Pasquale Di Bari (Max Planck, Munich) COSMO 06, Tahoe Lake, September 25-29, 2006 Flavor effects in leptogenesis Reference paper: S. Blanchet, PDB hep/ph

Outline From the see-saw mechanism to leptogenesis The traditional picture Beyond the traditional picture Flavor effects General implications on leptogenesis bounds Role of Majorana phases  testing leptogenesis at low energies ?  testing leptogenesis at low energies ?Conclusions

From the see-saw mechanism to … From the see-saw mechanism to … already Compared to any other baryogenesis model, leptogenesis relies on a piece of new physics that has been already observed: neutrino masses neutrino massesneutrino massesneutrino masses and on the simplest way to explain them: and on the simplest way to explain them: the see-saw mechanism Adding to the SM (3) RH neutrinos with Yukawa couplings h and a Majorana mass M, a usual Dirac mass m D = v * h is also generated after SSB. For M >> m D : 3 light LH neutrinos: 3 light LH neutrinos: 3 heavy RH neutrinos: N 1, N 2, N 3 3 heavy RH neutrinos: N 1, N 2, N 3,

CP asymmetry 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, m D, m are complex matrices  natural source of CP violation (Fukugita,Yanagida ’86) … leptogenesis

Kinetic Equations ``decay parameters´´ CP violation in decays Wash-out term from inverse decays Strong wash-out when K i  3 Weak wash-out when K i  3

flavor composition of leptons is neglected hierarchical heavy neutrino spectrum asymmetry generated from lightest RH neutrino decays (N 1 -dominated scenario) The traditional picture

N 1 - dominated scenario

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

Neutrino mass bounds m 1 =0  M 1

beyond the hierarchical limit N 2 -dominated scenario flavor effects Beyond the traditional picture

(Barbieri et a l. ’01; Endo et al. ’04; Pilaftsis,Underwood ’05; Nardi,Roulet’06;Abada et al.’06;Blanchet,PDB’06) Flavor composition: Does it play any role ? However for lower temperatures the charged lepton Yukawa couplings, are strong enough to break the coherent evolution of the and of the, that are then projected on a flavor basis: ‘flavor’ is measured and comes into play ! Flavor effects It is then necessary to track the asymmetries separately in each flavor:

How flavor effects modify leptogenesis? The kinetic equations then become : First type of effect: inverse decays wash-out in each flavor is suppressed by the projectors: Second type of effect: additional contribution to the individual CP asymmetries: Same as before! (Nardi et al., 06) Interestingly one has that this additional contribution depends on U !

NiNi L NO FLAVOR NjNj Φ Φ LeLe LµLµ LτLτ

NiNi WITH FLAVOR NjNj Φ Φ LeLe LµLµ LτLτ

General implications on the bounds Upper bound on the individual CP asymmetries (Abada, et al., 06) : Notice that it does not decrease when the active neutrino mass scale increases  This can potentially remove the upper bound on neutrino masses Possible general scenarios: –Alignment case (Nardi et al., 05) –Democratic (semi-democratic) case (Blanchet, PDB, 06) –One-flavor dominance (Blanchet, PDB, 06) and potentially big effect!

Lower bound on M 1 The lowest bounds independent of the initial conditions (at K 1 =K * ) don’t change! (Blanchet, PDB ‘06) 3x10 9 alignment democratic semi- democratic But for a fixed K 1, there is a relaxation of the lower bounds of a factor 2 (semi-democratic) or 3 (democratic), but it can be much larger in the case of one flavor dominance.

A relevant specific case  Semi-democratic case Let us consider: For m 1 =0 (fully hierarchical light neutrinos)  Since the projectors and flavored asymmetries depend on U  one has to plug the information from neutrino mixing experiments Flavor effects represent just a correction in this case !

The role of Majorana phases However allowing for a non-vanishing m 1 the effects become much larger especially when Majorana phases are turned on ! m 1 =m atm  0.05 eV  1 = 0  1 = - 

Leptogenesis testable at low energies ? Let us now further impose  real setting Im(  13 )=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) and neutrino mixing (Dirac phase) Moreover considering the degenerate limit these lower bounds can be relaxed ! (Blanchet,PDB 06)

Conclusions Leptogenesis is fastly developing in last years becoming more and more quantitative; The most interesting recent achievement is represented by an account of flavor effects; They typically reduce the range of the strong wash- out regime without relaxing the lower bounds on M 1 and on T reh (for this one needs to consider a degenerate heavy neutrino spectrum) but removing the upper bound on neutrino masses that holds in the unflavored case; Very interestingly they make possible to have successful leptogenesis just from low energy phases testable in neutrino experiments:  0 decay experiments (Majorana phases) and neutrino mixing experiments (Dirac phase)

Neutrino masses: m 1 < m 2 < m 3

WEAK WASH-OUT z´ M 1 / T zdzd K 1 ´ t U (T=M 1 )/   STRONG WASH-OUT

Beyond the hierarchical limit Assume: partial hierarchy: M 3 >> M 2, M 1 heavy N 3 : M 3 >> GeV 3 Effects play simultaneously a role for  2  1 : (Pilalftsis ’97, Hambye et al ’03, Blanchet,PDB ‘06)

For  The lower bound on M 1 disappears and is replaced by a lower bound on M 2. The lower bound on T reh remains (PDB’05) N 2 -dominated scenario See-saw orthogonal matrix: