06 Steve Blanchet

Dirac phase leptogenesis: 

Dirac phase leptogenesis Steve Blanchet Max-Planck-Institut für Physik, Munich International Conference on Topics in Astroparticle and Underground Physics September 11-15, 2007, Sendai, Japan September 11, 2007 Based on: arXiv:0707.3204, with A. Anisimov and P. Di Bari

Outline: 

Outline Modern view of leptogenesis Unflavored leptogenesis Fully-flavored leptogenesis Fully-flavored leptogenesis CP violation and leptogenesis Dirac-phase leptogenesis (±-leptogenesis) Hierarchical limit for the heavy neutrinos Degenerate limit: link between low-energy observables and the BAU Conclusion

Modern view of leptogenesis: 

Modern view of leptogenesis Leptogenesis [Fukugita and Yanagida, 1986] stands for the generation of a lepton asymmetry by the decay of heavy right-handed neutrinos , and its subsequent conversion into a baryon asymmetry by the sphaleron processes [Kuzmin, Rubakov, Shaposhnikov, 1985]. Being the cosmological consequence of the see-saw mechanism, it offers an elegant and simple explanation to the puzzle of the baryon asymmetry of the Universe (BAU), i.e. why [WMAP,06] The extension of the Standard Model is given by

Slide4: 

However, if the lepton-lepton interactions coming from are fast (i.e. in equilibrium , but also faster than the inverse decay rate when the asymmetry is produced [SB, Di Bari, Raffelt, 06]), they impose a different description of leptogenesis. [Nardi, Nir, Racker, Roulet, 06; Abada, Davidson, Josse-Michaux, Losada, Riotto, 06] Thanks to the Yukawa interaction , the heavy RH neutrinos decay and are repopulated by inverse decay , where we define the state as Modern view of leptogenesis

Slide5: 

The flavored states leμ and lτ have to be considered: fully-flavored lep. applies. l1 is the good quantum state: Unflavored leptogenesis applies. 2 1 Modern view of leptogenesis Flavor starts to matter when the τ Yukawa interaction enters equilibrium, at a temperature of ~1012 GeV. The μ interaction enters equilibrium only much later, at ~109 GeV. So, between ~1012 GeV and ~109 GeV, a 2-flavor problem must be tackled, with flavors denoted τ and eμ.

Slide6: 

N1 l1 NO FLAVOR EFFECTS N1 Φ Φ 1

Slide7: 

WITH FLAVOR EFFECTS lμ lτ N1 l1 N1 Φ Φ 2

Fully-flavored leptogenesis: 

Fully-flavored leptogenesis The fundamental (classical) Boltzmann equations are CP violation Out-of-equilibrium condition Sphalerons conserve Δα ! The CP violation parameter is given by , the important decay parameter. [Barbieri, et al, 99;Nardi, et al., 06; Abada, et al., 06]

Fully-flavored leptogenesis: 

Fully-flavored leptogenesis The projectors [Barbieri, Creminelli, Strumia, Tetradis, 99] are given by New source of CP violation! The flavored CP asymmetries can indeed be written as Even when the total CP asymmetry, , is 0, the flavored ones can be non-zero. This new source of CP violation depends on the lepton mixing matrix, contrary to !

CP violation and leptogenesis: 

Pictorially, the two sources of CP violation can be seen as follows CP violation and leptogenesis e+μ e+μ τ τ Very interestingly, in fully-flavored leptogenesis, the CP phases in the PMNS matrix can be uniquely responsible for the generation of the BAU! [SB, Di Bari, 06; Pascoli, Petcov, Riotto, 06; Branco, Gonzalez Felipe, Joaquim, 06]

CP violation and leptogenesis: 

CP violation and leptogenesis The see-saw has many new parameters (18!) compared to the Standard Model, among which 6 are CP-violating phases. A useful parametrization is given by [Casas,Ibarra, 01] 3 high-energy (unmeasurable) phases 3 low-energy (measurable) phases: 2 Majorana phases and 1 Dirac phase ± The matrix can be parametrized by three complex rotations:

±-leptogenesis [Anisimov, SB, Di Bari, arXiv:0707.3024]: 

In the hierarchical limit it is possible to explain the BAU only with this source of CP violation [Pascoli, Petcov, Riotto, 06] ±-leptogenesis [Anisimov, SB, Di Bari, arXiv:0707.3024] Assume from now on that only the Dirac phase ± is turned on. This is a minimal condition on the necessary CP violation for successful leptogenesis because this phase appears only in combination with the small µ13 angle (<0.2 at 3¾). Problem: it is quite constrained and in the weak wash-out! Example:

±-leptogenesis in the HL: 

±-leptogenesis in the HL The generation of the BAU from the second RH neutrino, N2, is also possible: [Di Bari, 05] The asymmetry is given by the second RH neutrino: The situation is as constrained as in the previous case… Solution: Go to degenerate RH neutrino masses!

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±-leptogenesis in the DL In the degenerate limit (DL), , the CP asymmetry can be enhanced [Covi, Roulet, Vissani, 96] , Note that in the DL, contrary to the HL, all three RH neutrinos contribute to the asymmetry and the wash-out from each of them must be taken into account: until one hits a resonance [Pilaftsis, 99] (RL) when ⇒ strong wash-out

±-leptogenesis in the RL: 

±-leptogenesis in the RL We found a nice link between low-energy parameters (µ13, mass hierarchy, absolute neutrino mass scale, Dirac phase) and the BAU. [Anisimov, SB, Di Bari, 07] Theoretical uncertainty (Far) future sensitivity Allowed regions In the RL, the final asymmetry is essentially independent of the RH neutrino mass ⇒ TeV scale possible! [Pilaftsis, 99]

Conclusions: 

Conclusions Thermal leptogenesis is an attractive way to explain the BAU. The latest developments (flavor effects) impose a description of leptogenesis where low-energy phases play an important role. When the Dirac phase acts as the only source of CP violation (±-leptogenesis), the situation is quite constrained in the HL. In the DL, this tension is relaxed and the asymmetry is produced in the strong wash-out, with no dependence on the initial conditions. Very interestingly, in the extreme case of resonant lep., in order to produced the BAU, an upper bound on m1 which depends on the angle µ13 was obtained.

Conclusions: 

Conclusions If ± is discovered, then we might know for the first time that there is a sufficient source of CP violation at hand to explain the BAU. The lower the bound on µ13 is, the more stringent the upper bound on m1 becomes. Note that there is also a dependence of the asymmetry on the neutrino mass hierarchy and on the phase ±.

Slide18: 

Condition of validity for each picture Full density matrix calculation required… [SB, Di Bari, Raffelt, hep-ph/0611337] Qualitative condition for the validity of the fully-flavored regime