Pasquale Di Bari (INFN, Padova)

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

2. Outline • The minimal picture (‘vanilla’ leptogenesis) Beyond the minimal picture: • Extra-term in the total CP asymmetry • Adding flavor to vanilla leptogenesis • Beyond the hierarchical limit • N2 – dominated scenario

3. SEE-SAW m n  M 1) Minimal see-saw mechanism 3 light LH neutrinos: N2 heavy RH neutrinos: N1, N2 , …

4. The see-saw orthogonal matrix

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

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

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

8. 4) N1 - dominated scenario  N3 does not interfere with N2-decays: It does not depend on U!

9. Efficiency factor decay parameter 1

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

11. A first interesting coincidence !

12. 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) The lower bounds on M1 and Treh becomes more stringent when m1 increases (PDB’04) 3x109 GeV Lower bound on Treh: Treh 1.5 x 109 GeV (Buchmüller, PDB, Plümacher ’04; Giudice,Notari,Raidal,Riotto,Strumia’04)

13. A second interesting coincidence

14. A very hot Universe for leptogenesis ? Notice also that such large M1 values are a problem in many models (e.g. SO(1O))

15. Beyond vanilla leptogenesis • Extra-term in the total CP asymmetry • Adding flavor to vanilla leptogenesis • Beyond the hierarchical limit • N2 - leptogenesis

16. 1) CP asymmetry bound revisited If M3  M2 3M1: (Hambye,Notari,Papucci,Strumia ’03; PDB’05; Blanchet, PDB ‘06 )

17.  = R12(12)R13(13)R23(23) M3 >> M2 = 3 M1 |23| < 10 |ij| < 1 If R23 is switched off the extra-term does not help to relax the bounds !

18. 2) Flavor effects (Nardi,Roulet’06;Abada, Davidson, Josse-Michaux, Losada, Riotto’06, Blanchet,PDB, Raffelt’06 Flavour composition: () Does it play any role ? But for M1 1012 GeV, -Yukawa interactions, and are fast enough to break the coherent evolution of Imposing a more restrictive condition: 2 - ( and a overposition of  + e) If M1 109 GeV then also- Yukawas are in equilibrium 3 - flavor regime

19. 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:  ( = , +e) Interestingly one has that now this additional contribution depends on U!

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

21. Do flavour effects relax the bounds on neutrino masses ? consider first|ij|1and m1<< matm: Analytically: Numerically: unflavored M1(GeV) M1(GeV) flavored K1 Flavor effects do not relax the lower bound on M1 and Treh !

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.  = R13 Arbitrary  PMNS phases off Red: Green: Blue :

25. Neutrino mass bounds ? (Abada,Davidson, Losada, Riotto’06; Blanchet, PDB’06) 0.12 eV M1 (GeV) EXCLUDED INTERMEDIATE REGIME Condition of validity of a classic description in the fully flavored regime FULLY FLAVORED REGIME EXCLUDED EXCLUDED m1(eV) Is the fully flavoured regime suitable to answer the question ? No ! There is an intermediate regime where a full quantum kinetic description is necessary ! (Blanchet,PDB,Raffelt ‘06)

26. Red: Green: Blue :

27. Leptogenesis from low energy phases ? (Blanchet, PDB ’06) Let us now further impose­ real1= 0 M1min traditional unflavored case 1= - ¼/2 2= 0  = 0 Majorana phases 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) (difficult) and more realistically in neutrino • mixing (Dirac phase)

28. Dirac phase leptogenesis (Anisimov, Blanchet, PDB, arXiv 0707.3024 ) 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 !

29. Full degenerate limit: M1  M2  M3 The maximum enhancement of the CP asymmetries is obtained in so called resonant leptogenesis: • lower bound on sin 13and upper bound on m1

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 not dis

31. 3) Beyond the hierarchical limit (Pilaftsis ’97, Hambye et al ’03, Blanchet,PDB ‘06) Different possibilities, for example: • partial hierarchy: M3 >> M2 , M1 • M3 >>1014 GeV : 

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

33. 4) N2-dominated scenario (PDB’05) Four things happen simultaneously: For a special choice of =R23  Equivalent to assume: The lower bound on M1 disappears and is replaced by a lower bound on M2 …that however stillimplies a lower bound on Treh !

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

35. Conclusions • The minimal scenario (vanilla leptogenesis) grasps the main features of leptogenesis neutrino mass bounds but there are important novelties introduced by various effects beyond • 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 109 GeV down to 108 GeV • The upper bound on neutrino masses needs a final answer from a full density matrix approach • 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 • The N2 - dominated scenario is a good option with potential interesting applications

36. (Blanchet, PDB ’06) R R FULLY FLAVORED REGIME Lτ N1 Φ Lµ l1 N1 Φ

37. In pictures: 1) N1 + 2)   N1  