Six Parts in Ten Billion: Why the Matter–Antimatter Puzzle Remains Unsolved — Epoche B2
The problem: a suspiciously small number Every structure we can see — stars, galaxies, our own bodies — is made of matter, not antimatter. Antimatter exists: every particle has a partner of identical mass and opposite charge, and antiprotons and positrons are made routinely in accelerators. But when a particle meets its antiparticle the pair annihilates into photons, so a Universe containing appreciable amounts of both would glow with the gamma rays of the boundary regions, and no such glow is seen. The imbalance must therefore be nearly total. The imbalance is measured by the baryon-to-photon ratio. A baryon is a particle made of three quarks — protons and neutrons are the ones that survive — and baryon number $B$ counts baryons minus antibaryons. Writing $n_B$, $n_{\bar B}$ and $n_\gamma$ for the number densities of baryons, antibaryons and photons, $$\eta \equiv \frac{n_B - n_{\bar B}}{n_\gamma} \approx 6 \times 10^{-10}.$$ Two entirely independent measurements agree on this figure, which is why it is trusted. The first comes from the abundances of the light elements forged in the first few minutes: the amount of deuterium (heavy hydrogen) left over is a steep function of how densely packed the nucleons were, so measuring deuterium in ancient, unprocessed gas fixes $\eta$. The second comes from the cosmic microwave background, the relic radiation released when the Universe first became transparent: baryons weigh down the oscillating photon–baryon fluid of that era, and this asymmetric loading makes alternate peaks in the observed pattern of temperature fluctuations unequal in height. The Planck satellite's measurement of the baryon density, $\Omega_b h^2 \approx 0.0224$, translates into the same $\eta \approx 6\times10^{-10}$ obtained from deuterium. The number tells a specific story about the early Universe. When the cosmos was hot enough for quarks and antiquarks to be freely created, both were about as abundant as photons. As it cooled, essentially all of them annihilated in pairs, and their annihilation products are the photons we count today. So $\eta \approx 6\times10^{-10}$ says that for roughly every billion antiquarks there were about a billion and six quarks; the billion pairs became light, and the six left over became everything material. The question is where that surplus of six came from. A popular explanation says the Big Bang simply started with slightly more matter than antimatter. This sounds like an answer, but it is only a restatement of the question — it names the surplus as a brute initial condition rather than explaining it. Worse, it is quantitatively untenable if the early Universe passed through inflation, a brief phase of accelerated expansion invoked to explain the observed flatness and uniformity of space. Inflation stretches lengths by a factor of at least $e^{60}$, so any number density, which scales as one over volume, is reduced by $e^{180} \sim 10^{78}$. An asymmetry present beforehand would be diluted not merely to something small but to far less than one baryon in the entire observable Universe. The asymmetry must therefore have been generated dynamically, after inflation ended. The problem is to explain how. The conditions any solution must meet In 1967 Andrei Sakharov showed that any physical process creating a net baryon number from a symmetric start must satisfy three conditions. They are not a model but a filter: any proposed mechanism failing one of them is dead without further calculation. Baryon number violation: some interaction must change $B$. This is close to a tautology, but a necessary one — if every interaction conserves $B$, then $B$ is a constant of the motion and $B = 0$ stays $B = 0$ forever, whatever else happens. C and CP violation: charge conjugation ($C$) is the operation of replacing every particle by its antiparticle; parity ($P$) is reflection in a mirror, which reverses spatial directions; $CP$ is the two applied together. If $C$ were an exact symmetry, then for every process producing baryons at some rate there would be a mirror-image process producing antibaryons at exactly the same rate, and the two would cancel. $CP$ must fail as well, because the interactions that violate $B$ act differently on left- and right-handed particles, so a $C$-violating rate difference can still be cancelled by summing over the two handednesses unless $CP$ is violated too. Departure from thermal equilibrium: the CPT theorem — the result that any local quantum field theory obeying special relativity is invariant under $C$, $P$ and time reversal $T$ applied together — forces particles and antiparticles to have exactly equal masses. In thermal equilibrium the abundance of a species depends only on its mass and the temperature, so equal masses mean equal abundances: any asymmetry produced would immediately be washed out by the reverse reactions. Something must therefore happen faster than the plasma can re-equilibrate. Testing the Standard Model against the conditions Remarkably, the Standard Model of particle physics contains all three ingredients in principle. For the first, Kuzmin, Rubakov and Shaposhnikov (1985) showed that the weak interaction violates baryon number at high temperature. The vacuum of the weak force has infinitely many equivalent configurations separated by energy barriers, and passing from one to the next changes $B$. At everyday temperatures the barrier — about $9$ TeV, in the form of the unstable field configuration called the sphaleron — makes this unobservably rare, but above roughly $100$ GeV, the temperature scale at which the weak force's symmetry is restored, thermal fluctuations carry the field over the barrier freely. Each crossing changes $B$ by three units and lepton number $L$ by three: one unit of each per generation of matter, and there are exactly three generations. The combination $B - L$ is left untouched, while $B + L$ is destroyed — a fact which will matter shortly. For the second, the quark mixing matrix