1. Pasquale Di Bari (Max Planck, Munich) ‘The path to neutrino mass’, Aarhus, 3-6 September, 2007 Recent developments in Leptogenesis

2. Symmetric Universe with matter- anti matter domains ? Excluded by CMB + cosmic rays )   = (  ±  x    >>   (WMAP 2006) Pre-existing ? It conflicts with inflation ! (Dolgov ‘97) ) dynamical generation (baryogenesis) A Standard Model Solution ?   ¿   : too low ! New Physics is needed! CMB SM CMB (Sakharov ’67) Matter-antimatter asymmetry

3. From phase transitions: - Electroweak Baryogenesis: * in the SM * in the MSSM * ……………. Affleck-Dine: - at preheating - Q-balls - ………. From Black Hole evaporation Spontaneous Baryogenesis ………………………………… From heavy particle decays: - GUT Baryogenesis - LEPTOGENESIS Models of Baryogenesis

4. Tritium  decay : m e < 2.3 eV (Mainz 95% CL)  0 : m  < 0.3 – 1.0 eV (Heidelberg-Moscow 90% CL, similar result by CUORICINO ) using the flat prior (  0 =1): CMB+LSS :  m i < 0.94 eV (WMAP+SDSS) CMB+LSS + Ly  :  m i < 0.17 eV (Seljak et al.) Neutrino masses: m 1 < m 2 < m 3

5. 3 limiting cases : pure Dirac: M R = 0 pseudo-Dirac : M R << m D see-saw limit: M R >> m D Minimal RH neutrino implementation

6. 3 light LH neutrinos: 3 light LH neutrinos: N  2 heavy RH neutrinos: N 1, N 2, … N  2 heavy RH neutrinos: N 1, N 2, … m  M SEE-SAW - the `see-saw’ pivot scale  is then an important quantity to understand the role of RH neutrinos in cosmology See-saw mechanism

7.  * ~ 1 GeV m>  *  high pivot see-saw scale  `heavy’ RH neutrinos m<  *  low pivot see-saw scale  `light’ RH neutrinos

8. The see-saw orthogonal matrix

9. CP asymmetry If  i ≠ 0 a lepton asymmetry is generated from N i decays and partly converted into a baryon asymmetry by sphaleron processes if T reh  100 GeV ! efficiency factors  # of N i decaying out-of-equilibrium (Kuzmin,Rubakov,Shaposhnikov, ’85) M, m D, m are complex matrices  natural source of CP violation (Fukugita,Yanagida ’86) Basics of leptogenesis

10. Unflavoured regime Semi-hierarchical heavy neutrino spectrum : ‘Vanilla’ leptogenesis

11. Total CP asymmetry (Flanz,Paschos,Sarkar’95; Covi,Roulet,Vissani’96; Buchm¨uller,Pl ¨umacher’98) (Davidson, Ibarra ’02; Buchmüller,PDB,Plümacher’03;PDB’05 ) It does not depend on U !

12. Efficiency factor (Buchm¨uller,PDB, Pl ¨umacher ‘04)

13. WEAK WASH-OUT z´ M 1 / T zdzd K 1 ´ t U (T=M 1 )/   STRONG WASH-OUT (Blanchet, PDB ‘06)

14. m 1  m sol M 1  10 14 GeV Neutrino mixing data favor the strong wash-out regime ! Dependence on the initial conditions

15. 0.12 eV Upper bound on the absolute neutrino mass scale (Buchmüller, PDB, Plümacher ‘02) 3x10 9 GeV Lower bound on M 1 (Davidson, Ibarra ’02; Buchmüller, PDB, Plümacher ‘02) Lower bound on T reh : T reh  1.5 x 10 9 GeV (Buchmüller, PDB, Plümacher ‘04) Neutrino mass bounds ~ 10 -6 ( M 1 / 10 10 GeV)

16. Need of a very hot Universe for Leptogenesis

17. M 2  M 3 N 2 -dominated scenario beyond the hierarchical limit flavor effects Beyond the minimal picture

18. A poorly known detail If M 3  M 2 : (Hambye,Notari,Papucci,Strumia ’03; PDB’05; Blanchet, PDB ‘06 )

19.  The lower bound on M 1 disappears and is replaced by a lower bound on M 2 …that however still implies a lower bound on T reh ! (PDB’05) For a special choice of the see-saw orthogonal matrix: N 2 -dominated scenario Four things happen simultaneously:

20. Different possibilities, for example: partial hierarchy: M 3 >> M 2, M 1 heavy N 3 : M 3 >> 10 14 GeV 3 Effects play simultaneously a role for  2  1 : (Pilaftsis ’97, Hambye et al ’03, Blanchet,PDB ‘06) Beyond the hierarchical limit

21. (Nardi,Roulet’06;Abada et al.’06;Blanchet,PDB’06) Flavour composition: Does it play any role ? are fast enough to break the coherent evolution of the fully flavored regime and quantum states and project them on the flavour basis within the horizon  potentially a fully flavored regime holds! but for lower values of M 1 the  -Yukawa interactions, Flavor effects

22. Let us introduce the projectors (Barbieri,Creminelli,Strumia,Tetradis’01) : 1.In each inverse decay the Higgs interacts now with incoherent flavour eigenstates !  the wash-out is reduced and 2. In general and this produces an additional CP violating contribution to the flavoured CP asymmetries: These 2 terms correspond to 2 different flavour effects : Interestingly one has that this additional contribution depends on U ! Fully flavoured regime

23. In pictures: 1) N1N1 2) N1N1    

24. The asymmetries have to be tracked separately in each flavour: Classic Kinetic Equations in the fully flavored regime conserved in sphaleron transitions !

25. General scenarios (K 1 >> 1) –Alignment case –Democratic (semi-democratic) case –One-flavor dominance and big effect! Remember that:  the one-flavor dominance scenario can be realized if the  P 1  term dominates !

26. The lowest bounds independent of the initial conditions (at K 1 =K * ) don’t change! (Blanchet, PDB ‘06) 3x10 9 alignment democratic semi- democratic But for a fixed K 1, there is a relaxation of the lower bounds of a factor 2 (semi-democratic) or 3 (democratic) that can become much larger in the case of one flavor dominance. (Blanchet,PDB’06) Lower bound on M 1

27.  Semi-democratic case Let us consider: For m 1 =0 (fully hierarchical light neutrinos)  Since the projectors and flavored asymmetries depend on U  one has to plug the information from neutrino mixing experiments Flavor effects represent just a correction in this case ! A relevant specific case

28. However allowing for a non-vanishing m 1 the effects become much larger especially when Majorana phases are turned on ! m 1 =m atm  0.05 eV  1 = 0  1 = -  M 1 min (GeV) K1K1 The role of Majorana phases

29. Is the upper bound on neutrino masses removed by flavour effects ? 0.12 eV EXCLUDED (Abada,Davidson,Losada,Riotto’06) m 1 (eV) M 1 (GeV) (Blanchet, PDB ’06) PDB ’06) FULLY FLAVORED REGIME EXCLUDED Is the fully flavoured regime suitable to answer the question ?

30. N1N1 l1l1 NO FLAVOR N1N1 Φ Φ (Blanchet, PDB ’06)

31. WITH FLAVOR LµLµ LτLτ N1N1 l1l1 N1N1 Φ Φ RR (Blanchet, PDB ’06)

32. (Blanchet,PDB,Raffelt ‘06) Consider the rate   of processes like (Nardi et al. ’06; Abada et al. ‘06) The condition   > H (Nardi et al. ’06; Abada et al. ‘06) (equivalent to T  M 1  10 12 GeV) is sufficient for the validity of the fully flavored regime and of the classic Boltzmann equations only in the weak wash- out regime where H >  ID, however all interesting flavour effects occur in the strong wash-out regime !! In the strong wash-out regime the condition   >  ID is stronger than   > H and is equivalent to: If K 1   K 1  W ID  1  M 1  10 12 GeV but if K 1  > 1  much more restrictive ! This applies in particular to the one-flavor dominated scenario through which the upper bound on neutrino masses would be removed in a classic description. When the fully flavored regime applies ?

33. 0.12 eV A definitive answer requires a genuine quantum kinetic calculation for a correct description of the `intermediate regime’ ! ? Condition of validity of a classic description in the fully flavored regime m 1 (eV) M 1 (GeV) Is the upper bound on neutrino masses killed by flavor effects ?

34. Let us now further impose  real setting Im(  13 )=0 traditional unflavored case M 1 min The lower bound gets more stringent but still successful leptogenesis is possible just with CP violation from ‘low energy’ phases that can be tested in  0 decay (Majorana phases) (very difficult) and more realistically in neutrino mixing (Dirac phase)  1 = -  /2  2 = 0  = 0 Majorana phases Dirac phase Leptogenesis from low energy phases ? (Blanchet, PDB ’06)

35.  -Leptogenesis M 1 (GeV) In the hierarchical limit (M 3 >> M 2 >> M 1 ): In this region the results from the full flavored regime are expected to undergo severe corrections that tend to reduce the allowed region Here some minor corrections are also expected  -leptogenesis represents another important motivation for a full Quantum Kinetic description Going beyond the hierarchical limit these lower bounds can be relaxed : (Anisimov, Blanchet, PDB, in preparation ) sin  13 =0.20  1 = 0  2 = 0  = -  /2

36. Unflavored versus flavored leptogenesis Unflavored Flavored Lowest bounds on M 1 and T reh ~ 10 9 GeV Unchanged Upper bound on m 1 0.12 eV ? (QKE needed) N 2 - dominated scenario for  ~ R 23 Domain is enlarged but no drastic changes Leptogenesis from low energy phases Non-viableViable (only marginally in the HL  DL is needed)

37. A wish-list for see-saw and leptogenesis SUSY discovery with the right features: - Electro-weak Baryogenesis non viable (this should be clear) - discovery of LFV processes, discovery of EDM’s T reh  100 GeV (improved CMB data ? Discovery of GW background ?) Electroweak Baryogenesis non viable discovery of CP violation in neutrino mixing normal hierarchical neutrinos discovery of  0 discovery of heavy RH neutrinos: - dream: directly at LHC or ILC - more realistically: some indirect effect (EW precision measurements?, some new cosmological effect, [e.g. RH neutrinos as DM] ? …… )

38. Leptogenesis Leptogenesis provides a strong motivation fro heavy RH neutrinos and flavor effects open new prospects to test it in  0 decay experiments (Majorana phases) and (more realistically) in neutrino mixing experiments (Dirac phase) Summary  CDM model Cosmological observations   CDM model in conflict with the SM: 4 puzzles aiming at new physics Discovery of neutrino masses strongly motivates to search for solutions in terms of neutrino physics; adding RH neutrinos and taking the see-saw limit seems the simplest way to explain neutrino masses and to address in an attractive way some of the puzzles; Between light and heavy RH neutrinos the second option appears currently more robustly motivated (things could change for example if a  N  0 is discovered); A unified picture of leptogenesis and dark matter is challenging but maybe not impossible ! However a simultaneous solution of all puzzles seems to require a deeper SM extension like (at least) GUT’s