Kajagoogooooooo said:
Interactions out of thermal equilibrium: isn't it trivial? our universe is expanding so, of course, it out of equilibrium.
No, it is not trivial. Just like you need CP violation to be large enough, you need a system that is sufficiently far away from thermal equilibrium. For this to occur you essentially need the Hubble rate to be larger than the interaction rate of whatever process would keep your system in thermal equilibrium or, in other words, the timescale of interactions needs to be larger than the age of the universe.
Kajagoogooooooo said:
CP violation: I`ve read that Cronin and Fitch experiment proves that issue, the problem is that the amount of the CP violation there is too small to explain the baryon asymmetry in the universe.
More precisely, the known CP violation in the quark sector is to small for electroweak baryogenesis to produce the observed baryon asymmetry.
Kajagoogooooooo said:
Baryon number B violation
Baryon number is violated in the SM. Let us come back to this.
Kajagoogooooooo said:
My question is how can you solve problem 2. 3. using the lepton sector. Or more precisely by using the Majorana neutrinos in the lepton sector, making a lepton asymmetry.
Let us go by steps. First, the creation of a lepton asymmetry is subject to the same Sakharov conditions as baryon number generation, but of course with L rather than B violation.
A popular way of introducing small neutrino masses into the SM is to extend it with right-handed (RH) neutrinos. This allows Yukawa couplings between the left-handed lepton doiblet, RH neutrinos, and the Higgs field that when the Higgs field takes a vev results in a Dirac mass term for neutrinos. However, since they are SM singlets, the RH neutrinos also allow for a Majorana mass term. A priori, the mass scale of this mass term is unknown as it is unrelated to any known scale. If it is chosen to be very large, it suppresses the masses of the LH neutrinos, which essentially go as ##m^2/M## where m is the Dirac mass and M the RH Majorana mass, giving a possible explanation of why SM neutrinos are so light. It is also quite natural to consider large M as a result of an extended symmetry broken at some high scale.
So far we have only wanted to explain neutrino masses, but let us consider the phenomenological implications in the early Universe. At the very early stage, the RH neutrinos would be held in thermal equilibrium with the SM. However, at some point the number of RH neutrino freezes out and are therefore out of equilibrium. The RH neutrinos decay through the very same Yukawa couplings as mentioned earlier. With CP violation in these Yukawa couplings, the branching ratio to final states containing a lepton will not be the same as that to final states containing an anti-lepton, thus providing violation of both CP and L and therefore all Sakharov conditions for producing a lepton asymmetry are satisfied.
Kajagoogooooooo said:
And how do you convert it to a baryon asymmetry using the sphaleron reactions? (An explanation about those reactions would be nice since I'm not that familiar with them).
They are typically referred to as sphaleron processes, not reactions, as they are a non-perturbative QFT effect. It is not easy to provide an I-level explanation (it is not easy to provide an A-level explanation either), but let us wave our hands around for a bit.
In the classical SM, both B and L are accidental symmetries and therefore conserved. However, on the quantum level, the B and L currents are anomalous, implying that their divergence is non-zero, leading to a B and L source term. Thus B and L are not conserved, but their non-conservation is proportional to an integer set by the different between different vacuum configurations of the electroweak gauge fields. The integer is proportional to the number of generations, ie, 3 in the SM, meaning that between different electroweak vacua, the baryon and lepton numbers changes by three units. However, the B-L current is non-anomalous and B-L is therefore conserved while B+L is not. At the present, these transitions are suppressed by an energy barrier, but in the early Universe they were very active as the temperature was higher. This means that part of whatever B or L symmetry will be transferred to the other sector as long as the sphaleron processes are in equilibrium. You can find out what this ratio is by considering the chemical potentials of all species in the early Universe. In other words, if you produce an asymmetry in L while sphaleron processes are active, part of that asymmetry will be converted into a baryon asymmetry.
For the baryon asymmetry, the Sakharov conditions of out of thermal equilibrium and C and CP violation are satisfied by the (extended) lepton sector, while baryon number violation occurs through the SM sphaleron processes.
Standard introductory references on leptogenesis are
Leptogenesis for pedestrians or
Baryogenesis via leptogenesis. You can probably find more information in those introductions.
Of course, there is quite a bit more going on than what I had time to discuss here and you can discuss many many more effects and possibilities to lower the scale at which leptogenesis occurs, but the above covers the main ideas.