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Baryon-number washout is erasure of a baryon asymmetry by reactions that violate baryon number. Inverse decays and scattering can drive the plasma toward its zero-asymmetry thermal equilibrium. The relevant comparison is their rate against the Hubble parameter, not just the decay width that initially produced the asymmetry.

A branching fraction is the probability that a decay occurs through a particular mutually exclusive channel, equal to its partial decay width divided by the total decay width. Inclusive channel fractions sum to one. Rounding displayed fractions can make their numerical sum differ from one.

For an isolated particle resonance of spin $J_R$, the Breit-Wigner approximation relates a production-and-decay cross section to its partial decay widths. In natural units, $p_i$ is either incident particle's momentum magnitude in the centre-of-momentum frame, $g=(2J_R+1)/[(2J_a+1)(2J_b+1)]$ for unpolarized incident particles, and $\Gamma$ is the total width. The formula assumes the stated spin counting and neglects nonresonant backgrounds and their interference. Multiplication by $(\hslash c{)}^2$ converts an inverse-squared-energy cross section to area when momenta are expressed in energy units.

Brookhaven's proton beam struck stationary beryllium. A two-arm magnetic pair spectrometer measured electron–Positron momenta and directions. Cherenkov detectors, tracking chambers and shower counters rejected the much larger hadron background. Calibration used an electron beam; timing and track matching rejected accidental coincidences. The pair invariant mass distribution showed a narrow excess. Reducing magnet currents left its reconstructed position unchanged; changing target thickness and reversing spectrometer polarity supplied further checks. The unresolved intrinsic width did not mean a zero decay width.^[ref]

The logic of the magnet-current check is especially useful. A real state should retain its reconstructed invariant mass when a calibrated change of magnetic field makes its daughters follow different accepted paths. A feature tied to one detector location or one setting need not do so. This checks a possible instrumental origin; it does not by itself determine the state's quark composition.

At leading order, for final fermions much lighter than the Z boson, the partial decay width is proportional to $N_c(|g_L{|}^2+|g_R{|}^2)$. Here $N_c$ is the final-state color multiplicity in a decay width, and $g_L=T_{3L}-Q{\sin }^2{\theta }_W$, $g_R=T_{3R}-Q{\sin }^2{\theta }_W$ are the dimensionless left- and right-chirality couplings. The common normalization cancels in ratios.

For an electron, $g_L=-1/2+{\sin }^2{\theta }_W$, $g_R={\sin }^2{\theta }_W$. For one active neutrino flavour, $g_L=1/2$, $g_R=0$. ThereforeThere is no extra flavour factor for a single specified neutrino species. Summing the three active species produces three times that invisible partial width, within the same massless approximation.

For a colorless parent decaying through a color-diagonal interaction into a quark and antiquark, the three orthogonal matching-color states add incoherently. The inclusive flavor decay width is $N_c=3$ times the one-color width. In a parton scattering rate, an initial color average instead cancels the matching final color sum.

In a CPT-invariant vacuum, a subatomic particle and its antiparticle have equal masses and total decay widths, equal spin magnitudes and opposite conserved additive charges. CPT exchanges initial and final states in a scattering experiment; it relates a process to the reversed process with antiparticles and reversed spins. It does not force equality of every pair of conjugate partial decay widths when CP violation is present.

The invariant decay amplitude is the transition matrix element for one incoming particle and a specified on-shell final state, with the overall momentum delta function factored out. For covariantly normalized states, write the connected S-matrix element as $i(2\pi {)}^4{\delta }^4(p_i-p_f)\mathcal{M}(i\to f)$. Its overall phase does not affect the decay width. The rate is $\Gamma =(2M_i{)}^{-1}{\sum }_{\mathrm{spins}}\int d{\Phi }_f|\mathcal{M}{|}^2$, with the initial spin average included when the initial state is unpolarized. For a spin-zero parent and an angle-independent two-body amplitude, the two-body Lorentz-invariant phase space gives $\Gamma =|\mathbf{k}|\sum |\mathcal{M}{|}^2/(8\pi M_i^2)$. In leptonic pion decay, contracting the axial hadronic matrix element with the chiral weak charged current makes this amplitude proportional to the charged-lepton mass, proving helicity suppression.

A decay channel specifies a possible final state of a particle decay, such as an electron, a neutrino and an antineutrino in a specified muon decay. Different channels can have different interaction amplitudes, available phase space and experimental visibility.

For disjoint final-state classes, the partial decay widths add: ${\Gamma }_{\mathrm{total}}={\sum }_i{\Gamma }_i$. The branching fraction is ${\Gamma }_i/{\Gamma }_{\mathrm{total}}$, so increasing one partial width changes the fractions assigned to the others even if their own amplitudes are unchanged. Intermediate resonances leading to the same final state can interfere; they cannot always be treated as mutually exclusive counting bins.

The Delta baryon listing distinguishes a Breit-Wigner mass near $1232\mathrm{MeV}$ and decay width near $117\mathrm{MeV}$ from complex-pole parameters. External tabulated values cannot replace readings from a missing experimental figure.

The Delta baryon ground multiplet is a short-lived baryon resonance family with isospin $3/2$ and spin-parity $3/2^{+}$. Its four charge states have ordinary valence contents $uuu$, $uud$, $udd$ and $ddd$, with charges $+2,+1,0,-1$ in elementary-charge units.

The familiar Delta-plus baryon and the proton share valence flavor content but differ in their spin coupling and mass. Strong decay into a nucleon and a pion gives the Delta resonance a broad decay width. In scattering, a resonance appears through an energy-dependent amplitude and cross section, not as an indefinitely stable additional constituent of every atomic nucleus.^[ref]

A direct CP asymmetry compares decay widths for a process and its CP symmetry conjugate. Let two decay amplitudes contribute with real nonnegative magnitudes $a_1,a_2$, absorptive phases ${\delta }_i$ and weak phases ${\varphi }_i$. Then $\mathcal{A}=a_1{e}^{i({\delta }_1+{\varphi }_1)}+a_2{e}^{i({\delta }_2+{\varphi }_2)}$ and $\overline{\mathcal{A}}=a_1{e}^{i({\delta }_1-{\varphi }_1)}+a_2{e}^{i({\delta }_2-{\varphi }_2)}$. Expanding the absolute squares givesThus two nonzero contributions and both kinds of relative phase are required in this example. Equal total decay widths under CPT symmetry constrain the sum over channels and do not forbid individual channel asymmetries.

Direct CP violation concerns the decay transition itself. At leading order, the charged and neutral two-pion decay amplitude ratios separate a common $ϵ$ from channel-dependent ${ϵ}^{\prime }$.^[ref]

For the corresponding double ratio of partial decay widths,The expansion follows from $(1-2x)/(1+x)=1-3x+O(x^2)$. A single nonzero long-lived two-pion yield does not isolate $x$: it can already occur with ${ϵ}^{\prime }=0$. Thus the 1964 evidence for CP violation must be distinguished from the later experimental establishment of direct CP violation through ${ϵ}^{\prime }$.

A decaying particle-antiparticle pair is described by a two-dimensional effective Hamiltonian for neutral-meson mixing with dispersive matrix $M$ and decay matrix $\Gamma$, both Hermitian matrices. The effective Hamiltonian for neutral-meson mixing itself is generally not a Hermitian matrix. CPT symmetry equates its diagonal entries, by separately equating diagonal masses and decay widths. For $H_{\mathrm{eff}}=\left(\begin{array}{cc}a& b\\ c& a\end{array}\right)$ the eigenvalues are $a\pm \sqrt{bc}$ and generic eigenvectors are $(\sqrt{b},\pm \sqrt{c}{)}^T$, with correlated square-root branches. Complex eigenvalues give masses and decay widths through $\mu =m-i\Gamma /2$.

Single-photon electron-positron annihilation can directly form quarkonium with $J^{PC}=1^{--}$. A vector S-wave quarkonium can annihilate back through a virtual photon into a charged-lepton pair. At leading nonrelativistic order, its electronic partial decay width is proportional to ${\alpha }^2{Q}_q^2|\psi (0){|}^2/M^2$, where the wavefunction at the origin describes the quark-antiquark annihilation overlap.

Below the threshold for a pair of heavy-light mesons, hadronic decays require annihilation, primarily into three gluons for a color-singlet $1^{--}$ state. One gluon cannot carry a color-singlet initial state, and two gluons have the wrong charge-conjugation parity. Above the heavy-light pair threshold, a strong interaction can instead separate the heavy quark and antiquark into different mesons after creating a light pair. This can greatly increase the total decay width without comparably changing the short-distance electronic partial width. A specific example is the contrast between the first three Upsilon mesons and the $4S$ state. Higher radial states can additionally undergo hadronic or radiative transitions to lower quarkonium states.

Gregory Breit and Eugene Wigner explained strong variations in slow-neutron capture through resonant nuclear excitation. In modern notation, an isolated nuclear resonance has a contribution proportional to ${\Gamma }_n{\Gamma }_{\gamma }/[(E-E_r{)}^2+{\Gamma }^2/4]$, apart from spin and kinematic factors. Here ${\Gamma }_n$ and ${\Gamma }_{\gamma }$ describe the entrance and radiative channels, while $\Gamma$ is the total decay width. With slowly varying prefactors, moving $\Gamma /2$ to either side of $E_r$ halves the peak, connecting its observed width with the unstable intermediate state.^[ref]

Hadronization is the conversion of colored quarks and gluons into color-neutral hadrons. It affects exclusive final-state distributions even when an inclusive observable can be approximated through a short-distance partonic calculation. A tree-level partonic decay width does not by itself model this conversion.

Consider equal initial abundances of a heavy boson $X$ and its antiparticle. Two decay channels with different baryon numbers, for example $X\to uu$ and $X\to \bar{d}{e}^{+}$, have branching fractions $r$ and $1-r$. The conjugate channels have branching fractions $\bar{r}$ and $1-\bar{r}$. Their mean baryon numbers are $r-1/3$ and $-\bar{r}+1/3$, so each particle-antiparticle pair produces $r-\bar{r}$, or $ϵ$ per decaying particle. Unequal branching fractions require CP violation; equal total decay widths are consistent with CPT symmetry. Baryon number cannot be assigned so that both channels conserve it. An initial abundance decaying outside thermal equilibrium, after inverse production becomes ineffective, can therefore generate a nonzero baryon asymmetry. At the microscopic level a decay-rate difference caused by CP violation requires interference of decay amplitudes with both a relative weak phase and an absorptive phase; complex couplings alone do not guarantee it. Subsequent baryon-number washout must be ineffective for the produced asymmetry to survive.

A spin-zero parent decaying through a chiral weak charged current to a charged lepton and a massless neutrino cannot supply the helicities selected by a massless interaction. A charged-lepton mass insertion makes the amplitude proportional to $m_{\ell }$ and the decay width proportional to $m_{\ell }^2$. A spin-one W boson does not suffer this suppression.

At leading order, neglecting phase-space suppression and radiative corrections, Higgs decay to a fermion pair has partial decay width proportional to $N_c^f{m}_f^2$, with $N_c=3$ for a quark and one for a lepton. A known sum of branching fractions therefore fixes the proportionality between these weights and individual branching fractions without requiring the Higgs vacuum expectation value. The same normalization estimates a small additional fermionic channel if its weight is not included in the known sum.