Three Neutrino Oscillations

2. Three Neutrino Oscillations Neutrino Mixing Weak eigenstate Mass eigenstate small m3 n3 m2 n2 CP phase m1 n1 Solar KamLAND Atmospheric LBL LBL (future) Reactor factory

7. L. Wolfenstein Tri/bimaximal Mixing P. F. Harrison D. H. Perkins W. G. Scott S.Chang,SK.,S.Kim 2/3 1/3 0 - 1/6 1/3 1/2 1/6 - 1/3 1/2 Utbm = U23(p/4)U12 Utbm = n3 is bi-maximally mixed - maximal 2-3 mixing - zero 1-3 mixing - no CP-violation n2is tri-maximally mixed

12. Baryogenesis via Leptogenesis

13. Introduction • Why do we exist ? • matter antimatter asymmetry • What created this tiny excess matter? • Baryogenesis • B number non-conservation • CP violation • Non-equilibrium

14. Models of Baryogenesis • Baryogenesis at the Electroweak Phase Transition: (Kuzmin, Rubakov, Shaposhinikov PLB155(1985)) • GUT Baryogenesis through the decay of a heavy particle: (Yoshimura, PRL41 (1978), Dimopoulos, Suskind, PRD18(1978) • Baryogenesis via Leptogenesis • (Fukugida, Yanagida, PLB174 (1986) )

15. Baryogenesis in Standard Model • Sakharov’s conditions • B violation EW anomaly • CP violation KM phase • Non-equilibrium 1st order phase trans. • Standard Model may satisfy all 3 conditions! • Electroweak Baryogenesis(Kuzmin, Rubakov, Shaposhnikov) • Two big problems in the Standard Model • 1st order phase transition requires mH<60GeV • CP violation too small because • J  det[Yu†Yu, Yd†Yd]~ 10–20<< 10–10

16. Original GUT Baryogenesis • GUT necessarily breaks B. • A GUT-scale particle X decays out-of-equilibrium with direct CP violation • Now direct CP violation observed: e’ !!! • But keeps B–L0“anomaly washout” • Also monopole problem

17. Leptogenesis • One of the most attractive possibilities for baryogenesis • Well motivated due to neutrino oscillation • Realized in the framework of seesaw mechanism • Asymmetry is generated via decay of RH neutrinos • Seesaw Mechanism Yanagida, Gell-Mann Slansky, Ramond,

18. You generate Lepton Asymmetry first • from the direct CP violation in NR decay • L gets converted to B via EW anomaly •  More matter than anti-matter •  We have survived “The Great Annihilation” (complex matrices mD and M natural CPV source)

19. Ingredients of Leptogenesis • CP Asymmetry • Interference between tree level and (vertex+self energy) 1-loop diagrams:

20. Out-of-equilibrium condition • slow lepton number violating processes • The efficiency factor(due to washout) • if N1 decay out-of-equilibrium In equilibrium

21. processes which can put N1 in thermal eq. : • inverse decay process • scattering • In practice,to calculate the efficiency factor • we need to solve Boltzmann eq. (Bari ‘04) • Conversion L into B via Sphaleron process • conversion factor :

22. Lower Bound on Lightest Heavy Neutrino Mass (Davidson & Ibarra ’02, Buchmuller et al.’02) • Assuming very hierarchical Mi for fully herarchical neutrinos

23. For hierarchy can be large : not small for large not zero for (ex) compatible with successful leptogenesis for special configuration of Yukawa matrix (Hambye et al ‘04, Raidal, Strumia, Turzynski ‘04)

24. Quasi-degenerate case : Resonant Leptogenesis (Pilaftsis) If , resonant effects can enhance Resonant condition :

25. No more lower limit on for successful leptogenesis • possible TeV scale leptogenesis • Much larger upper limit on light neutrino masses • (Hambye, Lin, Notari, Papucci, Strumia’ 04.) For bound on A degeneracy allows already successful Leptogenesis with

26. Type II leptogenesis (Antusch, King, E.J.Chun et al. ) where Bound on asymmetry and M

28. Pastor (Moriond05)

29. Questions • Is the mechanism directly testable ? may be impossible if M is very large • Can we probe any effects of leptogenesis at low energy experiments? Connection between Leptogenesis and Low E CP violation

30. Neutrino Mixing parametrized by UMNS • UPMNS Dirac Phase • Majorana phases • source of CPV : complex Yukawa couplings • concerned with both phases CP violation in neutrino sectors Dirac Phase : CP violation measurable in neutrino oscillations Majorana Phase : Neutrinoless double beta decay Leptogenesis

31. CP violation in Early Universe : Observable in low energy phenomenology? • Minimal seesaw model : contains two generations of RH neutrino (Frampton, Glashow, Yanagida, ‘02 : Endoh, Kang, Kaneko, Morozumi, Tanimoto, ‘02) May be, in some models

32. Connection between low energy CP violation and leptogenesis • In minimal seesaw with • 2 heavy Majorana neutrinos •  mD contains 3 phases (Endo,Kaneko,Kang,Morozumi,Tanimoto) PRL89(2002) Existence of a correlation between

33. Models of maximal atmospheric mixing and leptogenesis (Grimus and Lavoura ‘04, Mohapatra, Nasri, Yu ’05, Ahn, Kang, Kim, Lee.) Warrant Search for models with these features enforced by symmetry • Maximal atmospheric neutrino mixing • Vanishing can be realized in some models with discrete neutrino flavor symmetry

34. mu-tau symmetry Z2 , D4 symmetry • Angles : • Phases: no CKM phase 2 Majorana phases

35. leptogenesis (Grimus and Lavoura ’04)

36. Soft breaking of the discrete symmetries generating non-vanishing deviation of from maximal mixing (Mohapatra, Nasri, Yu ’05)

37. Alternatively, ( Ahn, Kang, Kim, Lee )

38. Leptogenesis in SUSY • Gravitino problem • BBN constraints on the • abundance of gravitino for • 0.1 ~ 1 TeV • yield the bound (Kawasaki et al.’04) •  incompatible with bound from leptogenesis !! • To avoid gravitino problem: • Non-thermal leptogenesis • (Giudice et al. Asaka , Kawasaki et al.) • Heavy gravitino scenario • anomaly mediation (Ibe et al.’04) • Gravitino LSP scenario • Alternatives to avoid : • Soft Leptogenesis : using • soft breaking terms as source of L-violations which do not lead to seesaw neutrino masses • (Grossman et al., D’ambrosio et al., • Boubekeur et al., Allahverdi et al., • E.J.Chun) • ResonantLeptogenesis(Pilaftsis) • L-asymmetry is resonantly enhanced through the mixing of nearly degenerate heavy Majorana neutrinos (~TeV) • Various models for Low Scale Leptogenesis

39. Conclusions • Massive neutrinos may be responsible for our existence Leptogenesis • We have studied some neutrino mass constraints arisen from leptogenesis. • There may exist some correlation between leptogenesis and low energy neutrino observables.