m, n2m Eigenstates depend on ne, E Eigenvalues m12/2E, m22/2E H1m, H2m instantaneous nf nmass q ne n1 n2m nf nH n1m q qm n2 Mixing angle determines flavors (flavor composition) of the eigenstates nm qm

  17. Resonance In resonance: sin2 2qm = 1 sin2 2qm Flavor mixing is maximal Level split is minimal n n sin2 2q= 0.08 ln = l0 cos 2q sin2 2q= 0.825 ~ Vacuum oscillation length ~ Refraction length For large mixing: cos 2q ~ 0.4 the equality is broken: strongly coupled system shift of frequencies ln / l0 ~ n E Manifestations depend on density profile Resonance width: DnR = 2nR tan2q Determines scale of r and E of strong flavor transition occurs Resonance layer: n = nR + DnR

  18. Physical picture 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

  19. Resonance enhancement of oscillations oscillations determined by qm and lm (D H) Constant density Detector ne ne n Source F(E) F0(E) Layer of length L k = p L/ l0 sin2 2q = 0.824 F (E) F0(E) sin2 2q = 0.824 k = 10 k = 1 thick layer thin layer E/ER E/ER A Yu Smirnov

  20. High energy neutrinos in the mantle of the Earth (constant density is a good first approximation) Atmospheric neutrinos Applications: Accelerator neutrinos, LBL experiments sin2 2q = 0.08 F (E) F0(E) k = 10 k = 1 thick layer thin layer E/ER E/ER A Yu Smirnov

  21. The MSW - effect Adiabatic or partially adiabatic flavor conversion of neutrinos in medium with varying density Flavor of the neutrino state follows density change

  22. Physical picture Adiabatic case Admixtures of the eigenstates do not change (adiabaticity) Determined by mixing qm0 in the production point Flavors of the eigenstates follow the density change Flavor: qm = qm(r(t)) f = (H1 - H2) t Phase difference of the eigenstates changes leading to oscillations A Yu Smirnov

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  25. Resonance density mixing is maximal A Yu Smirnov

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  28. Adiabaticity External conditions (density) change slowly the system has time to adjust them dqm dt Adiabaticity condition << 1 H2 - H1 Essence: transitions between the neutrino eigenstates can be neglected The eigenstates propagate independently n1m <--> n2m Crucial in the resonance layer: - the mixing changes fast - level splitting is minimal if vacuum mixing is small DrR > lR lR = ln/sin2q Oscillation length in resonance Width of the res. layer DrR = nR / (dn/dx)Rtan2q If vacuum mixing is large, the point of maximal adiabaticity violation is shifted to larger densities n(a.v.) -> nR0 > nR nR0 = Dm2/ 2 2 GF E

  29. Adiabatic conversion formula n(0) = ne = cosqm0 n1m(0) + sinqm0 n2m(0) Initial state: Adiabatic evolution to the surface of the Sun (zero density): n1m(0) --> n1 n2m(0) --> n2 -if Final state: n(f) = cosqm0 n1 + sinqm0 n2 e Probability to find ne averaged over oscillations P = |< ne| n(f) >|2 = (cosq cosqm0+ sinq sinqm0 )2 = 0.5[ 1 + cos 2qm0cos 2q ] P = sin2q + cos 2q cos2qm0

  30. Spatial Oscillations picture survival probability Adiabatic conversion distance survival probability distance A Yu Smirnov

  31. Oscillations versus MSW Both require mixing, MSW is usually accompanying by oscillations What is essential difference between oscillations and the MSW effect? Oscillations Adiabatic conversion Vacuum or uniform medium with 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 increase between the eigenstates f qm Different degrees of freedom In non-uniform medium: interplay of both processes

  32. 3. Analyzing results Very simple at this level: - essentially reduced to 2n –problem - parameters can be immediately evaluated from observations without complicated analysis Nature was extremely collaborative. Next step will be much more complicated

  33. Solar Neutrinos 4p + 2e- 4He + 2ne + 26.73 MeV electron neutrinos are produced Adiabatic conversion F = 6 1010 cm-2 c-1 J.N. Bahcall total flux at the Earth n Oscillations in matter of the Earth r : (150 0) g/cc

  34. Physics of conversion 1. Adiabaticity lm - oscillation length in matter; h – height of the density profile Adiabaticity parameter lm(x) 4ph(x) g (x) = ~ 10 -4 Corrections are g2 Also relevant for oscillation in the Earth where affect ~ g 2. Loss of coherence 3. Oscillations in the matter of the Earth

  35. Solar neutrinos E = 10 MeV Resonance layer: nR Ye = 20 g/cc RR= 0.24 Rsun In the production point: sin2qm0 = 0.94 cos2 qm0 = 0.06 n2m n1m Large mixing MSW conversion provides the solution of the solar neutrino problem (Homestake, Kam…) Dm2 = (5 – 10) 10-5 eV2 tan2q = 0.40 – 0.50

  36. LMA MSW: Picture of conversion n1m <-->n2m I. High energy, n0 >> nR P = sin2q Non-oscillatory transition n2m n1m n2 n1 interference suppressed Resonance Mixing suppressed II. Intermediate energies, n0 > nR Adiabatic conversion + oscillations n2m n1m n2 n1 III. Low energies n0 < nR Small matter corrections n2m n1m n2 n1 ne

  37. Oscillations inside the Earth Oscillations in multi-layer medium Solar and supernova neutrinos: ``mass to flavor transitions’’ vacuum n2 mantle Accelerator neutrinos LBL experiments atmospheric neutrinos: flavor to flavor transitions core Regeneration of the ne flux Variety of possibilities depending on - trajectory, - neutrino energy and - channel of oscillations

  38. Oscillations inside the Earth 1). Incoherent fluxes of n1 and n2 arrive at the surface of the Earth 2). In matter the mass states oscillate 3). the mass-to-flavor transitions, e.g. n2 --> ne are relevant Regeneration factor: P2e = sin2q + freg Pee = 0.5[ 1 + cos 2qm0cos 2q ] - cos2qm0freg 4). The oscillations proceed in the weak matter regime: 2EV(x) Dm2 e (x)= << 1

  39. Physical picture LMA MSW: profile of the effect npp nBe Adiabatic edge nB Survival probability Earth matter effect sin2q Synthetic solution I III II ln / l0 ~ E Conversion with small oscillation effect Non-oscillatory transition Oscillations with small matter effect Conversion + oscillations

  40. Kamioka Large Anti-Neutrino Detector KamLAND Dm2 = (7- 9) 10-5 eV2 tan2q = 0.2 – 0.8 Reactor long baseline experiment 150 - 210 km Liquid scintillation detector ne + p---> e+ + n Epr > 2.6 MeV Total rate energy spectrum of events LMA precise determination of the oscillation parameters 10% accuracy Detection of the Geo-neutrinos Epr > 1.3 MeV 1 kton of LS

  41. Testing the Theory of oscillations Solar neutrinos 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 oscillations the oscillation phase is irrelevant Oscillation phase is crucial for observed effect Adiabatic conversion formula Vacuum oscillations formula Dm2 , q Coincidence of these parameters determined from the solar neutrino data and from KamLAND results testifies for the correctness of the theory (phase of oscillations, matter potential, etc..)

  42. Atmospheric neutrinos Parametric effects in nm - ne oscillations for core crossing trajectories ne atmosphere p p m nm N e nm nm - ne oscillations in matter n core cosmic rays At low energies: r = Fm /Fe = 2 nm - nt vacuum oscillations n mantle detector Dm2 = (2 – 3) 10-3 eV2 sin22q = 1.00 > 0.92 (90% CL)

  43. L/E dependence oscillations m-like events decay decoherence In the first oscillation maximum (dip): f = p Dm2 = 2p E/L data: L/E ~ 500 km/GeV Dm2 ~ 2.5 10-3 eV2 Super-Kamiokande PRL, 93 101801 (2004)

  44. K2K KEK to Kamioka nm -> nm Dm2 = (2 - 4) 10-3 eV2 sin22q = 1.0 SuperKamiokande

  45. K2K results 107 events observed 151 +12/-10 -expected best fit spectrum with oscillations 1 osc. Max. no-oscillation Normalized (57 events) reconstructed neutrino energy spectra Allowed regions of parameters

  46. CHOOZ and U_e3 Ue3 = sin q13 e-id = <ne | n3 > CHOOZ atmospheric CHOOZ+atmospheric tan q13 sin22q13

  47. Mass spectrum and mixing ne nm nt |Ue3|2 ? n3 n2 Dm2sun n1 mass Dm2atm Dm2atm mass |Ue3|2 n2 Dm2sun n1 n3 Normal mass hierarchy (ordering) Inverted mass hierarchy (ordering) Type of mass spectrum: with Hierarchy, Ordering, Degeneracy absolute mass scale Type of the mass hierarchy: Normal, Inverted Ue3 = ? A Yu Smirnov

  48. Global fit A. Strumia, F. Vissani hep-ph/0503246

  49. G.L. Fogli, E. Lisi, A Marrone, A. Palazzo, A.M. Rotunno hep-ph/0506307, 0506083 Global fit

  50. Plausible values of paremeters No new physics apart from 3 massive and mixed neutrinos Bari S-V Dm122 8.0 10-5 eV2 7.9 10-5 eV2 sin2q120.3100.314 Dm232 2.5 10-3 eV2 2.4 10-3 eV2 sin2q230.500.44 sin2q13 0.00 [< 0.013 ] 0.009 [< 0.020] [1s ]

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