Pasquale Di Bari (Max Planck, Munich)

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

2. CMB CMB SM Matter-antimatter asymmetry • Symmetric Universe with matter- anti matter domains ?Excluded by CMB + cosmic rays )B = (6.1± 0.2) x 10-10>>B (WMAP 2006) • Pre-existing ? It conflicts with inflation ! (Dolgov ‘97) ) dynamical generation (baryogenesis) • A Standard Model Solution ?B ¿ B : too low ! (Sakharov ’67) New Physics is needed!

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. Neutrino masses: m1 < m2 < m3 Tritium  decay : me < 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 :  mi < 0.94 eV (WMAP+SDSS) CMB+LSS + Ly :  mi < 0.17 eV (Seljak et al.)

5. Minimal RH neutrino implementation • 3 limiting cases : • pure Dirac: MR= 0 • pseudo-Dirac : MR << mD • see-saw limit: MR >> mD

6. See-saw mechanism 3 light LH neutrinos: N2 heavy RH neutrinos: N1, N2 , … SEE-SAW m n  M • the `see-saw’ pivot scale  is then an important quantity to understand the role of RH neutrinos in cosmology

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

8. The see-saw orthogonal matrix

9. Basics of leptogenesis (Fukugita,Yanagida ’86) M, mD, mare complex matrices  natural source of CP violation CP asymmetry If i≠ 0 alepton asymmetryis generated from Ni decays and partly converted into a baryon asymmetry by sphaleron processes if Treh 100 GeV ! (Kuzmin,Rubakov,Shaposhnikov, ’85) efficiency factors# of Ni decaying out-of-equilibrium

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

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. z´ M1/ T K1´ tU(T=M1)/1 (Blanchet, PDB ‘06) WEAK WASH-OUT STRONG WASH-OUT zd

14. Dependence on the initial conditions m1 msol M11014 GeV Neutrino mixing data favor the strong wash-out regime !

15. Neutrino mass bounds ~ 10-6 ( M1 / 1010 GeV) Upper bound on the absolute neutrino mass scale (Buchmüller, PDB, Plümacher ‘02) 0.12 eV Lower bound on M1 (Davidson, Ibarra ’02; Buchmüller, PDB, Plümacher ‘02) 3x109 GeV Lower bound on Treh: Treh 1.5 x 109 GeV (Buchmüller, PDB, Plümacher ‘04)

16. Need of a very hot Universe for Leptogenesis

17. Beyond the minimal picture • M2 M3 • N2-dominated scenario • beyond the hierarchical limit • flavor effects

18. A poorly known detail If M3  M2 : (Hambye,Notari,Papucci,Strumia ’03; PDB’05; Blanchet, PDB ‘06 )

19. N2-dominated scenario (PDB’05) Four things happen simultaneously: For a special choice of the see-saw orthogonal matrix:  The lower bound on M1 disappears and is replaced by a lower bound on M2 …that however stillimplies a lower bound on Treh !

20. Beyond the hierarchical limit (Pilaftsis ’97, Hambye et al ’03, Blanchet,PDB ‘06) Different possibilities, for example: • partial hierarchy: M3 >> M2 , M1 • heavy N3: M3 >> 1014 GeV 3 Effects play simultaneously a role for 2  1 :

21. Flavor effects (Nardi,Roulet’06;Abada et al.’06;Blanchet,PDB’06) Flavour composition: Does it play any role ? but for lower values of M1 the-Yukawa interactions, are fast enough to break the coherent evolution of the and quantum states and project them on the flavour basis within the horizon  potentially a fully flavored regime holds!

22. Fully flavoured regime Let us introduce theprojectors (Barbieri,Creminelli,Strumia,Tetradis’01) : These 2 terms correspond to 2 different flavour effects : • 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: Interestingly one has that this additional contribution depends on U!

23. In pictures: 1) N1 2)   N1  

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

25. General scenarios (K1 >> 1) • Alignment case • Democratic (semi-democratic) case • One-flavor dominance and and Remember that: big effect!  the one-flavor dominance scenario can be realized if the P1 term dominates !

26. Lower bound on M1 semi-democratic (Blanchet,PDB’06) alignment The lowest bounds independent of the initial conditions (at K1=K*) don’t change!(Blanchet, PDB ‘06) democratic 3x109 But for a fixed K1, there is a relaxation of the lower boundsof a factor 2 (semi-democratic) or 3 (democratic) that can become much larger in the case of one flavor dominance.

27. A relevant specific case • Let us consider: • Since the projectors and flavored asymmetries depend on U • one has to plug the information from neutrino mixing experiments • For m1=0(fully hierarchical light neutrinos) •   Semi-democratic case Flavor effects represent just a correction in this case !

28. The role of Majorana phases • However allowing for a non-vanishing m1 the effects become much • larger especially when Majorana phases are turned on ! 1= 0 1= -  M1min (GeV) m1=matm 0.05 eV K1

29. Is the upper bound on neutrino masses removed by flavour effects ? (Blanchet, PDB ’06) 0.12 eV EXCLUDED (Abada, Davidson, Losada, Riotto’06) M1 (GeV) FULLY FLAVORED REGIME EXCLUDED EXCLUDED m1(eV) Is the fully flavoured regime suitable to answer the question ?

30. (Blanchet, PDB ’06) NO FLAVOR N1 N1 Φ l1 Φ

31. (Blanchet, PDB ’06) R WITH FLAVOR Lτ N1 Φ Lµ l1 N1 Φ

32. When the fully flavored regime applies ? (Blanchet,PDB,Raffelt ‘06) • Consider the rate  of processes like • The condition  > H (Nardi et al. ’06; Abada et al. ‘06) • (equivalent to T  M1 1012GeV) 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 K1K1 WID  1M1  1012 GeV • but if K1<< K1 WID >> 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.

33. Is the upper bound on neutrino masses killed by flavor effects ? ? 0.12 eV M1 (GeV) Condition of validity of a classic description in the fully flavored regime m1(eV) A definitive answer requires a genuine quantum kinetic calculation for a correct description of the `intermediate regime’ !

34. Leptogenesis from low energy phases ? (Blanchet, PDB ’06) Let us now further impose  real setting Im(13)=0 M1min traditional unflavored case Majorana phases 1= - /2 2= 0  = 0 Dirac phase • 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)

35. -Leptogenesis (Anisimov, Blanchet, PDB, in preparation ) In the hierarchical limit (M3>> M2 >> M1 ): In this region the results from the full flavored regime are expected to undergo severe corrections that tend to reduce the allowed region M1 (GeV) 1= 0 2= 0  = -/2 sin13=0.20 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 :

36. Unflavored versus flavored leptogenesis

37. A wish-list for see-saw and leptogenesis • Treh  100 GeV (improved CMB data ? Discovery of GW background ?) • Electroweak Baryogenesis non viable • normal hierarchical neutrinos • discovery of CP violation in neutrino mixing • discovery of 0 • SUSY discovery with the right features: • - Electro-weak Baryogenesis non viable (this should be clear) • - discovery of LFV processes, discovery of EDM’s • 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. Summary • Cosmological observations CDM model in conflict with the SM: • 4 puzzles aiming at new physics • Leptogenesisprovides 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) • 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 addressin an attractive way some of the puzzles; • Between lightand 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