1. New aspects of leptogenesis
Cosmo 08
August 25-29, 2008, Madison, Wisconsin, USA
New aspects of leptogenesis
Steve Blanchet
August 28, 2008

2. Outline Modern view of leptogenesis See-saw mechanism and cancellation
New aspects
Usual lower bound in the hierarchical limit can be relaxed
Effect of the Higgs asymmetry
N2 is generically non-negligible
Leptogenesis in ‘Adjoint SU(5)’
Summary

3. 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,08]
The extension of the Standard Model is given by

4. Modern view of leptogenesis
Thanks to the Yukawa interaction , the heavy RH neutrinos decay and are repopulated by inverse decay , where we define the state as
However, if the charged 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 called flavored leptogenesis.
[Nardi, Nir, Racker, Roulet, 06; Abada, Davidson, Josse-Michaux, Losada, Riotto, 06]

5. 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.
`1 is the good quantum state: Unflavored leptogenesis applies. 1
The flavored states `eμ and `τ have to be considered: 2-flavor lep. applies. 2
3-flavor leptogenesis must be considered. 3

6. See-saw mechanism and cancellation
Let us first introduce the convenient orthogonal parametrization [Casas, Ibarra; 2001]
complex orthogonal matrix
The matrix ­ is expected to be of order 1 for a conventional see-saw mechanism, i.e.
in which the neutrino mass estimation in the one generation case works with the Dirac mass at the EW scale and M~1014 GeV.
But the entries of the matrix ­ are free parameters, and can actually be arbitrarily large! If they are large, the smallness are not only explained by a „see-saw“ mechanism, but rather by a cancellation mechanism, which can however be motivated by symmetry arguments [Kersten, Smirnov; 2007] .

7. New aspect 1: lower bound [SB, Di Bari, 2008]
The second term in the flavored CP asymmetry formula [Covi, Roulet, Vissani, 1996] ,
cannot be simplified using the orthogonality of ­, and therefore goes like ­2 for large ­ values.
This effect is suppressed like M1 =M2 for hierarchical RH neutrinos.
This implies that the usually quoted lower bound for hierarchical RH neutrinos,
can be evaded if one allows some a larger cancellation to occur, i.e. larger ­ values.
Example:

8. New aspect 2: Higgs asymmetry
[SB, P. Di Bari, 2008]
It is typically neglected that the Higgs asymmetry contributes to the washout of the asymmetry as well:
Note that our matrix in the 2-flavor regime
differs from the result in the literature
[Abada et al., 2006]
Including the Higgs asymmetry, one obtains
When using the analytical expression present in the literature, one neglects the off-diagonal elements, allowing for 20% error. In this case, it is more precise to use the coefficients 1 and 1, instead of

9. New aspect 3: N2 effects
[SB, P. Di Bari, 2008]
Within flavored leptogenesis, the second heavier RH neutrino can typically not be neglected.
The production of asymmetry is typically large enough to explain the BAU, and the washout from N1 is very much reduced thanks to flavor effects.
Note that the heaviest, N3, typically decays in the unflavored regime (M3>1012 GeV), and the production is therefore very suppressed.

10. Leptogenesis in Adjoint SU(5)
[SB, P. Fileviez Perez, 2008]
Adjoint SU(5) is a realistic renormalizable GUT theory which includes neutrino masses with a Type I + Type III see-saw mechanism [P. Fileviez Perez, 2007] .
One introduces beyond minimal SU(5) new fermionic fields in a 24-plet, two of which, a triplet ½3 under SU(2) and singlet ½0, lead to small neutrino masses. Note that since only two fields contribute, the lightest neutrino will be massless in this model.
From the unification of the gauge couplings in the model, one obtains that ½3 has to be the lightest field and that ½0 is at least 40 times heavier [P. Fileviez Perez, H. Iminniyaz, G. Rodrigo, 2008] .
Concerning leptogenesis, in this model we have that:
The self-energy contribution to the CP asymmetry vanishes.
Even including flavor effects, the contribution from ½0 is negligible.

11. Leptogenesis in Adjoint SU(5)
[SB, P. Fileviez Perez, 2008]
Since the asymmetry is produced by a fermionic triplet, one has to include in the Boltzmann eqs. a gauge scattering term, which quickly thermalizes ½3 but reduces the efficiency factor.
Solving numerically the relevant set of Boltzmann eq., we obtain the following allowed regions, for normal and inverted hierarchy of light neutrinos:

12. Summary
Leptogenesis is an attractive way to explain the BAU because of the connection with the origin of neutrino masses.
I have discussed 3 new aspects:
It is possible to relax the lower bound on the scale of leptogenesis for hierarchical heavy neutrinos if one allows some cancellation in the see-saw.
The Higgs asymmetry should be taken into account for a more precise computation. This can be very easily done.
The contribution for the second heavier RH neutrino is generically non-negligible.
Finally, I have described how leptogenesis can be precisely computed in an attractive GUT model, „Adjoint SU(5)“. The model can then be efficiently constrained imposing successful leptogenesis.

13. Back up

14. 1
NO FLAVOR EFFECTS N1 N1 Φ l1 Φ

15. τR 2
WITH FLAVOR EFFECTS lτ N1 τR Φ
leμ l1 N1 Φ