---
title: Matter-Antimatter Asymmetry and Open Questions
module: Beyond the Standard Model
moduleNumber: 12
lessonNumber: 6
order: 1206
summary: >
  The universe is made of matter, with about one extra baryon for every billion
  photons and no antimatter regions. Sakharov identified the three conditions any
  dynamical explanation must meet: baryon-number violation, C and CP violation, and
  a departure from thermal equilibrium. The Standard Model contains all three in
  principle, but its CP violation falls short by some ten orders of magnitude, so
  baryogenesis requires new physics — leptogenesis being the leading route. A
  closing survey collects the open questions and the experiments aimed at them.
topics: [Beyond the Standard Model]
draft: false
sources:
  - book: Thomson
    ref: "Ch. 14 & 18 — CP violation and physics beyond the Standard Model"
  - book: Griffiths
    ref: "Ch. 12 — Afterword (open questions)"
  - book: Perkins
    ref: "Ch. 12 — Physics beyond the Standard Model (baryogenesis)"
---

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,

$$
\eta = \frac{n_B - n_{\bar B}}{n_\gamma} \approx 6\times10^{-10},
$$

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.

$$
% caption: The same asymmetry read as the number of photons per surviving net
% baryon, so the scale uses positive powers of ten. There are about two billion
% photons for every baryon left after annihilation.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[black, thick] (0,0) -- (9.0,0);
  \foreach \x in {0,1.5,3.0,4.5,6.0,7.5,9.0} \draw[black] (\x,0.12) -- (\x,-0.12);
  \node[black, below, font=\scriptsize] at (0,-0.2) {$10^{0}$};
  \node[black, below, font=\scriptsize] at (3.0,-0.2) {$10^{4}$};
  \node[black, below, font=\scriptsize] at (6.0,-0.2) {$10^{8}$};
  \node[black, below, font=\scriptsize] at (9.0,-0.2) {$10^{12}$};
  \node[black, below, font=\scriptsize] at (7.6,-0.75) {photons per net baryon};
  % marker near 1.6e9 photons per baryon: between 10^8 (x=6) and 10^12 (x=9): ~x=6.9
  \fill[acc] (6.9,0) circle (2.8pt);
  \node[acc, above, font=\scriptsize, align=center] at (6.9,0.5) {about two billion\\per baryon};
  \node[black, above, font=\scriptsize] at (1.6,0.5) {equal amounts leave\\no net baryons};
\end{tikzpicture}
$$

## The Sakharov conditions

Sakharov showed that any theory generating a baryon asymmetry dynamically from a
symmetric start must satisfy three conditions simultaneously.[^sakharov]

- **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.

> **Theorem (Sakharov conditions).** A dynamical baryon asymmetry can arise from a
> baryon-symmetric initial state only if the interactions violate baryon number,
> violate both C and CP, and act out of thermal equilibrium. All three are
> necessary; the failure of any one keeps the net baryon number at zero.

$$
% caption: The three Sakharov conditions as a checklist. A baryogenesis mechanism
% must satisfy all three at once; any single failure returns the net baryon number
% to zero.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0,
  row/.style={draw, minimum width=64mm, minimum height=8mm, font=\scriptsize, align=left}]
  \definecolor{acc}{HTML}{4A6FA5}
  \node[row] (a) at (0,1.8) {1. baryon-number violation};
  \node[row] (b) at (0,0.9) {2. C and CP violation};
  \node[row] (c) at (0,0.0) {3. departure from equilibrium};
  \node[right, font=\scriptsize, align=left] at (3.6,0.9) {all three\\required};
\end{tikzpicture}
$$

## 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](/particle-physics/weak-interaction/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** $J \approx 3\times10^{-5}$, 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

$$
\delta_{CP} \sim \frac{J\,\prod_{i<j}(m_i^2 - m_j^2)}{T_{\text{EW}}^{12}} \sim 10^{-20},
$$

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.

$$
% caption: The CP violation available in the Standard Model against the amount the
% observed baryon asymmetry requires. The CKM phase falls short by roughly ten
% orders of magnitude, so baryogenesis needs a new source.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0]
  \definecolor{acc}{HTML}{4A6FA5}
  \draw[->] (0,0) -- (0,4.2) node[above, font=\scriptsize, align=left] {log of CP\\strength};
  % required bar (tall)
  \draw[fill=black!12] (0.8,0) rectangle (2.1,3.6);
  \node[below, font=\scriptsize, align=center] at (1.45,0) {required};
  \node[above, font=\scriptsize, align=center] at (1.45,3.6) {ten billionth};
  % SM bar (short)
  \draw[fill=black!12] (3.5,0) rectangle (4.8,0.9);
  \node[below, font=\scriptsize, align=center] at (4.15,0) {CKM phase};
  \node[above, font=\scriptsize, align=center] at (4.15,0.9) {far smaller};
  % shortfall bracket
  \draw[acc, <->, thick] (5.6,0.9) -- (5.6,3.6);
  \node[acc, right, font=\scriptsize, align=left] at (5.7,2.25) {shortfall\\$10$ orders};
\end{tikzpicture}
$$

## 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](/particle-physics/neutrinos/neutrino-mass-pmns),
  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](/particle-physics/neutrinos/neutrino-mass-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](/particle-physics/beyond-standard-model/hierarchy-problem-naturalness)
of the Higgs mass, the origin of charge quantization
([grand unification](/particle-physics/beyond-standard-model/grand-unified-theories)
offers a partial answer), and the roughly twenty free parameters the model takes as
input.

$$
% caption: The confirmed empirical gaps in the Standard Model and the experimental
% programs aimed at each. Every entry demands physics the framework does not
% contain.
\begin{tikzpicture}[>=stealth, font=\footnotesize, scale=1.0,
  q/.style={draw, minimum width=34mm, minimum height=7mm, font=\scriptsize, align=center},
  e/.style={draw, minimum width=42mm, minimum height=7mm, font=\scriptsize, align=center}]
  \definecolor{acc}{HTML}{4A6FA5}
  \node[q] (n) at (0,2.4) {neutrino mass};
  \node[q] (d) at (0,1.4) {dark matter};
  \node[q] (b) at (0,0.4) {baryon asymmetry};
  \node[e] (ne) at (5.2,2.4) {oscillation, double-beta};
  \node[e] (de) at (5.2,1.4) {direct, indirect, collider};
  \node[e] (be) at (5.2,0.4) {electric-dipole, colliders};
  \draw[->] (n) -- (ne);
  \draw[->] (d) -- (de);
  \draw[->] (b) -- (be);
\end{tikzpicture}
$$

## 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,
$\eta \approx 6\times10^{-10}$, 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.[^th-baryo][^gr-open][^pk-baryo]

[^sakharov]: The three necessary conditions for dynamical baryogenesis are due to A. D. Sakharov, "Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe" (1967).

[^th-baryo]: Thomson, Ch. 14 develops the CKM CP violation and the Jarlskog invariant; Ch. 18 covers the baryon asymmetry, the Sakharov conditions, the electroweak-baryogenesis shortfall, and leptogenesis.

[^gr-open]: Griffiths, Ch. 12 (Afterword), lists the open problems of the Standard Model — the free parameters, the generation structure, the hierarchy problem, and the absence of gravity.

[^pk-baryo]: Perkins, Ch. 12, treats baryogenesis, sphalerons, and the leptogenesis scenario; the baryon-to-photon ratio $\eta \approx 6\times10^{-10}$ and the cosmological measurements are compiled in the Particle Data Group reviews, [pdg.lbl.gov](https://pdg.lbl.gov).