1. Pasquale Di Bari (INFN, Padova) Melbourne Neutrino Theory Workshop, 2-4 June 2008 New Aspects ofLeptogenesis Neutrino Mass Bounds (work in collaboration with Steve Blanchet to appear soon)

2. Outline  The minimal picture (‘vanilla’ leptogenesis) Beyond the minimal picture: Beyond the minimal picture:  Extra-term in the total CP asymmetry  Adding flavor to vanilla leptogenesis  Beyond the hierarchical limit  N 2 – dominated scenario

3. 1) Minimal see-saw mechanism 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 n  M SEE-SAW

4. The see-saw orthogonal matrix

5. Total CP asymmetriesTotal CP asymmetries 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 D is complex in general  natural source of CP violation (Fukugita,Yanagida ’86) 2) Unflavoured leptogenesis

6. Total CP asymmetries (Flanz,Paschos,Sarkar’95; Covi,Roulet,Vissani’96; Buchmüller,Plümacher’98) It does not depend on U !

7. (Davidson, Ibarra ’02; Buchmüller,PDB,Plümacher’03;Hambye et al ’04;PDB’05 ) ) Upper bound on the CP asymmetry of the lightest RH neutrino 3) Semi-hierarchical heavy neutrino spectrum

8.  N 3 does not interfere with N 2 -decays: It does not depend on U! 4) N 1 - dominated scenario

9. Efficiency factor decay parameter 1

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

11. A first interesting coincidence !

12. 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; Giudice,Notari,Raidal,Riotto,Strumia’04) Neutrino mass bounds ~ 10 -6 ( M 1 / 10 10 GeV) The lower bounds on M 1 and T reh becomes more stringent when m 1 increases (PDB’04)

13. A second interesting coincidence

14. A very hot Universe for leptogenesis ? Notice also that such large M 1 values are a problem in many models (e.g. SO(1O)) Notice also that such large M 1 values are a problem in many models (e.g. SO(1O))

15. Beyond vanilla leptogenesis 1. Extra-term in the total CP asymmetry 2. Adding flavor to vanilla leptogenesis 3. Beyond the hierarchical limit 4. N 2 - leptogenesis

16. 1) CP asymmetry bound revisited If M 3  M 2  3M 1 : (Hambye,Notari,Papucci,Strumia ’03; PDB’05; Blanchet, PDB ‘06 )

17.  = R 12 (  12 ) R 13 (  13 )R 23 (  23 ) M 3 >> M 2 = 3 M 1 If R 23 is switched off the extra-term does not help to relax the bounds ! |  ij | < 1 |  23 | < 10

18. (Nardi,Roulet’06;Abada, Davidson, Josse-Michaux, Losada, Riotto’06, Blanchet,PDB, Raffelt’06 Flavour composition: Does it play any role ? are fast enough to break the coherent evolution of But for M 1  10 12 GeV,  -Yukawa interactions, 2) Flavor effects () and Imposing a more restrictive condition: If If M 1  10 9 GeV then also  - Yukawas are in equilibrium  3 - flavor regime 2 - (  and a overposition of  + e)

19. Let us introduce the projectors (Barbieri,Creminelli,Strumia,Tetradis’01) : 1. 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 now this additional contribution depends on U ! Fully flavoured regime (  = ,  +e)  

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

21. consider first |  ij |  1 and m 1 << m atm : Flavor effects do not relax the lower bound on M 1 and T reh ! Numerically: M 1 (GeV) K1K1K1K1 Analytically: unflavored flavored Do flavour effects relax the bounds on neutrino masses ? M 1 (GeV)

22. A new effect for large |  ij | It dominates for |  ij |  1 but is upper bounded because of  orthogonality: It is usually neglected but since it is not upper bounded by orthogonality, for |  ij |  1 it can be important The usual lower bound gets relaxed

23. Red: Green: Arbitrary  Blue :  = R 13 PMNS phases off

25. 0.12 eV EXCLUDED m 1 (eV) M 1 (GeV) EXCLUDED Is the fully flavoured regime suitable to answer the question ? FULLY FLAVORED REGIME EXCLUDED (Abada,Davidson, Losada, Riotto’06; Blanchet, PDB’06) ? Condition of validity of a classic description in the fully flavored regime No ! There is an intermediate regime where a full quantum kinetic description is necessary ! (Blanchet,PDB,Raffelt ‘06) INTERMEDIATE REGIME Neutrino mass bounds

26. Red: Green: Blue :

27. Let us now further impose ­ real   1 = 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) (difficult) and more realistically in neutrino mixing (Dirac phase)  1 = - ¼ /2  2 = 0  = 0 Majorana phases Dirac phase Leptogenesis from low energy phases ? (Blanchet, PDB ’06)

28. 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 ! (Anisimov, Blanchet, PDB, arXiv 0707.3024 ) sin  13 =0.20  1 = 0  2 = 0  = -  /2 Dirac phase leptogenesis

29. Full degenerate limit: M 1  M 2  M 3 The maximum enhancement of the CP asymmetries is obtained in so called resonant leptogenesis : ” ” lower bound on sin  13 and upper bound on m 1

30. Some remarks on  -leptogenesis : there is no theoretical motivation …however, within a generic model where all 6 phases are present, it could be regarded as an approximate scenario if the contribution from  dominates  it is interesting to know that something we could discover in neutrino mixing experiments is sufficient to explain (in principle) a global property of the Universe On the other hand notice that: if we do discover CP violation in neutrino mixing it does not prove leptogenesis notdis

31. Different possibilities, for example: partial hierarchy: M 3 >> M 2, M 1 (Pilaftsis ’97, Hambye et al ’03, Blanchet,PDB ‘06) 3) Beyond the hierarchical limit  M 3 >> 10 14 GeV :

32. 3 Effects play simultaneously a role for  2  1 : 1. 1.Asymmetries add up 2. 2.Wash-out effects add up as well 3. 3.CP asymmetries get enhanced For  2  0.01 ( degenerate limit ) the first two effects saturate and:

33.  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  =R 23 4) N 2 -dominated scenario Four things happen simultaneously: Equivalent to assume:

34. An analytical summarizing expression heavy neutrino flavor index lepton flavor index CP asmmetry enhancement for degenerate RH neutrinos Extra-term violating the ‘usual’ CP asymmetry upper bound Contribution from heavier RH neutrinos FLAVOR EFFECTS Vanilla leptogenesis

35. Conclusions 1.The minimal scenario (vanilla leptogenesis) grasps the main features of leptogenesis neutrino mass bounds but there are important novelties introduced by various effects beyond 2.A lower bound on the reheating temperature is a solid feature in the hierarchical limit. However, flavor effects introduce a new possibility that, though at expenses of a mild tuning, can relax the lower bound from 10 9 GeV down to 10 8 GeV 3.The upper bound on neutrino masses needs a final answer from a full density matrix approach 4.Flavor effects make possible a scenario (Dirac phase leptogenesis) where the final asymmetry stems only from the same source of CP violation (sin  13 sin  ) that is testable in neutrino mixing 5.The N 2 - dominated scenario is a good option with potential interesting applications

36. FULLY FLAVORED REGIME LµLµ LτLτ N1N1 l1l1 N1N1 Φ Φ RR (Blanchet, PDB ’06) RR

37. In pictures: 1) N1N1 2) N1N1     +