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“Leptogenesis and Neutrino Masses” by Pasquale di Bari

March 17, 2011

As the last theory talk of the day, there has been an overview on how neutrinos enter the topic of Leptogenesis. Lepto has been originally introduced to explain the matter-antimatter asymmetry and it is intimately linked to neutrinos.  Furthermore, Lepto in principle is able to provide interesting infos on BSM physics and help in the flavour model building.

The basic concept is that the baryon asymmetry in the universe can be originated through a dynamical mechanism: a lepton asymmetry is first generated and after translated into baryon asymmetry through non-perturbative effects.

The minimal scenario is the type I See-Saw in which three RH neutrinos are responsible for the smallness of the light neutrino masses. In the standard type I See-Saw, the mass of these RH neutrinos should be very large, more than 10^9 GeV. It is obvious that such energies cannot be reproduce at our experiments and therefore direct detection of RH neutrinos is excluded. However, it could be possible to get indirect bounds. Let’s investigate on this possibility.

The neutrino Lagrangian is given by


and we are interested in the possibility of constraining mD and M. In this 3×3 matrices there are some non-physical parameters and therefore it is convenient to move to a basis with only physical parameters: the Casas-Ibarra parametrization helps,


Counting the number of parameters, we have 2×3 masses for the light and heavy neutrinos and 2×6 angles and phases for the matrices U and Ω.
On the other hand, neutrino experiments can give infos only on 9 parameters, the low energy ones.
—> Leptogenesis is important to get infos on the high energy parameters

Let’s enter more in details. The simplest description – Vanilla Leptogenesis – is based in a series of approximations:

1) neglecting in the decay of the RH neutrinos the flavour composition of final leptons, but just considering different rates for decays in leptons and in anti-leptons.

The difference among the two Γ’s is proportional to the parameter ε, that controls the total CP asymmetry. If ε is non-vanishing then lepton asymmetry is generated and partly converted into baryon asymmetry, ηB, by sphaleron processes, if the reheating temperature is higher than 100 GeV.
The final result depends also on the number of RH neutrinos that are out-of equilibrium at the moment of the decay. The out-of-equilibrium condition is necessary otherwise any contribution would get cancelled.

Concentrating on the origin of the ε parameter, it is computed by the interference of tree level and loops:


Notice that in the analytical expression appears the product mD^† mD, in green, that does not depend on the PMNS matrix. This is the link between the leptogenesis and the high energy parameters of the type I See-Saw.

2) There is a strong hierarchy among the RH neutrinos

3) The heaviest RH neutrino does not interfere with the decays of N2, the second heaviest state. In this case, the CP asymmetry of the lightest RH neutrino is dominant wrt the other ε and therefore we are discussing a N1-dominanted scenario.

4) Fine-tuned mass cancellation are avoided. This translates in an upper bound on ε1 in terms of the light neutrino masses and M1

5) The classical kinetic equations are integrated on momenta.

Under all these assumptions, it is possible to identify:
——–> upper bound on the light LH neutrino mass
——–> lower bound on the lighter heavy RH neutrino

An interesting observation is related to the wash-out: simply speaking, the wash-out removes all the pre-existing asymmetries and therefore it removes the dependence from any, even strange, physics at higher temperatures that could contribute to the baryon asymmetry, in addition to leptogenesis.

This simplified scenario can be improved in several different ways:

Pasquale concentrated only on few of these possibilities. Regarding the first approximation, that one on the flavour of the final leptons in the RH neutrino decays, it is well justified only for RH neutrino masses larger than 10^12 GeV. Otherwise, the τ-Yukawa interactions are fast enough to break the coherent evolution of the lepton states (this means that the evolving lepton states become a mixture of a τ and of μ+e). If we go further below in energy, if M1<10^9 GeV then also the μ-Yukawas are in equilibrium and therefore we get a 3-flavour regime.


In this way, the contribution to the baryon asymmetry accounts for three different contributions, one for each final lepton flavour.


The consequences of considering flavour are in the bounds of the Vanilla Leptogenesis: they get relaxed and now they DO depend on the PMNS phases.

It is possible to distinguish 10 different RH neutrino mass patterns, related to the energy at which the different lepton Yukawas enter the equilibrium. Pasquale continued with a detailed description on a heavy flavored scenario, with a lot of very nice plots and discussions. I encourage you to take a look of the talk in the webpage of the conference.

I just conclude this brief summary with the main message of the talk:
Leptogenesis is a complementary tool to low energy neutrino experiments in order to investigate the neutrino parameter space.
However, this interplay is not sufficient to over-constrain the See-Saw parameter space and it is necessary to either look for additional phenomenologies, such as LFV, or restrict the parameter space with additional assumptions, such as in BSM frameworks like GUT’s.

Today is almost over, but tomorrow I will be here again for the last day of the conference. Stay tuned!

(posted by Luca Merlo)

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