1. Lepton number violation in cosmology and particle physics M. Yoshimura Introduction: Symmetry and its breakdown ・ Sources of B non-conservation : electroweak at high T Leptogenesis: L-nonconservation in universe ・ Thermal L-genesis and general remarks ・ Possible nightmare : gravitino overproduction ・ Ways out ・ L-number violation in terrestrial laboratories Conclusion

2. Symmetry principle and its breakdown Symmetry organizes indivisual events and leads to conservation law 2 important discoveries of last century 1. Local gauge symmetry Associated with force (interaction) 2. Spontaneous breaking of symmetry Symmetric dynamical law and breaking in realized states

3. Well known example Electric charge conservation: 1 st case of gauge symmetry and led to successful QED Standard theory of particle physics: unified weak and electromagnetic forces, and explained difference of force ranges

4. How about baryon and lepton numbers ? ・ My personal prejudice: Breakdown of empirical conservation laws not protected by the gauge principle, such as the lepton number, the baryon number, the flavor changing process, CP violation are all expected. Question is only the rate. We might already have many hints on these!

5. Recent developments in particle physics SUSY coupling unification

6. Neutrino physics Neutrino oscillation  Evidence of neutrino mass! Cosmic rays Neutrinos UpwardDownward

7. WMAP results Precise measurement of baryon abundance and bound on neutrino mass m < 0.23eV

8. Mystery of our existence Why are we here ? Despite that the law of microphysics is almost matter-antimatter symmetric, and Despite that in the early universe antimatter production is energetically possible and equilibrium has been established by the laws of gravity and thermodynamics

9. Generation of B-asymmetry Key quantity Is imbalance for matter is a hint on some symmetry breakdown ?

10. How to produce the asymmetry ： 3 conditions Necessary ingredients in the early universe

11. Delicacy of CP ： Quantum interference Baryon excess from a pair of particle and antiparticle process, e.g. CP violation Rescattering phase Interference computed by Landau-Cutkovsky rule ＝

12. Sources of B nonconservation GUT Electroweak at high T SUSY （ Affleck-Dine mechanism) Black hole evaporation

13. Electroweak damping Electroweak baryon noncnoservation suppressed at T=0 by enhanced at finite T by barrier crossing Can destroy preexisting B and L while keeping B-L Gauge and Higgs Mechanism due to level crossing of fermions caused by nontrivial gauge and higgs configuration of sphaleron and alike Electroweak baryon nonconservation

14. Baryogenesis in standard model unsuppressed at finite T KM phase Out of equilibrium: 1 st order phase transition via bubble formation

15. Difficulties of EW B-genesis No strong 1 st order phase transition due to experimental Higgs lower mass bound: >115GeV Theory requires a large radiative correction to the Higgs potential, to obtain more than quartic terms Magnitude too small due to KM phase alone

16. Electroweak redistribution of B and L For standard model of 3 generations Ｄａｍｐｉｎｇ ｅｆｆｅｃｔｉｖｅ ＠ B-L conserved and never washed out. e.g. Luty

17. L genesis and B conversion L-genesis of amount first and electroweak conversion into B, via For standard model of 3 generations Interesting in view of possible connection to observed neutrino masses

18. Likely mechanism of small neutrino mass generation Seesaw mechanism Heavy Majorana type of masses of neutrino partner, independent of standard theory of particle physics, generates a tiny left-handed neutrino masses and mixing a la Necessarily violates lepton number conservation Agent of L-asymmetry generation provided by righthanded partner

20. Thermal L genesis Fukugita-Yanagida Minimal extention of standard model with seesaw Right-handed Majorana decay CP asymmetry with neutrino mass matrix For 3 R-Majoranas = CP phase

21. Great impacts on neutrino masses and thermal history of universe Connection to neutrino masses heaviest neutrino (WMAP 0.23eV) lightest R-neutrino Reheat temperature With hierarchy of masses, dependence on 3 parameters Giudice et al

22. Prejudices for simplification Completely general analysis meaningless due to many (18) parameters of matrices Constraints: known quantities Some sort of hierarchy hierarchy for Dirac masses Symmetry GUT or flavor symmetry for Dirac term Effective parameters not directly observable

23. Gravitino problem: a possible nightmare both for GUT B- and L-genesis Superpartner of graviton mass lifetime Usual estimate of gravitino abundance and constraint from nucleosynthesis, including hadronic decay Possible to produce ？

24. Ways out EW baryogenesis Affleck-Dine mechanisim Gauge mediation LSP = gravitino Preheating

25. SuperWIMP scenario Feng, Su, Takayama hep-ph/0404198 0404231 LSP = gravitino NLSP = stau Lifetime of stau = stau -> gravitino + tau possibility of making a reservoir of stau @LHC

26. A possible resolution, using preheating after inflation Important new element for particle production and B- and L-genesis after inflation Non-perturbative effect of parametric resonance, leading to Complicated high energy phase of reheating, i.e. preheating 、 including dilution of gravitino abundance and generation of proper amount of B-asymmetry

27. Theory of particle production with chaotic potential Inflaton field oscillation given by (spatially homogeneous, periodic) Interaction by Producing a pair of particles For each momentum mode of massive particle

28. Problem of for large amplitude oscillation How to swing ： Need to vary center of your body periodically

29. Non-perturbative effect of parametric resonance, producing large mass particles ・ n-th band contribution like Large mass production possible if with large n Perturbative Born decay; from E-conservation

30. New features : preheating Initially highly non-thermal Possibility of producing GUT scale and R- Majorana particles Estimate based on a single reheat temperature doubtful

31. Preheating stage and gravitino abundance e.g. B-generation during preheating and gravitino abundance lowed by perturbative estimate is possible

32. Lepton number violation in laboratories Work with Lim and Takasugi For details: talk by Lim @WG4 Systematically studied processes given by Still most promising is neutrinoless double beta ・ But neutrinoless double beta can vanish, despite all positive results of disapperance and appearance neutrino oscillation experiments High intensity beam and high density target is indispensable to determine complex Muon capture realizes both, but BR very small

33. Towards verification of (Majorana) CP violation 7 experiments needed, 4 more besides neutrino oscillation Both disappearance and appearance of Lepton number violating processes like A long way and many more works for important physics

34. Summary (B-L) genesis is a great hint on physics beyond the standard model, linking the micro and the macro worlds L-genesis interesting due to its possible connection to the neutrino sector and lepton flavor violation Watch out gravitino overproduction Test of L-nonconservation with CP violation in laboratories is not easy, needs fresh ideas

36. Model of inflation: Chaotic inflation Damped inflaton oscillation wth its mass and initial dimensionless amplitude

37. Theory of reheating Old view Coherent inflaton oscillation = aggregate of 0-momentum particles Independent particle decay Instantaneous thermalization due to fast interaction leading to reheat temperature with Born decay rate

38. Integration, with back-reaction and Einstein equation