Baryogenesis from a primordial lepton asymmetry

Any primordial asymmetry for baryogenesis is in danger of being washed out by sphaleron transitions unless it is protected. The possibility which will concern us here, is that the asymmetry was encoded in a conserved global quantum number such as B — L number [1]. This was generated (or set by hand) primordially, and after possible processing at the electroweak phase transition, was converted into the presently observed baryon number. Recent work [2, 3] has suggested that the three $$L_i \, - \,B/3$$ numbers may play this role (i is a generation index). These could have been produced by generational (and CP violating) differences in the out of equilibrium decays of lepto-quarks [2, 4]. The baryogenesis could have occurred after the electro-weak phase transition as a results of mass effects. For this to be possible it is necessary that sphalerons remained in equilibrium for some time implying a second-order transition. Campbell, Davidson, Ellis, and Olive [5] have taken this idea further by demonstrating how to avoid the m 2/T 2 suppression through lepton-violating interactions. Provided that some, but not all, lepton flavours are violated by ΔL ≠ 0 interactions in equilibrium, B may be regenerated without the m 2 /T 2 lepton mass effects. Instead B depends only on the initial asymmetry of the non-equilibrating modes. For example, if lepton-violating interactions equilibrate L 1 — B/3 and L 2 — B/3 to zero, then the non-zero L 3 — B/3 biases baryon production via sphalerons: $$B \propto B - L = B/3 - L_3 \ne 0$$ .