Microphysical mechanisms for producing the baryon excess -- baryogenesis

We are faced with compelling observational evidence that the universe contains more matter than antimatter. Unless we are willing to make the unappealing assumption that the initial condition of the universe was matter-antimatter-asymmetric, we have to find a mechanism to generate the asymmetry from symmetric initial conditions. This process of generating the asymmetry is called ``baryogenesis''. It was Sakharov who first proposed that the universe might have started out symmetric, and who determined the conditions that any baryogenesis mechanism must fulfill [6]. These conditions are called the ``Sakharov conditions'' in his honor. We summarize them in the following section; then we discuss the various asymmetry generation mechanisms that have been proposed.

Sakharov conditions

To produce a matter-antimatter asymmetry from equal initial abundances of matter and antimatter, the baryogenetic mechanism must satisfy the following conditions:

$B$ violation

The net baryon number $B$ (i.e. the number of baryons minus the number of antibaryons in the universe) must be violated. This is a rather obvious condition, but quite difficult to fulfill -- no process observed terrestrially has violated $B$ so far.

$C\!P$ violation

The combined operation of charge conjugation ($C$) and parity inversion ($P$) transforms a particle into its antiparticle. ``$C\!P$ violation'' describes the phenomenon of observing a process involving particles (say a generic inhabitant $X$ of the very early universe decaying through some intermediate particles into protons), then observing the same process with all particles replaced by their antiparticles ( $\overline X\rightarrow \dots \rightarrow \overline p$), and finding that the particle process differs from the antiparticle process, for example in the decay rate: ${\Gamma(X\rightarrow \dots \rightarrow p)} \neq {\Gamma(\overline X\rightarrow \dots \rightarrow \overline p)}$. Recall that we are trying to make a particle excess out of initially equal abundances of particles and antiparticles ($X$ and $\overline X$); to accomplish this, we need a higher decay rate to particles than to antiparticles -- and thus $C\!P$ violation.

Departure from thermal equilibrium

As long as the universe is in thermal equilibrium, statistical mechanics will take care of keeping particle and antiparticle abundances equal. This is so because the only intrinsic property of the particles on which the equilibrium distributions depend is the particle mass. We have no experimental evidence to believe that particle and antiparticle masses differ, and compelling theoretical reasons to believe particle and antiparticle masses are exactly the same. To make particles more abundant than antiparticles, then a departure from thermal equilibrium is required.

Electroweak baryogenesis

The Standard Model of particle physics contains all the ingredients necessary to satisfy the Sakharov conditions. $C\!P$ violation is described by the Kobayashi-Maskawa mechanism [7]. $B$ violation is implemented in ``sphaleron'' interactions. These interactions are in some ways like quantum tunneling. The vacuum has a degenerate ground state, but the ground states are separated by an energy barrier. (See the sketch in Fig. 5.) In making the transition from one ground state to the other, $B$ and the lepton number $L$ are violated. At low temperature these transitions are rare because of the height of the barrier; at higher temperature they can occur much more frequently and lead to large $B$ and $L$ violation. The sphaleron mechanism violates $B$ and $L$ but conserves $B-L$; this will be important in a few sections when we discuss leptogenesis. Finally, a departure from equilibrium may occur when the electroweak symmetry is broken; whether this is the case depends on the mass of Higgs boson.

The current limit on the Higgs mass ($m_H > 114$ GeV) almost rules out the electroweak phase transition as a source of disequilibrium. The large mass of the Higgs combined with the smallness of the observed $C\!P$ violation almost entirely excludes the parameter space in which the standard model can account for the observed baryon asymmetry. Supersymmetric extensions to the standard model expand the parameter space; we will know a great deal more about the feasibility of electroweak baryogenesis once supersymmetry is explored experimentally at the next generation of colliders.

Figure 5: The sphaleron process takes the vacuum from one ground state to another. In the process $B$ and $L$ are violated (but $B-L$ is conserved). The process involves tunneling through a barrier; it is a rare process at zero temperature, but it can be efficient at high temperature.

Planck-scale baryogenesis

At the Planck scale we expect quantum gravity to become the dominant interaction. In quantum-gravitational interactions, we should not expect any quantum numbers to be conserved. An intuitive way to see this is to note that black holes are fully described by their mass, their angular momentum and their entropy; quantum-gravitational interactions involving the exchange of virtual black holes therefore have no knowledge of the interacting particles' other quantum numbers and can violate all of them.

If quantum gravity is the mechanism for baryogenesis, then we are in an unfortunate position; the relevant energy scale is $10^{19}$ GeV, which will remain inaccessible to colliders for the foreseeable future. We'll be left with a mechanism untestable by experiment. We can draw comfort from the following argument. The Planck scale is in all likelihood higher than the energy scale at the end of inflation; whatever baryon excess was generated by quantum gravity is washed out by inflation; and so the present-day baryon excess is probably not generated by quantum gravity. That clears the way for a more testable mechanism.

GUT-scale baryogenesis

The strong, weak and electromagnetic couplings, when extrapolated from the energies that are currently experimentally accessible to us, are approximately equal to each other at $\sim 10^{16}$ GeV. This observation has motivated theorists to propose that the strong and electroweak interactions ``unify'' at that energy. Theories that accomplish this unification are called ``grand unified theories'' (GUT).

These theories involve heavy bosons ( $m \sim 10^{16}$ GeV) that couple quarks to leptons. $B$ violation is in effect built into GUTs from the start. $CP$ violation can come from KM mechanism as in the standard model or from the newly introduced couplings to the heavy bosons. Thus, it is possible that baryogenesis occurred at the GUT energy scale.

GUT-scale baryogenesis poses a similar problem to Planck-scale baryogenesis. It occurs at energies so high that it eludes testing in terrestrial experiments. Once again we can take heart in the fact that inflationary scenarios disfavor this mechanism. If the reheating of the universe at the end of inflation exceeds a certain temperature, more WIMPs are produced than is consistent with the observed $\Omega_m$. In many circles the reheating temperature limit is believed to lie below the GUT scale, ruling out GUT baryogenesis after the inflationary era.

Leptogenesis

Leptogenesis [8] is currently the favored mechanism for baryogenesis. In this mechanism the universe first acquires a lepton excess, which is then converted into a baryon excess by a process that violates $B$ and $L$ but conserves $B-L$ -- for example the standard-model sphaleron mechanism.

The initial lepton excess that is required in this mechanism can come from, for example, heavy Majorana neutrinos ($N$). A Majorana neutrino is its own antiparticle. If the Majorana neutrino decays, for example, to a Higgs boson and a light lepton, $N\rightarrow \dots \rightarrow \ell + \overline \phi$, then the $C\!P$-conjugate decay is $N\rightarrow \dots \rightarrow \overline \ell + \phi$. If $C\!P$ is violated, then the decay rates of the $N$ into $\ell$ and $\overline\ell$ can differ, and the universe can end up containing more leptons than antileptons:

$$\Gamma(N\rightarrow \dots \rightarrow \ell + \overline \phi) \neq \Gamma(N\rightarrow \dots \rightarrow \overline \ell + \phi).$$

The reason the leptogenesis mechanism is popular is that the parameter space in which it is viable has not yet been constrained almost to death, as is the case for standard-model electroweak baryogenesis. At the same time, a major test of its viability is not too far in the future: within the decade, experiments should tell us the magnitude of $C\!P$ violation in the neutrino sector.

Affleck-Dine baryogenesis

The Affleck-Dine scenario for baryogenesis notes that in supersymmetric theories, where each of the ordinary fermion fields from standard-model physics has a scalar partner, the early universe contained baryon- and lepton-number-carrying scalar fields. Through interactions with the inflaton field $C\!P$-violating and $B$-violating effects can be introduced. As the scalar particles decay to fermions, the net baryon number the scalars carry can be converted into an ordinary baryon excess [9]. ([9] is a recent and very thorough review not only of Affleck-Dine baryogenesis but of baryogenesis in general.)

The Affleck-Dine mechanism is also a mechanism for dark-matter creation. Fluctuations in the scalar quark fields (``Q-balls'') are a dark-matter candidate if they are stable. If they are unstable, they can still decay into dark matter. If the Affleck-Dine mechanism is indeed played out in nature, then its dual role of producing baryons and producing dark matter opens up the possibility of explaining the ratio between $\Omega_m$ and $\Omega_{_B}$ from first principles.