Matter v Antimatter III: Leptogenesis

I’ve been blogging the last few weeks about the question of the baryon asymmetry of the universe – the measured excess of matter over antimatter in the universe. Having already discussed electroweak baryogenesis, I’d now like to turn to another possible way that this asymmetry may have come about – leptogenesis.

In order to explain this, I’ll switch gears for a moment to a seemingly unrelated issue in contemporary particle physics, that of neutrino masses. Neutrinos are electrically neutral particles that, until the last decade, were thought to be exactly massless (and indeed are precisely so in the standard model of particle physics). There exists one neutrino particle associated with each electron-like particle (one for the electron, one for the muon, and one for the tau lepton, going by the imaginative names electron neutrino, etc.).

However, careful experiments on neutrinos created both in the Sun and in the upper atmosphere have conclusively demonstrated that neutrinos have an extremely small but non-zero mass. Fortunately for me, and for you, I don’t need to go into my own explanation of why this is so because Heather Ray did a fantastic job of it in her guest post on the MiniBooNE results from April of last year.

Explanations for unusually small masses, like those that neutrinos seem to have, aren’t easy to come by, but one popular and seemingly natural way to achieve them in the so-called seesaw mechanism. This isn’t the place to go into that in detail, but the important point is that one needs to postulate a heavy right-handed neutrino, the mass of which then conspires with the electroweak scale to generate the unusually light scale characterizing the masses of the left-handed neutrinos.

Having told this little story about the possible origin of small neutrino masses, let’s return to the issue of the baryon asymmetry of the universe. As I’ve just described, there is a somewhat compelling argument for the existence of a very heavy (it turns out to be close to the GUT scale) right-handed neutrino. The interactions of this field are such that they violate lepton number, and so this opens up the possibility of generating an asymmetry of leptons over antileptons, as long as a couple of other crucial conditions are satisfied.

If our right-handed neutrino was light, say at the electroweak scale, then the expansion rate of the universe when it was decaying would be so slow that the decay products could easily find one another, and thus the reverse interactions would balance the decays and no net lepton asymmetry would result. This is a heuristic way of saying that the interactions of a sufficiently light neutrino would be in approximate thermal equilibrium, and hence no net evolution can occur. However, because the right-handed neutrino in question is heavy, it decays at early times, when the universe is expanding extremely rapidly, and because of this the decays occur out of equilibrium.

A final requirement is that the decays be CP-violating, but this is a generic feature of theories beyond the standard model and so we needn’t dwell on it here.

So, we’ve used the measured non-zero masses of neutrinos to infer the possible existence of a heavy right-handed neutrino decaying out of equilibrium in a lepton number and CP-violating way in the early universe. All the ingredients necessary to generate an asymmetry of leptons over their antiparticles.

But wait a minute. Weren’t we looking to explain the baryon asymmetry, not a lepton asymmetry? Fortunately, the standard model contains a handy way of partially converting a lepton asymmetry to a baryonic one – and we’ve already discussed it! My post on anomalous baryon number violation in the standard model described the way in which nonperturbative effects allow for processes in which more baryons than antibaryons are produced. One thing I neglected to say though, is that there is an identical anomaly in the lepton number symmetry and, remarkably, the combination of the two symmetries, B-L, has no anomaly at all! Another way to say this is that whenever there is an anomalous process that produces more baryons than antibaryons, it is guaranteed to be accompanied by the production of more leptons than antileptons (up to subtle numerical factors that need not concern us here, equal numbers are produced).

So if we have a way of efficiently generating a leptonic asymmetry in the early universe, anomalous electroweak processes can then equilibrate that asymmetry into one partly in leptons and partly in baryons – yielding our required baryon asymmetry! This whole process is known as leptogenesis.

Leptogenesis has always been a cute idea, but the discovery of neutrino masses has provided more support for it and it may well be that this is how the baryon asymmetry was generated, leading to the light elements, and ultimately us.