Matter-Antimatter Asymmetry and Open Questions

The observable universe contains matter and almost no antimatter. If the two had been created in exactly equal amounts, they would have annihilated completely, leaving a universe of radiation with no galaxies, stars, or observers. That the matter survives means a small asymmetry was present after annihilation: for every billion antibaryons there were a billion-and-one baryons, and the leftover one baryon in $10^9$ is everything now visible. Explaining that number from an initially symmetric universe requires dynamics that distinguish matter from antimatter, and the Standard Model, though it contains the necessary ingredients, produces far too little. This closing lesson states the requirements, measures the Standard Model shortfall, and surveys the open questions of the field.

The measured asymmetry

The baryon asymmetry is quantified by the ratio of the net baryon number to the photon number,

measured two independent ways that agree: from the primordial abundances of the light elements produced in big-bang nucleosynthesis, and from the acoustic-peak heights in the cosmic microwave background. The absence of antimatter is separately established — no diffuse gamma-ray glow from matter-antimatter annihilation at the boundaries between regions is seen, so the universe is matter everywhere, not a patchwork.

The Sakharov conditions

Sakharov showed that any theory generating a baryon asymmetry dynamically from a symmetric start must satisfy three conditions simultaneously.¹

• Baryon-number violation. The net baryon number must change, since it begins at zero and ends nonzero. No process that conserves $B$ can produce an excess.
• C and CP violation. If C (charge conjugation) were exact, the rate of any baryon-producing process would equal the rate of its charge-conjugate antibaryon-producing process, and no net baryon number would build up. CP violation is needed in addition, because a combination of C and P symmetry would otherwise still equalize the rates for left- and right-handed configurations.
• Departure from thermal equilibrium. In thermal equilibrium the CPT theorem guarantees equal particle and antiparticle masses, so the number densities are equal and any asymmetry generated by a reaction is undone by its inverse. The asymmetry must be produced while the universe is expanding faster than the reactions can equilibrate.

The Standard Model has all three

In principle, the Standard Model already contains each ingredient.

• Baryon-number violation occurs through nonperturbative electroweak processes. The baryon and lepton currents are anomalous, and field configurations called sphalerons change $B$ and $L$ by equal amounts (conserving $B-L$) at a rate that is unsuppressed at temperatures above the electroweak scale.
• C and CP violation are present: the weak interaction violates C maximally, and the CKM matrix carries a single CP-violating phase, observed in kaon and B-meson decays.
• Departure from equilibrium could come from the electroweak phase transition as the universe cools through the Higgs transition, if that transition were strongly first-order.

The mechanism, electroweak baryogenesis, is therefore possible in outline within the Standard Model alone. It fails quantitatively on two counts.

Why the Standard Model falls short

The CP violation available in the CKM matrix is far too small. Its strength is set by the Jarlskog invariant $J\approx 3\times 10^{-5}$, and any CP-violating effect must be proportional to $J$ multiplied by the quark-mass differences that make the three generations distinguishable, divided by the relevant temperature scale. The resulting dimensionless asymmetry is of order

ten orders of magnitude below the observed $\eta \sim 10^{-10}$. The mass factors, which suppress the effect because the light-quark masses are tiny compared to the electroweak temperature, are what kill it.

The second failure is the phase transition itself. For the electroweak transition to be strongly first-order — proceeding by bubble nucleation that drives the plasma out of equilibrium — the Higgs boson would need to be light, below about $70$ GeV. The measured Higgs mass of $125$ GeV makes the transition a smooth crossover instead, with no departure from equilibrium. The Standard Model thus supplies the ingredients but not the magnitude.

Baryogenesis beyond the Standard Model

Two classes of extension supply the missing asymmetry.

• Electroweak baryogenesis with new physics. Adding scalars (as in supersymmetric or two-Higgs models) can make the electroweak transition strongly first-order and provide new CP-violating phases beyond the CKM one, generating the asymmetry at the electroweak bubble walls. This route is directly testable, since it requires new particles near the electroweak scale and new sources of CP violation visible in electric-dipole-moment searches.
• Leptogenesis. Heavy right-handed Majorana neutrinos, the same states that give the light neutrinos their mass through the seesaw mechanism, decay out of equilibrium in the early universe. Their decays violate lepton number and CP, generating a lepton asymmetry. Sphaleron processes, which conserve $B-L$ but violate $B+L$, then partially convert that lepton asymmetry into a baryon asymmetry. Leptogenesis links the baryon asymmetry to neutrino masses and to CP violation in the PMNS matrix, and is the leading scenario precisely because the seesaw is independently motivated.

Both routes require physics beyond the Standard Model — new CP phases, new scales, or both — so the matter-antimatter asymmetry, like the neutrino masses and the dark matter, is direct evidence that the model is incomplete.

Open questions

The Standard Model is a complete and predictive theory of the known particles, yet it leaves a definite list of facts unexplained. The confirmed gaps, each demanding new physics, are the following.

• Neutrino masses. Nonzero, unlike the original model, with a mixing pattern (PMNS) unrelated to the quark mixing and an unknown Dirac-versus-Majorana nature.
• Dark matter. A stable neutral particle of unknown identity, five times the baryon density.
• The baryon asymmetry. Requiring CP violation beyond the CKM phase.
• Dark energy. The accelerating expansion, parametrized but not explained.
• Gravity. Absent from the gauge structure entirely, and not quantized within the framework.

The structural puzzles, which the model describes but does not derive, add to the list: the three generations and their mass hierarchy, the pattern of mixing angles, the hierarchy problem of the Higgs mass, the origin of charge quantization (grand unification offers a partial answer), and the roughly twenty free parameters the model takes as input.

Future experiments

The programs aimed at these questions span energy and precision frontiers. Higher energies would be reached by a next-generation hadron collider beyond the LHC, probing the multi-TeV scale where naturalness and WIMP dark matter live. Precision electroweak and Higgs measurements would come from a proposed $e^{+}{e}^{-}$ Higgs factory, which would measure the Higgs couplings and self-coupling and so test the shape of the potential responsible for the electroweak phase transition. Dedicated neutrino-oscillation experiments would fix the mass ordering and search for CP violation in the lepton sector, testing leptogenesis. Underground detectors extend the reach for proton decay and neutrinoless double-beta decay, and ever-larger direct-detection experiments continue to close in on the WIMP. No single machine addresses all of the open questions, so the field advances on several fronts at once.

Summary

The universe holds about one extra baryon per billion photons, $\eta \approx 6\times 10^{-10}$, and no antimatter regions. Sakharov's three conditions — baryon-number violation, C and CP violation, and departure from equilibrium — are each present in the Standard Model through sphalerons, the CKM phase, and the electroweak transition, but the CKM CP violation is smaller than required by some ten orders of magnitude and the $125$ GeV Higgs makes the transition a crossover rather than first-order. Baryogenesis therefore needs new physics, with leptogenesis through heavy Majorana neutrinos the leading route, tying the asymmetry to neutrino mass. The asymmetry joins neutrino masses, dark matter, dark energy, and gravity as the confirmed evidence that the Standard Model is an effective description awaiting a deeper theory.²³⁴