Strong thermal leptogenesis and the absolute neutrino mass scale

We show that successful strong thermal leptogenesis, where the final asymmetry is independent of the initial conditions and in particular a large pre-existing asymmetry is efficiently washed-out, favours values of the lightest neutrino mass $m_1 \gtrsim 10\,{\rm meV}$ for normal ordering (NO) and $m_1 \gtrsim 3\,{\rm meV}$ for inverted ordering (IO) for models with orthogonal matrix entries respecting $|\Omega_{ij}^2| \lesssim 2$. . We show analytically why lower values of $m_1$ require a high level of fine tuning in the seesaw formula and/or in the flavoured decay parameters (in the electronic for NO, in the muonic for IO). We also show how this constraint exists thanks to the measured values of the neutrino mixing angles and can be tighten by a future determination of the Dirac phase. Our analysis also allows to place more stringent constraint for a specific model or class of models, such as $SO(10)$-inspired models, and shows that some models cannot realise strong thermal leptogenesis for any value of $m_1$. A scatter plot analysis fully supports the analytical results. We also briefly discuss the interplay with absolute neutrino mass scale experiments concluding that they will be able in the coming years to either corner strong thermal leptogenesis or find positive signals pointing to a non-vanishing $m_1$. Since the constraint is much stronger for NO than for IO, it is very important that new data from planned neutrino oscillation experiments will be able to solve the ambiguity.

Neutrino mixing parameters ("pre-T2K")   On average one N i decay produces a B-L asymmetry given by the total CP asymmetries Seesaw parameter space The 6 parameters in the orthogonal matrix Ω encode the 3 life times and the 3 total CP asymmetries of the RH neutrinos and is an invariant • Iso-asymmetry surfaces η B (U, m i ;λ 1 ,..,λ 9 ) = η B CMB (if they "close up" the leptogenesis bound can remove more than one parameter in this case)

3) N 3 does not interfere with N 2 -decays:
From the last two assumptions 4) Barring fine-tuned mass cancellations in the seesaw ( Flavor composition of lepton quantum states: are fast enough to break the coherent evolution of The conditions for the wash-out of a pre-existing asymmetry ('strong thermal leptogenesis') can be realised only within a N 2 -dominated scenario where the final asymmetry is dominantly produced in the tauon flavour Residual "pre-existing" asymmetry possibly generated by some external mechanism Asymmetry generated from leptogenesis ……… ……

Crossing level solutions (Akhmedov, Frigerio, Smirnov '03)
At the crossing the CP asymmetries undergo a resonant enhancement The measured η B can be attained for a fine tuned choice of parameters: many models have made use of these solutions but as we will see there is another option

RH neutrino scenario revisited
Unflavoured only N 1 asymmetry + N 2 asymmetry In the 2 RH neutrino scenario the N 2 production has been so far considered to be safely negligible because ε 2α were supposed to be strongly suppressed and very strong N 1 wash-out. But taking into account: -the N 2 asymmetry N 1 -orthogonal component -an additional unsuppressed term to ε 2α New allowed N 2 dominated regions appear These regions are interesting because they correspond to light sequential dominated neutrino mass models realized in some grandunified models Re z Re z Re z Im z M 1 /10 10 GeV iso-contours M 1 /10 10 GeV iso-contours M 1 /10 10 GeV iso-contours Flavour projection (Engelhard,Nir,Nardi '08 ,Bertuzzo,PDB,Marzola '10) Assume Contribution from heavier RH neutrinos orthogonal to l 1 and escaping N 1 wash-out Component from heavier RH neutrinos parallel to l 1 and washed-out by N 1 inverse decays The heavy neutrino flavour basis cannot be orthonormal otherwise the CP asymmetries would vanish: this complicates the calculation of the final asymmetry

Phantom Leptogenesis
What happens to N B-L at T ∼ 10 12 GeV?

Remarks on phantom Leptogenesis
In conclusion ....phantom leptogenesis introduces additional strong dependence on the initial conditions We assumed an initial N 2 thermal abundance but if we were assuming An initial vanishing N 2 abundance the phantom terms were just zero ! The reason is that if one starts from a vanishing abundance during the N 2 production one creates a contribution to the phantom term by inverse decays with opposite sign and exactly cancelling with what is created in the decays N phant om Phantom terms cannot contribute to the final asymmetry in N 1 leptogenesis but (canceling) flavoured asymmetries can be much bigger than the baryon asymmetry and have implications in active-sterile neutrino oscillations NOTE: in strong thermal leptogenesis phantom terms are also washed out: full independence of the initial conditions!