= Solution
The <baryon asymmetry> is an excess of net <baryon number> over zero, conveniently measured by $\eta_B=(n_B-n_{\bar B})/n_\gamma$. Ordinary matter contains abundant <baryons>, whereas no comparable primordial <antibaryon> population is observed. Large nearby domains of matter and <antimatter> would produce radiation through <particle-antiparticle annihilation> at their boundaries. Antiparticles produced in energetic collisions are not evidence for a cosmological antimatter domain. The small nonzero <baryon-to-photon ratio> inferred from <Big Bang nucleosynthesis> is independently tested by <baryon-density consistency between nucleosynthesis and the microwave background>.
Starting with zero net <baryon number>, the <Sakharov conditions> require \b[baryon-number violation, C and CP violation, and departure from thermal equilibrium]. Conservation of <baryon number> would keep the initial value zero. <C symmetry> or <CP symmetry> would pair baryon production with equal antibaryon production; <CP rate cancellation in baryogenesis> explains why <C violation> alone does not suffice. In <thermal equilibrium> with zero imposed charge <chemical potentials>, <CPT symmetry> forbids the required net <baryon number>. An asymmetric rate in one reaction must not be mistaken for net production after all reverse reactions are included.
A simple example is <heavy-boson decay baryogenesis>. Take equally many heavy $X$ <bosons> and their <antiparticles>, with decay channels
$$
X\longrightarrow uu\quad(r),\qquad X\longrightarrow\bar d e^+\quad(1-r),
\qquad
\bar X\longrightarrow\bar u\bar u\quad(\bar r),\qquad
\bar X\longrightarrow d e^-\quad(1-\bar r).
$$
The symbols in parentheses are <branching fractions>. The two $X$ channels carry <baryon numbers> $2/3$ and $-1/3$, so both cannot conserve one assigned <baryon number> for $X$. Their mean <baryon number> is $r-1/3$, while the mean for $\bar X$ is $-\bar r+1/3$. Consequently,
$$
\boxed{\Delta B_{X\bar X}=r-\bar r,\qquad\epsilon=\frac{r-\bar r}{2},}
$$
where $\epsilon$ is the asymmetry per decaying particle. <CP violation> permits $r\ne\bar r$ without violating the equality of total <decay widths> required by <CPT symmetry>. Microscopically a <direct CP asymmetry> requires interference between <decay amplitudes> with both relative <weak phases> and <absorptive phases>; specifying complex couplings alone would not establish unequal partial <decay widths>.
For <radiation domination>, a sufficient decay condition is $\Gamma_X\lesssim H(T=M_X)=1.66\sqrt{g_*}M_X^2/m_P$. The heavy population can then survive as the equilibrium abundance drops, before decaying while inverse production is suppressed. Its actual abundance differs from its <thermal equilibrium> value. If subsequent <baryon-number washout> is negligible and <cosmological entropy conservation> holds, an initial total abundance $Y_X=(n_X+n_{\bar X})/s$ produces
$$
\boxed{Y_B\equiv\frac{n_B-n_{\bar B}}s=\epsilon Y_X.}
$$
Here $s$ is the <entropy density>. Residual <baryon-number washout> multiplies this expression by an efficiency factor below one. The example realizes all three <Sakharov conditions>; it illustrates a mechanism, rather than identifying the actual cosmological source of the <baryon asymmetry>.
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