# Baryogenesis via Leptogenesis: Spontaneous B and L violation

https://arxiv.org/abs/2103.13397

In this paper with Pavel Fileviez Perez and Clara Murgui, we study the mechanism of Leptogenesis in theories where Baryon and Lepton number are promoted to local gauge symmetries

We numerically solved the Boltzmann equations including the effects of the process $N N \leftrightarrow Z_L Z_L \leftrightarrow f \bar{f}$ and, depending on how large is the ratio $g_L/M_{Z_L}$, this new interaction can quickly bring the right-handed neutrino into thermal equilibrium

If the new gauge interaction is too large it will keep the right-handed neutrinos in thermal equilibrium and suppresses the final baryon asymmetry. Consequently, we find a lower bound on the symmetry breaking scale for $\text{U(1)}_L$ of

$\huge{\frac{M_{Z_L}}{g_L}} > 10^{10} \,\, {\rm GeV},$

in order to have successful leptogenesis.

the spontaneous breaking of a U(1) at such high temperatures leads to the formation of cosmic strings that radiate gravitational waves that could be probed by future Laser Interferometers such as LISA.

Furthermore, in this scenario the ‘t Hooft operator associated with the sphaleron effects is different from the SM since it needs to preserve the ${\rm U(1)}_B$ gauge symmetry:

and hence, sphaleron processes can transfer a lepton asymmetry and a dark matter asymmetry into a baryon asymmetry.

The theory has an automatic dark matter that is predicted from the cancellation of gauge anomalies. Namely, in the theory with 6 new representations, the DM candidate is generically a Dirac fermion ($\chi$)

Then, the question arises: How can we generate a dark matter asymmetry?

Well, it turns out that by just adding a new complex scalar phi the theory nicely accommodates the mechanism proposed in https://arxiv.org/abs/1101.4936

In this mechanism, the out-of-equilibrium decays of $N_1 \to \phi \chi$ and $N_1 \to \phi^* \bar{\chi}$ can also generate a dark matter asymmetry. Then, the lepton and dark matter asymmetries are partially converted into a baryon asymmetry via sphaleron processes

Thus, theories with local Baryon and Lepton number can explain the baryon asymmetry, dark matter and neutrino masses.