1. Francis Ngouniba Ki Tezpur University, Ind ia Quasi-Degenerate Neutrinos and Leptogenesis Ist IAS-CERN, NTU-SINGAPORE Jan 26, 2012 Specialized Knowledge Promotes Creativity

2. 2 Cosmology Leptogenesis Through Through seesaw models

3. Outline I. Background +II. QDN III. Particle Cosmology 3

4. I. Background-3 Thought Provoking Statements: 1. Neutrino Physics is all about neutrino mass ??? 2. Noble Prize in Neutrino Mass ??? 3. Ironically, neutrino oscillations is not yet recognized by Noble Prize (evidence follows).  Talk Strategy: -Fast on Accepted Standard Conventions -Slow on Actual Works  How Studied? -Lies between Experimental & Hard Core Theory. -Mathematical Manipulations & Assumptions. 4

5. 2002 Noble Prize in Physics "for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos" Masatoshi Koshiba and Ray Davis Riccardo Giacconi (Comic X-rays source) 5

6. NEUTRINO OSCILLATION ?? Simple Pendulum 6

7. Neutrino Oscillation (1957) BRUNO PONTECORVO (Italy1913- Russia1993) Half of his ashes is now buried in the Protestant Cemetery in Rome, and another half in Dubna, Russia, according to his will. 7

8. We only know 8

9. Journey of Neutrino 1930-Pauli (neutron):[ 1934-Fermi-neutrino] 58 Years Later 1998-Kamioka Japan: Neutrino-Oscillations Year ???- Noble Prize in Physics (Smile)???: Absolute Neutrino Mass 9 Journey of Neutrino Neutrinos are Massive

10. 10 SINGARA, TAMULNADU, INDIA AIM: To Study Atmospheric Neutrinos and Measure a Precise Neutrino Mixing Parameters.

11. The absolute scale of masses, consequences: Addresses key issues in particle physics –hierarchical or degenerate neutrino mass spectrum –understanding the scale of new physics beyond SM, or a crucial datum for reconstructing PHYSICS Beyond SM –potential insight into origin of fermion masses Impacts cosmology and astrophysics –early universe, relic neutrinos (HDM), structure formation, anisotropies of CMBR –supernovae, origin of elements –potential influence on UHE cosmic rays. [0vbb Phys. Lett. B 586 (2004) 198] 11

12. 12

13. 13

14. Upper bound on absolute neutrino mass 14

15. Direct measurements of neutrino mass 15

16. What 16

17. Type of Neutrino ??? 17

18. 18

19. 19

20. mass & mixing -oscillation experiments 20

21. II. Quasi-Degenerate Oscillation QDN 21

22. 22

23. MOTIVATIONS To study the Compatibility of Theoretical Calculations with Experimental data: 1. Absolute neutrino masses (m 1,m 2, m 3 ). 2. 0  decay mass parameter m ee. 3 3. Cosmological bound / sum ∑(m i ) abs i 4. Solar mixing angle θ 12 for different CP-phases 5. Leptons Charged Corrections effects on θ 13. 23

24. 24

25. MAJORANA PHASES IN MASSES Majorana Phases: Diagonal mass matrix: 25

26. NEUTRINO OSCILLATIONS AND MNS MIXING MATRIX: Two neutrino eigenstates: Flavour and mass eigenstates Which may be greater or less than zero ( Neutrino mixing matrix is known as MNS mixing matrix due to Z. Maki, M. Nakagawa, S. Sakata)‏ 26

27. Types of Quasi-degenerate mass models We consider 3X3 mass matrices through parameterizations with two parameters in the present analysis. By taking particular choice of phases: 27

28. 28

29. 29

30. 30

31. Present status of neutrino mass, mixing and oscillation ←CHOOZ Table-5: Best-fit values and allows nσ ranges for the global three flavor neutrino oscillation parameters, from Ref. [21]. parameter s ∆m 2 21 (10 -5 eV 2 ) ‏ ∆m 2 23 (10 -3 eV 2 ) ‏ tan 2 θ 12 Sin 2 θ 13 Sin 2 θ 23 Σ |m i | eV |m ee | eV Best-fit7.672.390.3120.0160.466≤ 0.28 ≤ 0.27 1 σ 2 σ 3 σ 7.48-7.83 7.31-8.01 7.14-8.19 2.31-2.50 2.19-2.66 2.06-2.81 0.294-0.331 0.278-0.352 0.263-0.375 0.006-0.026 <0.036 <0.046 0.408-0.539 0.366-0.602 0.331-0.644 ≤ 0.28 ≤ 0.27 {[21] G.L.Fogli et al, Phys Rev.D 78, 033010 (2008) [arXiv: 0805.2517 [hep-ph]}. 31

32. 32

33. νμνμ Accelerator Detector l = 730 km (MINOS) & 250 km (K2K)‏ 33

34. Recently the last one has gone down to 0.28 eV (PRL 105, 031301 (2010)) ‏ 34

35. To compute various parameters To calculate m 1 and m 2 NH: α =, β =, Where = 7.60 x 10 -3 eV 2 and =2.40 x 10 -5 eV 2 [39]. m 1 = m 0 ; m 2 = m 0 ; = m 0. IH: α = -, β =+, where = 7.60 x 10 -3 eV 2 and = 2.40 x 10 -5 eV 2. m 1 = m 0 ; m2 = m 0 ; = m 0. {[39] T.Schwetz, M.Tortola.J.W.F.Valle, hep-hp/08082016; M. C. Gonzales-et al, arXiv: 0812.3161. G.L.Fogli et al, Phys Rev.D 78, 033010 (2008) }. 35

36. Table1. The absolute neutrino masses in eV estimated from oscillation data [8] (Using calculated value of β = 0.03166). Calculated α 0.015 0.24 0.375 QD-NH QD-IH TABLE-1

37. II. For Calculation of ε and η the following Expressions were used. For Type-IA (NH or IH): m 1 = (2 ε - 2 η ) m 0, m 2 = (- ε -2 η ) m 0, m 3 = m 0. For Type – IB/IC (NH or IH): m 1 = (1-2 ε -2 η ) m 0, m 2 = (1+ ε – 2 η ) m 0, m 3 = m 0. Where m 1 and m 2 are directly substituted from Tables A & B corresponding to each case. Calculations is easy so we simply give the final calculations of ε and η in Tables 1 to 4. 37

38. Parameters QD-NH Type-IA Type-IB QD-IH Type-IA Type-IB c d m 3 (eV) ε η 1.0 0.10 0.57972 0.14602 1.0 0.10 0.0015 0.0649 1.0 0.10 0.08 0.78004 0.19628 1.0 0.10 0.08 0.00169 -0.0855 m 1 (eV) m 2 (eV) m 3 (eV) Σ|m i | eV 0.08674 -0.0872 0.10 0.273 0.08672 0.08717 0.10 0.273 0.09340 -0.0938 0.08 0.267 0.09340 0.09380 0.08 0.267 Δm 2 21 eV 2 |Δm 2 23 |eV 2 tan 2 θ 12 |m ee | eV 7.6x10 -5 2.4x10 -3 0.50 0.0869 7.6x10 -5 2.4x10 -3 0.50 0.0869 7.6x10 -5 2.4x10 -3 0.50 0.0869 7.6x10 -5 2.4x10 -3 0.50 0.0869 Table-2: Predictions for tan 2 θ 12 = 0.50 & other parameters consistent with observations.

39. Table-3: Predictions for tan 2 θ 12 = 0.45 and other parameters consistent with observational data. Parameters QD-NH Type-IA Type-IB QD-IH Type-IA Type-IB c d m 3 (eV) ε η 0.86 1.025 0.10 0.6616 0.1655 0.945 0.998 0.10 0.00145 0.06483 0.868 1.0 0.08 0.88762 0.22317 0.96 1.002 0.08 0.00169 -0.0855 m 1 (eV) m 2 (eV) m 3 (eV) Σ|m i | eV 0.08754 -0.0879 0.0996 0.275 0.08676 0.08717 0.10002 0.274 0.09392 -0.0943 0.08 0.268 0.09341 0.09381 0.08001 0.267 Δm 2 21 eV 2 |Δm 2 23 |eV 2 tan 2 θ 12 |m ee | eV 7.7x10 -5 2.2 x10 -3 0.45 0.0877 7.3x 10 -5 2.4x 10 -3 0.45 0.0869 7.6 x10 -5 2.4x 10 -3 0.45 0.0936 7.4x 10 -5 2.4 x10 -3 0.45 0.0935

40. CHARGED LEPTONS CORRECTIONS = Where = [Ref [25]-Mohapatra et al Phys Lett B636 114 (2006)] is same as in the case of mass matrix diagonalization without Charged Leptons Corrections. 40

41. Cal VALUES CHARGED LEPTONS CORRECTIONS ParametersNormal OrderingInverted OrderingNH-IA**NH-IB** Type-IAType-IBType-IAType-IB c d m 3 (=mo ) eV   0.0863 1.0 0.08 0.88762 0.22317 0.945 0.998 0.10 0.0015 0.0648 0.863 1.0 0.08 0.88762 0.22317 0.96 1.002 0.08 0.0016917 -0.085456 0.863 1.0 0.40 0.6616 0.1655 1.0 0.1 0.0015 0.0649 tan 2 θ 12 tan 2 θ 23 Sinθ 13 0.50 0.94 0.026 0.50 0.94 0.026 0.50 0.94 0.026 0.50 0.94 0.026 0.55** 0.94 0.026 0.55** 0.945 0.0256 m 1 (eV) ‏ m 2 (eV) ‏ m 3 (eV) ‏ Σ |m i | (eV) ‏ ∆ m 2 21 (10 -5 eV 2 )‏ ∆m 2 23 (10 -3 eV 2 )‏ 0.0934533 -0.0938581 0.08 0.07959 7.7 2.25 0.0867551 0.0871879 0.100013 0.2739 7.3 2.39 0.0934533 -0.0938581 0.08 0.267 7.6 2.39 0.0934139 0.093814 0.0800137 0.2672 7.4 2.39 0.348958 -0.349118 0.40 1.098 7.6 2.39 0.08672 0.08717 0.10 0.27389 7.6 2.39 41

42. Parameters Without Charged Lepton Corrections. NH-IANH-IBIH-IAIH-IBNH-IA tan 2 θ 12 tan 2 θ 23 Sin θ 13 0.45 1.0 0.00 0.45 1.0 0.00 0.45 1.0 0.00 0.45 1.0 0.00 0.50* 1.0 0.00 With Charged Lepton Corrections. tan 2 θ 12 tan 2 θ 23 Sin θ 13 0.50 0.94 0.026 0.50 0.94 0.026 0.50 0.94 0.026 0.50 0.94 0.026 0.55* 0.945 0.026 Comparison 42

43. III. Particle Cosmology 43

44. The Early Universe Condition Big Bang now 44

45. The universe's timeline, from inflation to the WMAP. 45 NOWNOW

46. Neutrino Masses in Cosmology Primordial Neutrino as Hot Dark Matter 46

47. 1. Thermal leptogenesis See saw Mechanism Majorana decays into two modes CP asymmetry is caused by interference of tree level and one loop correction for decays of

48. Interference of Tree level and one loop correction

49. Lepton asymmetry for non-susy …Eq(2)..Eq(1)

51. For SUSY For susy case When x is large

52. B-L Conserved and B+L violated

53. Baryon and Photon densities Baryon number density over photon number density corresponds to BAU by

54. TABLE-4 TYPE NH-IA (6,2) (8,4) NH-IB (6,2) (8,4) IH-IA (6,2) (8,4) IH-IB (6,2) (8,4)

55. TABLE-5 TYPE NH-IA (6,2) (8,4) 2.62x10 -4 6.49x10 -8 2.25287 0.49905 3.62x10 -6 2.19x10 -4 6.64x10 -8 2.53x10 -10 2.25x10 -15 5.42x10 -16 NH-IB(6,2) (8,4) 8.50x10 -7 4.32x10 -9 0.13941 0.08731 8.99x10 -4 1.53x10 -3 1.82xl0 -8 1.32xl0 -12 1.13x10 -13 1.97x10 -17 IH-IA(6,2) (8,4) 2.31x10 -4 3.35x10 -8 15.354 0.27512 5.45x10 -6 4.22x10 -4 7.95x10 -8 2.65x10 -9 4.24x10 -15 1.09x10 -14 IH-IB(6,2) (8,4) 9.45x10 -7 4.33x10 -9 0.16653 0.09423 7.37x10 -4 1.08x10 -3 1.29xl0 -8 1.59x10 -12 9.30x10 -14 2.18x10 -17 Table 5: Thermal Leptogenesis for all neutrino mass models with tan 2 θ 12 = 0.45.

56. 2.Flavoured thermal leptogenesis Flavoured effects in thermal Leptogenesis, lepton asymmetry is Efficiency factor for the out-of-equilibrium This leads to the Baryon Asymmetry of the Universe-BAU

57. This leads to the BAU For single flavoured case Leading to BAU

58. TABLE-6 TYPE NH-IA (6,2) (8,4) 3.73x10 -6 3.03x10 -8 4.86x10 8 3.94x10 6 1.92x10 -7 1.55x10 -9 9.07x10 -12 7.32x10 -14 2.11x10 -11 1.71x10 -13 NH-IB(6,2) (8,4) 5.31x10 -7 4.30x10 -9 1.85x10 8 1.50x10 6 1.12x10 -14 8.87x10 -17 1.41xl0 -18 1.12xl0 -20 5.67x10 -13 4.71x10 -15 IH-IA(6,2) (8,4) 3.77x10 -6 3.05x10 -8 4.56x10 8 3.69x10 6 1.94x10 -7 1.57x10 -9 8.50x10 -12 6.88x10 -14 1.98x10 -11 1.60x10 -13 IH-IB(6,2) (8,4) 5.31x10 -7 4.30x10 -9 1.72x10 8 1.39x10 6 9.75x10 -15 7.80x10 -17 1.15xl0 -18 9.17x10 -21 5.95x10 -13 4.76x10 -15

59. 3.Non-thermal Leptogenesis(NTL) 59

60. 60

61. Neutrino Mass Models validity 61

62. TABLE-7 TYPE NH-IA (6,2) (8,4) NH-IB (6,2) (8,4) IH-IA (6,2) (8,4) IH-IB (6,2) (8,4) 62

63. 63

64. Conclusion 64

65. Future Challenge 1. Neutrino Physics: To Find a General Model or Method without parameterizations. 2. Particle Cosmology: CP violation in the leptogenesis/BAU. In this direction we are working out earnestly. 65

66. IAS, NTU Singapore 66