A. Yu. Smirnov

1. Physics of neutrino oscillations & flavor conversion A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Invisibles network INT Training lectures June 25 – 29, 2012

2. …in addition

3. Adiabatic conversion n2m n1m resonance x if density changes slowly - the amplitudes of the wave packets do not change - flavors of the eigenstates follow the density change

4. Adiabatic conversion probability Sun, Supernova From high to low densities n(0) = ne = cosqm0 n1m(0) + sinqm0 n2m(0) Initial state: Mixing angle in matter in 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)2+ (sinq sinqm0)2 = 0.5[ 1 + cos 2qm0cos 2q ] P = sin2q + cos 2q cos2qm0

5. Two aspects of mixing ne = cosqm n1m+ sinqmn2m n2m = sinqmne+ cosqm nm inversely nm = - sin qmn1m+ cos qmn2m n1m = cosqmne- sinqnmqm coherent mixtures of mass eigenstates flavor composition of the mass eigenstates n2m ne n2m n1m n1m n2m nm n1m flavors of eigenstates Wave packets Vacuum qm q n1mn1 n2mn2

6. resonance Him Level crossing sin22q12= 0.825 ne n2m V. Rubakov, private comm. N. Cabibbo, Savonlinna 1985 H. Bethe, PRL 57 (1986) 1271 nm n1m ln / l0 Dependence of the neutrino eigenvalues on the matter potential (density) Large mixing ln l0 2E V Dm2 = sin22q13= 0.08 ne ln l0 = cos 2q n3m nt ln / l0 n2m Crossing point - resonance - the level split is minimal - the oscillation length is maximal Small mixing

7. References Mass hierarchy, 2-3 mixing and CP-phase with Huge Atmospheric Neutrino Detectors. E.Kh. Akhmedov, SoeburRazzaque, A.Yu. Smirnov. e-Print: arXiv:1205.7071 [hep-ph] 1-3 leptonic mixing and the neutrino oscillograms of the Earth. Evgeny K. Akhmedov, Michele Maltoni, Alexei Yu. Smirnov , JHEP 0705 (2007) 077 e-Print: hep-ph/0612285 Neutrino oscillograms of the Earth: Effects of 1-2 mixing and CP-violation. EvgenyKh. Akhmedov, Michele Maltoni, Alexei Yu. Smirnov, JHEP 0806 (2008) 072 e-Print: arXiv:0804.1466 [hep-ph] and references therein

8. Vaccum vs. matter Can be treated on the same footing matter: vacuum: matter with constant density, (unless near topological defects) Flavor diagonal Mixes mass eigenstates Mass diagonal Mixes flavor states Flavor states oscillate Mass states oscillate in matter Flavor states and mass states change roles when matter and vacuum exchange

9. Supernova neutrinos How flavor diagonal interactions can lead to flavor off-diagonal elements of the Hamiltonian? Collective flavor trasformation Origin of collective effects MSW flavor conversion inside the star Propagation in vacuum Oscillations Inside the Earth

10. nn -scattering ne ne Refraction in neutrino gases ne nb Z0 Z0 nb nb nb ne A = 2 GF (1 – ve vb ) velocities ne ne (p) t-channel elastic forward scattering nb nb (q) ne J. Pantaleone ne (p) u-channel can lead to the coherent effect Momentum exchange  flavor exchange ne nb (q)  flavor mixing nb Collective flavor transformations

11. Flavor exchange J. Pantaleone S. Samuel V.A. Kostelecky ne projection nn – scattering in u-channel due to Z0 - exchange na ne nb coherent 1. Momentum exchange  flavor exchange nb background ne 2. Coherence if the background is in mixed state: projection nt |nib =Fie |ne + Fit |nt Coherent flavor changing transition Probe neutrino = background neutrino Potential depends on transition probability

12. Flavor exchange J. Pantaleone S. Samuel V.A. Kostelecky ne projection If the background is in the mixed state: ne nb |nib =Fie |ne + Fit |nt coherent nb Bet ~ SiFie*Fit background ne sum over particles of bg. w.f. give projections projection nt Contribution to the Hamiltonian in the flavor basis Flavor exchange between the beam (probe) and background neutrinos |Fie|2 Fie*Fit Hnn = 2 GF Si (1 – ve vib ) FieFit * |Fit|2

13. Evolution equation Ensemble of neutrino polarization vectorsPw Negative frequencies for antineutrinos dtPw =(- wB + lL + mP) x Pw Vacuum mixing term Usual matter potential Collective vector + inf - inf B = (sin 2q, 0, cos2q) P= dwPw L = (0, 0, 1) w = D m2 /2E l = V = 2 GF ne m = 2 GFnn (1 – cosqnn) The term describes collective effects

14. Neutrino propagation In the Earth

15. ``Set-up'' qn • zenith • angle Q = p - qn Q - nadir angle Oscillations in multilayer medium core-crossing trajectory Q = 33o Applications: flavor-to-flavor transitions - accelerator - atmospheric - cosmic neutrinos core mantle 9

16. Oscillations in multilayer medium Adiabaticity breaking at the borders of layers

17. Graphical representation Equation of motion (= spin in magnetic field) z dP dt = (B x P) ne B P where ``magnetic field’’ vector: 2p lm B = (sin 2qm, 0, cos2qm) nt, P = (Re ne+ nt, Im ne+ nt, ne+ ne - 1/2) x Phase of oscillations y f= 2pt/ lm Pee = ne+ne = PZ+ 1/2 = cos2qZ/2 Probability to find ne

18. Resonance enhancement in mantle 1 mantle 1 2 mantle 2 21

19. Parametric enhancement 1 mantle 2 3 1 4 core 2 mantle core mantle 3 mantle 4 22

20. Parametric enhancement of 1-2 mode 1 mantle core 3 4 2 2 mantle 4 3 1 23

21. Graphical representation a). b). a). Resonance in the mantle b). Resonance in the core c). Parametric ridge A c). d). d). Parametric ridge B e). Parametric ridge C f). Saddle point e). f).

22. 1 - Pee MSW-resonance peak, 1-3 mixing Parametric ridges 1-3 mixing MSW-resonance peak, 1-3 mixing Parametric peak 1-2 mixing MSW-resonance peaks 1-2 mixing 5p/2 3p/2 p/2

23. Evolution For E > 0.1 GeV ~ H = U13T U12THdiag U12 U13 ~ Propagation basis nf = U23Idn Hdiag = diag (H1m, H2m, H3m) CP-violation and 2-3 mixing - excluded from dynamics of propagation Id = diag (1, 1, eid ) ne ne ne ne Ae2 nm ~ ~ nm n2 n2 Ae3 ~ ~ nt n3 nt n3 projection propagation projection CP appears in projection only A22 A33 A23 A(nenm) = cosq23Ae2eid + sinq23Ae3 For instance:

24. E Kh Akhmedov, S Razzaque, A. Y.S. Probabilities for hierarchy determination, neglect 1-2 mixing effects P(ne nm) = s232|Ae3|2 ½ P(nm nm) = 1 – ½ sin2 2q23 - s234|Ae3|2 + ½ sin2 2q23 (1 - |Ae3|2) cos f Reduces the average probability Reduces the depth of oscillations interference Modifies phase f = arg (A22 A33*) ½ P(nm nt) = ½ sin2 2q23 - s232 c232|Ae3|2 - ½ sin2 2q23 (1 - |Ae3|2) cos f

25. Oscillation probabilities MSW resonance in core 2nd and 3rd parametric peaks ne nt nm MSW resonance in mantle

26. Oscillograms P. Lipari , T. Ohlsson M. Blennow M. Chizhov, M. Maris, S .Petcov T. Kajita … and physics of oscillations

27. excluded

28. 1 - Pee MSW-resonance peaks 1-3 frequency excluded Parametric ridges 1-3 frequency Parametric peak 1-2 frequency MSW-resonance peaks 1-2 frequency 5p/2 3p/2 p/2

29. Other channels mass e - e e - e hierarchy e - m e - m For 2n system normal  inverted neutrino  antineutrino m - m m - m 25

30. CP-violation domains Solar magic lines Three grids of lines: Atmospheric magic lines Interference phase lines

31. CP-violation d = 60o Standard parameterization

32. d = 130o

33. d = 315o

34. CP-interference Due to specific form of matter potential matrix (only Vee = 0) P(nenm) = |cos q23Ae2e id + sin q23Ae3|2 ``solar’’ amplitude ``atmospheric’’ amplitude dependence on d and q23is explicit For maximal 2-3 mixing f = arg (Ae2* Ae3) P(ne nm)d = |Ae2 Ae3| cos (f - d ) P(nm nm)d = - |Ae2 Ae3| cosf cos d P(nm nt)d = - |Ae2 Ae3| sinf sind S = 0

35. ``Magic lines" P. Huber, W. Winter V. Barger, D. Marfatia, K Whisnant, A.S. Explicitly P(ne nm) = c232|AS|2 + s232|AA|2 + 2s23c23|AS||AA|cos(f + d) f = arg (AS AA*) Pint = 2s23c23|AS||AA|cos(f + d) Dependence on d disappears, interference term is zero if AS = 0 - solar magic lines Pint = 0 - atmospheric magic lines AA = 0 - interference phase condition (f+d ) = p/2 + 2p k f(E, L) = - d + p/2 + p k depends on d 31

36. ``Magic lines'' For nmnm channel Pint ~ 2s23c23|AS||AA|cosf cosd • - The survival probabilities is CP-even functions of d • no CP-violation • dependences on phases factorize Dependence on d disappears AS = 0 AA = 0 Pint = 0 f= p/2 + p k interference phase does not depends on d Form the phase line grid 32

37. Sensitivity to CP phase d - true (experimental) value of phase df - fit value Interference term: D P = P(d) - P(df) = Pint(d) - Pint(df) For ne nm channel: DP = 2 s23 c23 |AS| |AA| [ cos(f + d) - cos (f + df)] (along the magic lines) AS = 0 AA = 0 D P = 0 (f+d ) = - (f + df) + 2p k int. phase condition f(E, L) = - ( d + df)/2 + p k depends on d

38. Int. phase line moves with d-change Grid (domains) does not change with d DP

39. DP

40. DP

41. Oscillograms contours of constant oscillation probability in energy- nadir (or zenith) angle plane 100 IceCube ne nm , nt NuFac 2800 0.005 CNGS 0.03 IC Deep Core 0.10 10 LENF E, GeV MINOS NOvA PINGU-1 HyperK T2KK T2K ICAL, INO 1 OK for CP LAr 0.1

42. Physics with HAND’s

43. Enormous physics potential which is not completely explored and largely unused Energy range: 0.01 – 105 GeV Baselines: 0 – 13000 km Matter effects: 3 – 15 g/cm3 Flavor content nue, numu which change with energy and zenith angle Lepton number nu - antinu Achievements: Discovery of neutrino oscillations Measurements of 2-3 mixing and mass splitting Bounds on new physics - sterile neutrinos - non-standards interaction -violation of fundamental symmetries, CPT

44. Uncertainties of original fluxes Limitations: Flavor identification Reconstruction of direction Statistics High statistics solve the problems Energy resolution from LAND to HAND TITAND? Y. Suzuki E. Kh Akhmedov M. Maltoni A.Y.S. JHEP 05, (2007) 077 [hep-ph/0612285] JHEP 06 (2008) 072 [arXiv:0804.1466] PRL 95 (2005) 211801 arXiv:0506064 unpublished, see M Maltoni talks Developments of new detection methods? A.Y.S. , hep-ph/0610198. E. Kh Akhmedov, S Razzaque, A.S. in preparation E Kh Akhmedov, A Dighe, P. Lipari, A Y. Smirnov , Nucl. Phys. B542 (1999) 3-30 hep-ph/9808270

45. Suppression of effects different flavors: ne and nm Screening factors (1 - r s232 ) Original fluxes neutrinos and antineutrinos (1 - ke) Reduces CP-asymmetry (1 – km) averaging and smoothing effects reconstruction of neutrino energy and direction Integration averaging identification of flavor Detection

46. Numbers of events Triple suppression NeIH - NeNH ~ (PA - PA) (1 – km) [r s232 - (1 – k e)/(1 - km)] CP asymmetry Neutrino - antineutrino factor Flavor suppression (screening factors) unavoidable can be avoided PA = |Ae3|2 ka = (s Fa)/(s Fa) NmIH - NmNH ~ (Pmm - Pmm) (1 – km) - r-1(1 – ke) (Pem - Pem)]

47. PINGU Precision IceCube Next Generation Upgrade Mass hierarchy, 2-3 mixing, CP

48. IC, DeepCore and PINGU Digital Optical Module IceCube : 86 strings (x 60 DOM) 100 GeV threshold Gton volume Deep Core IC : - 8 more strings (480 DOMs) - 10 GeV threshold - 30 Mton volume PINGU: 18, 20, 25 ? new strings (~1000 DOMs) in DeepCore volume Existing IceCube strings Existing DeepCore strings New PINGU strings D. Cowen

49. PINGU Geometry Denser array PINGU v2 20 new strings (~60 DOMs each) in 30 MTon DeepCore volume Few GeV threshold in inner 10 Mton volume Energy resolution ~ 3 GeV Existing IceCube strings Existing DeepCore strings New PINGU-I strings 125 m

50. Mass hierarchy Effective area, effective volume