# Baryogenesis via Leptogenesis

Baryon number is directly violated through electroweak anomaly and so does the Lepton number, for each transition from one vacuum to another. The two violations are of equal amount $\Delta B=\Delta L=N_f[N_{CS}(t_i)-N_{CS}(t_f)]$ since $(B-L)$ is anomaly free. Both the violations (i.e., $\Delta B,\Delta L$) will occur simultaneously for each transition. But in this manner $B$ is violated directly and I do not think that $L$ violation is inducing $B$ violation. Is this true? When standard model is extended with right-handed neutrinos, then decays of heavy Majorana neutrinos give rise additional to $L-$violation. How can this leptogenesis induce baryogenesis?

If the question is not clear enough I can clarify it further.

• I think it is possible, that this $L$-violation of the neutrinos can be converted to $L$-violation of the charged leptons, e.g. quarks, by W-boson loops. Therefore $B$-violating processes should be there as well. – Clever Jan 12 '15 at 11:31

## 2 Answers

I will try to give an answer, that contradicts a little my comment. I did not do any calculations, but I don't think that sphaleron processes have any influence here, since this should not only hold at very high temperatures. (BTW: this is the partial answer to one of your questions on how leptogenesis can lead to baryogenesis)

Through the seesaw mechanism, which implies Majorana neutrinos, it is actually possible to violate $B-L$. These neutrino oscillations $N \leftrightarrow \bar{N}$, where $\Delta(B-L)=2$, should happen above the TeV scale, but much below some GUT scale $(10^{16} GeV)$.

There are some interesting papers by Mohapatra on this subject. In GUT theories effective $(D>4)$-operators that violate $B-L$ can be constructed (see e.g. this paper by Andre de Gouvea, Juan Herrero-Garcia and Andrew Kobach.

I am sorry, that I cannot give you a more satisfying answer. If I find some time to read and think about it, I will post my thoughts/results.

When right handed neutrinos are introduced, they imply $L$ violation through their Majorana nature. Their decay into lepton and Higgs doublets $$N\,\longrightarrow l\,\Phi^\dagger$$ violates the lepton number (since $N$ has zero lepton number being Majorana). These decays take place out of thermal equilibrium, therefore a net lepton asymmetry is produced. However, in the Early Universe ($T\gtrsim 10^9\,\mbox{GeV}$) several other particle physics interactions are efficient. Among them, the so-called sphalerons, that violate $B$ and $L$, while still preserving $B-L$.
By considering all these additional processes which are in equilibrium at high temperatures, it is possible to show that the lepton asymmetry produced by the decay of $N$ (i.e. by the leptogenesis mechanism) is partly converted into a baryon asymmetry. Therefore, leptogenesis can be a viable mechanism to produce the baryon asymmetry of the Universe because the Standard Model itself provides the necessary way to link lepton and baryon asymmetry.