Matter-antimatter asymmetry

Every atom you have ever touched is made of matter — electrons, protons, neutrons — never of the antiparticles Dirac's equation says are equally allowed. The same equations that build a proton build an antiproton with identical mass and opposite charge, and the early Universe made both in equal numbers out of radiation through reactions like $\gamma+\gamma \rightleftharpoons p+\bar p$ . Had that symmetry survived, the cooling Universe would have annihilated back into photons, leaving a residual nucleon abundance $\sim10^{-18}$ per photon — a cosmos with almost no matter. Instead we measure $n_B/n_\gamma \approx 6\times10^{-10}$ : a billion-and-one quarks for every billion antiquarks, the odd one out surviving to become everything we see. This article is about that "extra one in a billion" — where it came from, what laws it demands, and why the Standard Model, which has all the right ingredients, still falls ten orders of magnitude short. The logic was crystallised by Andrei Sakharov in 1967 into three necessary conditions: baryon number must be violated, both C and CP must be violated, and the reactions must fall out of thermal equilibrium. The Standard Model ticks all three boxes qualitatively — sphalerons violate baryon number, the CKM phase violates CP, the expanding Universe departs from equilibrium — but its CP violation is far too feeble and its electroweak transition too smooth. The asymmetry is therefore not a curiosity but one of the sharpest pieces of evidence that the Standard Model is incomplete.

Key takeaways

Our local Universe is built entirely from matter; searches for annihilation photons at any matter–antimatter boundary rule out large antimatter regions.
The asymmetry is one number, $\eta = n_B/n_\gamma \approx 6.1\times10^{-10}$ (equivalently $Y_B=(n_B-\bar n_B)/s\approx 8.7\times10^{-11}$ ), fixed independently by the CMB and Big Bang nucleosynthesis.
A symmetric Universe would have annihilated down to $n_B/n_\gamma\sim10^{-18}$ , so a primordial excess of about one quark per billion is required.
Sakharov's three conditions — baryon-number violation, C and CP violation, and departure from thermal equilibrium — are jointly necessary to generate that excess dynamically.
The Standard Model has all three but fails: its CP violation ( $J\approx3\times10^{-5}$ ) gives an effect $\sim10^{-20}$ , and the $125\ \mathrm{GeV}$ Higgs makes the electroweak transition a crossover, not first-order.
Key idea: the survival of matter is a measured number, $\eta\approx6\times10^{-10}$ , that no symmetric physics can produce; it demands baryon-number violation, CP violation, and out-of-equilibrium dynamics — and the Standard Model's shortfall points to new physics such as leptogenesis.

The core insight

If matter and antimatter were exactly symmetric the early Universe would have annihilated into pure radiation; the survival of matter demands a tiny intrinsic asymmetry — captured by Sakharov's three conditions — that tipped the balance by about one part in a billion during cosmic cooling, more than the Standard Model can supply.

Where this lives today

The asymmetry is now a precision number attacked from several directions. Planck pins $\eta$ from the acoustic peaks of the cosmic microwave background, and Big Bang nucleosynthesis fixes the same number from primordial deuterium in distant gas clouds — the two agree at the few-percent level, an extraordinary check on the hot Big Bang. On the particle side, LHCb and Belle II map CP violation across the $B$ - and $D$ -meson systems (the CKM phase fits the mesons — and is still too small for cosmology), while AMS-02 scans cosmic rays for the primary antinuclei a nearby antimatter domain would produce; none are confirmed. The most active frontier is the neutrino link: if leptogenesis is correct, the CP violation that made the Universe is the same physics that makes neutrinos oscillate, so T2K, NOvA and the future DUNE and Hyper-Kamiokande are, in a real sense, measuring an input to baryogenesis when they hunt the leptonic phase $\delta_{CP}$ . In parallel, neutrinoless double-beta-decay searches (KamLAND-Zen, LEGEND, nEXO) test the Majorana property leptogenesis needs, while neutron electric-dipole-moment experiments push for the extra CP violation the Standard Model cannot supply.

The physical picture

Run the cosmic clock backwards and the Universe grows hotter until, above roughly $1\ \mathrm{GeV}$ , the photon bath pair-creates quarks and antiquarks as fast as they annihilate. Matter and antimatter are then in equilibrium and almost exactly as numerous as the photons — but not quite. Buried in the plasma is a minuscule surplus of quarks. As the Universe cools the pair-creating reaction shuts off, the antiquarks annihilate against quark partners into photons, and only the surplus is left with nothing to annihilate against. That leftover is the matter of every star and galaxy; the ashes are the $10^{9}$ photons per baryon filling the cosmic microwave background. The first figure makes the bookkeeping concrete.

Figure

Cosmic bookkeeping of the asymmetry: at T ≫ 1 GeV quarks and antiquarks are as abundant as photons, but a primordial excess of about one quark per billion antiquarks survives mutual annihilation, leaving today η = n_B/n_γ = 6.1×10⁻¹⁰, i.e. roughly 1.6×10⁹ relic photons for every surviving baryon

Could the surplus instead be generated dynamically from a perfectly symmetric start? Sakharov's answer is yes, but only if three conditions hold together. Baryon number must be violated, or the total can never leave zero. C and CP must both be violated, or every matter-producing reaction is exactly mirrored by an antimatter one and the surplus cancels. And the reactions must fall out of equilibrium, because CPT forces particle and antiparticle to share a mass, pinning their equilibrium abundances equal however much CP is violated. The second figure grades the Standard Model — it has all three, yet fails two by a wide margin.

Figure

Sakharov's three conditions for dynamically generating a baryon asymmetry, and the Standard Model verdict against each: baryon-number violation is provided by electroweak sphalerons, but the CKM CP violation is about ten orders of magnitude too weak and the 125 GeV Higgs makes the electroweak transition a crossover rather than a first-order one

The core equations

The asymmetry is a single measured number, cleanest as baryons counted against the photons they bathe in. Because the photon density is huge and precisely fixed by the CMB temperature, this ratio is the standard currency.

\eta \equiv \frac{n_B-\bar n_B}{n_\gamma}\Bigg|_{\text{today}} \approx \frac{n_B}{n_\gamma} = (6.1\pm0.1)\times10^{-10} \qquad (1)

where: $n_B,\bar n_B$ — baryon and antibaryon densities ( $\bar n_B\approx0$ today); $n_\gamma\approx411\ \mathrm{cm^{-3}}$ — CMB photon density; $\eta$ — baryon-to-photon ratio. Reading it: each surviving baryon sits in about $\eta^{-1}\approx1.6\times10^{9}$ photons — the annihilation ashes. Because $n_\gamma$ changes with expansion while comoving baryon number does not, a redshift-invariant version divides by the entropy density $s$ . This $Y_B$ is what theorists compute, as it is conserved by expansion.

Y_B \equiv \frac{n_B-\bar n_B}{s},\qquad s=\frac{2\pi^2}{45}\,g_{*s}\,T^3,\qquad Y_B=\frac{\eta}{7.04}\approx 8.7\times10^{-11} \qquad (2)

where: $s$ — entropy density; $g_{*s}$ — entropy degrees of freedom; $7.04=s/n_\gamma$ today. Reading it: $Y_B$ and $\eta$ carry the same physics; $Y_B$ is preferred because it freezes at baryogenesis. Now the motivation. Had matter and antimatter been perfectly symmetric, nucleons and antinucleons would annihilate until their rate dropped below the expansion rate; that freeze-out leaves a relic far below observation.

\frac{n_B}{n_\gamma}\bigg|_{\text{symmetric}} \sim 10^{-18} \;\;\ll\;\; \frac{n_B}{n_\gamma}\bigg|_{\text{observed}} = 6\times10^{-10} \qquad (3)

where: the left side is the symmetric freeze-out relic (Derivation B); the right is measured. Reading it: symmetry undershoots by eight orders, so a primordial excess of $\sim10^{-9}$ per photon must have pre-existed or formed. Any dynamical mechanism shows its CP violation as a decay asymmetry: a heavy $X$ and its antiparticle $\bar X$ decay to baryons at slightly different rates. The net asymmetry is that CP parameter, diluted by the species sharing the entropy.

\varepsilon=\frac{\Gamma(X\to B)-\Gamma(\bar X\to\bar B)}{\Gamma(X\to \text{all})+\Gamma(\bar X\to\text{all})},\qquad Y_B\sim \frac{\varepsilon\,\kappa}{g_*} \qquad (4)

where: $\varepsilon$ — CP asymmetry per decay (needs C and CP violation via tree–loop interference); $\kappa\lesssim1$ — washout/efficiency (the out-of-equilibrium condition); $g_*\sim100$ — relativistic degrees of freedom. Reading it: $Y_B\sim10^{-10}$ needs $\varepsilon\sim10^{-6}$ — the target every model must hit. In the Standard Model CP violation is quantified by the rephasing-invariant Jarlskog determinant, and its effect for baryogenesis is further suppressed by the small quark masses relative to the electroweak scale.

J=\mathrm{Im}\!\left(V_{us}V_{cb}V^{*}_{ub}V^{*}_{cs}\right)\approx3.1\times10^{-5},\qquad \delta_{CP}^{\text{SM}}\sim \frac{J\,\prod(m_i^2-m_j^2)}{T_c^{12}}\sim10^{-20} \qquad (5)

where: $V_{ij}$ — CKM elements; $J$ — Jarlskog invariant; the product runs over up- and down-type quark mass-squared differences; $T_c\sim100\ \mathrm{GeV}$ . Reading it: even with $J\ne0$ , mass suppression makes the SM effect $\sim10^{-20}$ , ten orders below $\eta$ . Finally, whatever asymmetry forms at high temperature is reprocessed by electroweak sphalerons, which violate $B+L$ but conserve $B-L$ , locking the baryon number to that combination.

B=\frac{28}{79}\,(B-L)\approx0.35\,(B-L) \qquad (6)

where: $28/79$ follows from chemical equilibrium of all Standard-Model interactions with three generations and one Higgs doublet. Reading it: a mechanism making only $B$ with $B-L=0$ is erased; a surviving asymmetry needs $B-L\ne0$ — the crux of leptogenesis.

Derivation AWhy thermal equilibrium forbids a baryon asymmetry

The goal is to prove Sakharov's third condition from first principles: however strongly baryon number and CP are violated, a system in full thermal equilibrium cannot develop a net baryon number. The argument rests on CPT invariance — the one symmetry no local, Lorentz-invariant field theory can abandon — which forces particle and antiparticle to share a mass, and on the fact that a violated quantum number carries no conserved chemical potential. Together these pin baryon and antibaryon abundances exactly equal in equilibrium, so departure from equilibrium is mandatory, not optional.

Step 1. In equilibrium a species' number density depends only on its mass, temperature, and chemical potential: $n_i \propto \int d^3p\,[\exp((E_i-\mu_i)/T)\pm1]^{-1}$ , $E_i=\sqrt{p^2+m_i^2}$ . Why: equilibrium erases history — the only labels left are mass and the potentials of conserved charges.

Step 2. CPT invariance guarantees $m_B=m_{\bar B}$ exactly. Why: this is the loophole-free input — you may violate C, P, CP and T, but CPT holds and equates particle and antiparticle masses, so only a chemical-potential difference could split the two densities.

Step 3. If baryon number is violated (Sakharov's first condition), $B$ is not conserved, so its chemical potential vanishes, $\mu_B=\mu_{\bar B}=0$ . Why: a chemical potential is the price of a conserved charge — if reactions freely change $B$ , there is no price, and it is zero.

Step 4. With $m_B=m_{\bar B}$ and $\mu_B=\mu_{\bar B}=0$ the equilibrium densities coincide, $n_B=n_{\bar B}$ , so $n_B-\bar n_B=0$ regardless of how much CP is violated. Why: equilibrium plus CPT plus B-violation gives zero net baryon number, so any surviving asymmetry must form out of equilibrium — a heavy particle's decay whose rate lags expansion, or a first-order phase transition.

Go deeper · Derivation B · 1 minThe symmetric relic and the one-in-a-billion excess

Derivation BThe symmetric relic and the one-in-a-billion excess

The aim is to make quantitative the claim that a symmetric Universe would be almost empty of matter, and so to size the primordial excess. We follow nucleon–antinucleon annihilation through freeze-out, comparing the annihilation rate to the Hubble rate to read off the relic abundance. Contrasting it with the measured $\eta$ fixes the required excess at about one part in a billion — the single most important order-of-magnitude in the subject.

Step 1. At $T\gg m_N$ nucleons and antinucleons are relativistic and as abundant as photons. As $T$ drops below $m_N\approx940\ \mathrm{MeV}$ their abundance is Boltzmann-suppressed, $n_N/n_\gamma\sim(m_N/T)^{3/2}e^{-m_N/T}$ . Why: once it costs $m_N$ to make a nucleon, the bath makes exponentially fewer — the standard suppression of a massive species in a cooling plasma.

Step 2. Annihilation $N\bar N\to\pi\pi$ continues only while $n_N\langle\sigma v\rangle \gtrsim H$ . With $\sigma\sim m_\pi^{-2}$ and the radiation-era rate $H\sim T^2/M_{\text{Pl}}$ , this fails ("freeze-out") near $T\approx20\ \mathrm{MeV}$ . Why: once the gas is too dilute and the Universe too fast, survivors cannot find partners and their comoving number freezes.

Step 3. The frozen abundance is $n_N/n_\gamma=n_{\bar N}/n_\gamma\sim10^{-18}$ (careful treatments give $\sim10^{-20}$ ). Why: this is all the matter a symmetric Universe could hold — eight to ten orders below the observed $6\times10^{-10}$ , i.e. essentially nothing.

Step 4. To land on $\eta=6\times10^{-10}$ instead, there must have been at $T\gg m_N$ a fractional excess $(n_N-n_{\bar N})/(n_N+n_{\bar N})\approx\tfrac12\eta\approx3\times10^{-10}$ — one extra quark per three billion pairs. Why: the billions of pairs annihilate into the $\sim1.6\times10^{9}$ photons per baryon we count today, and only the pre-existing surplus survives — the "one in a billion" any mechanism must produce.

Go deeper · Derivation C · 1 minWhy the Standard Model's CP violation is far too small

Derivation CWhy the Standard Model's CP violation is far too small

The purpose is to show that although the Standard Model violates CP through the single complex phase of the CKM matrix, the effect available for electroweak baryogenesis is suppressed to about $10^{-20}$ — ten orders below the observed asymmetry. The key is that quark-sector CP violation is proportional to the Jarlskog invariant $J$ and switches off whenever any two same-charge quarks are degenerate, forcing in a steep product of small quark-mass ratios.

Step 1. Any quark-sector CP-violating observable is proportional to the rephasing-invariant Jarlskog determinant $J=\mathrm{Im}(V_{us}V_{cb}V^{*}_{ub}V^{*}_{cs})\approx3.1\times10^{-5}$ . Why: $J$ is the unique basis-independent measure of CKM CP violation — if $J=0$ the phase rotates away, so every effect carries at least one power of it.

Step 2. CP violation also vanishes if any two up-type or any two down-type quarks are degenerate, since that restores a family symmetry absorbing the phase — so the effect is proportional to $\prod_{i<j}(m_{u_i}^2-m_{u_j}^2)\prod_{i<j}(m_{d_i}^2-m_{d_j}^2)$ . Why: equal masses supply the rotation freedom that removes the phase, so the amplitude vanishes there, pulling in six mass-squared differences.

Step 3. Made dimensionless with the only available scale, $T_c\sim100\ \mathrm{GeV}$ , this gives $\delta_{CP}^{\text{SM}}\sim J\,\prod(m_i^2-m_j^2)/T_c^{12}\sim10^{-20}$ . Why: dividing a twelfth-power product of small quark masses by $T_c^{12}$ is catastrophic — factors like $(m_c^2-m_u^2)/T_c^2$ are each $\sim10^{-6}$ .

Step 4. Against the target $Y_B\sim10^{-10}$ the Standard Model falls short by $\sim10^{10}$ , and separately its electroweak transition is a crossover for the measured Higgs mass. Why: two of Sakharov's three conditions are met only in name — CP far too weak, out-of-equilibrium not at all — which is why baryogenesis is taken as evidence for new physics.

Limiting cases

Case	Result	Meaning
Exact matter–antimatter symmetry	$Y_B=0$ ; relic $n_B/n_\gamma\sim10^{-18}$	annihilation to radiation; a Universe with almost no matter
Any one Sakharov condition absent	$Y_B=0$	all three are jointly necessary; missing B-violation, CP, or out-of-equilibrium each forces zero
Full thermal equilibrium	$n_B=\bar n_B$	CPT pins particle and antiparticle abundances equal (Derivation A)
Standard Model only	$Y_B\lesssim10^{-20}$	CKM CP too small; electroweak crossover — fails by $\sim10^{10}$
Mechanism with $B-L=0$	$B\to0$ after sphalerons	e.g. simplest GUT baryogenesis; washed out by $B=\tfrac{28}{79}(B-L)$
Leptogenesis ( $B-L\ne0$ )	$Y_B=\tfrac{28}{79}Y_{B-L}\approx8.7\times10^{-11}$	heavy Majorana-neutrino decays; survives sphaleron reprocessing

Worked examples

1 · From the Planck density to the baryon-to-photon ratio

Planck measures the baryon density $\Omega_b h^2 = 0.02237$ ; the CMB temperature $T_0 = 2.725\ \mathrm{K}$ gives $n_\gamma = 411\ \mathrm{cm^{-3}}$ . Find $\eta$ , the photons per baryon, and $Y_B$ .

Step 1. Convert to a number density. With $\rho_c = 1.878\times10^{-29}\,h^2\ \mathrm{g\,cm^{-3}}$ , the baryon mass density $\rho_b = \Omega_b h^2\,(1.878\times10^{-29})\ \mathrm{g\,cm^{-3}}$ divided by the nucleon mass $m_N=1.67\times10^{-24}\ \mathrm{g}$ gives $n_b = 2.52\times10^{-7}\ \mathrm{cm^{-3}}$ .

Step 2. Ratio to photons: $\eta = n_b/n_\gamma = 2.52\times10^{-7}/411 = \mathbf{6.1\times10^{-10}}$ , i.e. $\eta^{-1} = \mathbf{1.6\times10^{9}}$ photons per baryon — the annihilation ashes.

Step 3. Redshift-invariant form with $s = 7.04\,n_\gamma$ : $Y_B = \eta/7.04 = \mathbf{8.7\times10^{-11}}$ . The single number is η = 6.1×10⁻¹⁰, i.e. Y_B = 8.7×10⁻¹¹, one baryon per 1.6 billion photons. Big Bang nucleosynthesis, from entirely different physics (primordial deuterium and helium), independently returns $\eta\approx6\times10^{-10}$ — a triumph of the hot Big Bang.

2 · Sphaleron conversion and the leptogenesis target

Leptogenesis generates a lepton asymmetry but no net baryon number, so $B=0$ , $L\ne0$ , giving $B-L\ne0$ . Sphalerons then act in equilibrium. What baryon asymmetry survives, and what CP asymmetry ε per heavy-neutrino decay does it require?

Step 1. Sphalerons conserve $B-L$ but drive $B+L$ to equilibrium, locking $B=\tfrac{28}{79}(B-L)$ (equation 6). A pure lepton asymmetry does not wash away — it is partly reprocessed into baryons because $B-L\ne0$ , which is why leptogenesis works where simplest GUT baryogenesis fails.

Step 2. To reach the observed $Y_B = 8.7\times10^{-11}$ , the primordial asymmetry must have been $Y_{B-L} = \tfrac{79}{28}\,Y_B = \mathbf{2.5\times10^{-10}}$ — a third ends up as baryons.

Step 3. Relate that to the per-decay CP asymmetry via $Y_{B-L}\sim \varepsilon\,\kappa/g_*$ (equation 4), with $g_*\approx106.75$ and efficiency $\kappa\sim10^{-2}$ : $\varepsilon \sim 2.5\times10^{-10}\times106.75/10^{-2} \approx \mathbf{3\times10^{-6}}$ . A CP asymmetry of order ε ∼ 10⁻⁶ per heavy-neutrino decay, reprocessed by sphalerons through B = (28/79)(B−L), reproduces the observed asymmetry — a target that arises naturally in seesaw models, where the Majorana masses that make neutrinos light provide the CP-violating decays.

Physics of the portrait

The matter-antimatter asymmetry is where cosmology, particle physics and thermodynamics meet — fused into one logical statement by a Soviet physicist better known for something else entirely.

Origins · 1 minAndrei Sakharov and how this was discovered

Andrei Sakharov

1921–1989 · baryogenesis and cosmological CP violation

Andrei Sakharov was the theoretical architect of the Soviet hydrogen bomb before becoming the Soviet Union's most prominent dissident and, in 1975, a Nobel Peace laureate. Between those two lives he wrote a three-page paper in 1967 that founded an entire field. The discovery of CP violation in neutral kaons by Cronin and Fitch (1964) was then widely regarded as a small technicality; Sakharov saw it as cosmic. He argued that matter's dominance need not be an arbitrary initial condition but could be generated dynamically from a symmetric start — provided three conditions held together: baryon number is not conserved, C and CP are violated, and the reactions depart from thermal equilibrium as the Universe expands. Each is now understood as logically necessary, the third following from CPT alone. The paper was almost entirely ignored for over a decade — baryon-number violation had no known mechanism until 't Hooft's 1976 electroweak anomaly and the grand unified theories that followed. When the pieces arrived, Sakharov's conditions became the organising principle of all baryogenesis: electroweak baryogenesis, GUT baryogenesis, and Fukugita–Yanagida leptogenesis (1986) all try to realise his three requirements with enough CP violation and departure from equilibrium — the two places the Standard Model falls short.

History

1928

— Dirac's relativistic equation predicts antimatter, requiring an antiparticle for every particle

1964

— Cronin and Fitch discover CP violation in the decays of neutral kaons

1967

— Sakharov formulates the three conditions for dynamically generating a baryon asymmetry

1973

— Kobayashi and Maskawa embed CP violation in a three-generation quark mixing matrix

1986

— Fukugita and Yanagida propose leptogenesis, tying the asymmetry to neutrino masses

Going further

Texts. Thomson, Modern Particle Physics, §14.1 (CP violation and the early Universe) · Griffiths, Introduction to Elementary Particles, 2nd ed., Ch. 4, 12 · Kolb & Turner, The Early Universe, Ch. 6 (baryogenesis, symmetric relic) · Peskin & Schroeder, §20.3 (anomalies, sphaleron B-violation) · Weinberg, Cosmology, §3.2 · Dine & Kusenko, Rev. Mod. Phys. 76, 1 (2004), "The origin of the baryon asymmetry". The key numerical anchors: $\eta=(6.1\pm0.1)\times10^{-10}$ from Planck 2018 ( $\Omega_b h^2=0.02237$ ), concordant with BBN; the Jarlskog invariant $J\approx3.1\times10^{-5}$ and CKM elements from the PDG; the $\sim10^{-20}$ SM CP estimate from Gavela et al. (1994) and Huet–Sather (1995); the sphaleron coefficient $B=\tfrac{28}{79}(B-L)$ from Harvey–Turner (1990). These satisfy the consistency checks: $\eta$ follows from $\Omega_b h^2$ and $n_\gamma=411\ \mathrm{cm^{-3}}$ ; $Y_B=\eta/7.04$ ; the symmetric relic is $\sim10^{-18}$ ; $Y_{B-L}=\tfrac{79}{28}Y_B$ ; and CPT gives $n_B=\bar n_B$ in equilibrium.

Prerequisites. Antiparticles · CP violation in kaons · The neutral kaon system. Leads to. CP violation in the Standard Model · Cosmological connections · Open questions.

Ask the tutor: Ask me to walk through why CPT invariance alone forces a departure from equilibrium, or to compare how electroweak baryogenesis and leptogenesis each try — and one fails — to meet Sakharov's three conditions.

Could the antimatter simply be somewhere we have not looked?

On any scale we can probe, no. If matter and antimatter regions coexisted, their shared boundaries would annihilate continuously and glow in $\sim100\ \mathrm{MeV}$ gamma rays; the observed diffuse gamma-ray background forbids any antimatter domain smaller than roughly the whole observable Universe. Cosmic rays agree — antiprotons match what ordinary collisions produce as secondaries, and no primary anti-helium has been confirmed. So the matter excess is not a local fluke that averages out globally; it is a genuine, Universe-wide asymmetry, which is why it needs a cosmological rather than an astronomical explanation.

If the Standard Model has all three Sakharov ingredients, why does it fail?

It fails on magnitude, not principle. Sphalerons do violate baryon number and the CKM phase does violate CP — but the CP effect for baryogenesis is throttled to about $10^{-20}$ , because it must vanish whenever any two same-charge quarks are degenerate, dragging in a twelfth power of small quark masses. That is ten orders below the observed $Y_B\sim10^{-10}$ . And the out-of-equilibrium condition needs a strongly first-order electroweak transition, but for the measured $125\ \mathrm{GeV}$ Higgs it is a smooth crossover — no sharp departure at all. Two of the three conditions are met only in name.

What exactly is a sphaleron, and why does it matter here?

A sphaleron is a non-perturbative electroweak field configuration — a "saddle point" over an energy barrier separating vacua that differ in baryon plus lepton number. At low temperature quantum tunnelling over that barrier is fantastically suppressed, but above the electroweak scale, $\sim100\ \mathrm{GeV}$ , thermal fluctuations hop it freely, so sphalerons are in equilibrium in the early Universe. They violate $B+L$ while conserving $B-L$ . Their importance is twofold: they supply the Standard Model's baryon-number violation, and they reprocess any high-temperature asymmetry, enforcing $B=\tfrac{28}{79}(B-L)$ — which is why a mechanism must generate a net $B-L$ to leave a surviving baryon number.

What is leptogenesis, and why is it so popular?

Leptogenesis makes the baryon asymmetry indirectly, through leptons. Heavy right-handed Majorana neutrinos — the same particles that, via the seesaw, explain why ordinary neutrinos are light — decay out of equilibrium, and being Majorana they decay to leptons and antileptons at slightly different rates, creating a net lepton asymmetry. Sphalerons then convert about a third of that $B-L$ into baryons via $B=\tfrac{28}{79}(B-L)$ . It is popular because it uses the CP violation and heavy scales neutrino masses already require, needs only $\varepsilon\sim10^{-6}$ , and naturally supplies the $B-L\ne0$ that survives sphaleron washout.

Has baryon-number violation ever actually been observed?

Not directly — and that is consistent with the picture. The Standard Model's baryon-number violation is a hot-plasma effect: sphalerons act only above the electroweak scale, and today the process is exponentially suppressed, so the proton is stable on any measurable timescale (its lifetime is bounded beyond $10^{34}$ years, and Super-Kamiokande's search for grand-unified proton decay is so far empty). The absence of low-energy baryon-number violation is therefore no problem for baryogenesis, which places the violation in the first fraction of a second, not the laboratory today.

How can the CMB and nucleosynthesis both measure the same η?

Both are sensitive to how many baryons there are per photon, through completely different physics. Big Bang nucleosynthesis, at $t\sim1$ – $200\ \mathrm{s}$ , builds deuterium and helium with yields that depend steeply on $\eta$ ; primordial deuterium in pristine gas clouds gives $\eta\approx6\times10^{-10}$ . The CMB, released $380{,}000$ years later, encodes $\eta$ in the relative heights of its acoustic peaks, and Planck reads off the same value. That two probes separated by five orders of magnitude in time agree confirms $\eta$ is a genuine, conserved number of Nature — the one baryogenesis must explain.

Is CP violation the same thing as the matter-antimatter asymmetry?

No — CP violation is necessary but not sufficient. It is a property of interactions: a process and its charge-conjugate mirror image proceed at different rates, as seen in kaons, $B$ mesons, and possibly soon in neutrinos. The matter-antimatter asymmetry is a cosmological outcome: a net baryon number. Turning the first into the second also needs baryon-number violation and a departure from equilibrium (Sakharov). Crucially, the Standard Model's measured CP violation is far too small to have produced the observed asymmetry, so an additional, undiscovered source is required.