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Compare an unknown allowed branch of parent $P$ with a reference allowed decay of mean lifetime ${\tau }_R$ and unit branching fraction. Its branching fraction is the parent mean lifetime ${\tau }_P$ times the inferred partial rate. The phase-space ratio $f_X/f_R$ and the total vector-plus-axial strengths $S_X/S_R$ enter separately. Approximating both strengths by their Fermi transition contributions and both phase-space integrals by $Q^5$ gives a useful scale, but does not establish a unique branch fraction if the axial strengths are unknown.

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.

If two semileptonic decays differ by $s\to u$ versus $d\to u$, an equal-hadronic-strength approximation and a fifth-power phase space ansatz give $r_s=K{\sin }^2{\theta }_C{\Delta }_s^5$ and $r_d=K{\cos }^2{\theta }_C{\Delta }_d^5$. Their partial decay rates are $r_i=B_i/{\tau }_i$, where $B_i$ is the appropriate branching fraction and ${\tau }_i$ the total mean lifetime. Taking the ratio gives the displayed expression. Different hadronic hadronic form factors, finite electron mass and recoil corrections prevent this simplified extraction from being an exact determination.

James H. Christenson, James Watson Cronin, Val Logsdon Fitch and René Turlay reported the result in 1964. At Brookhaven's AGS, 30 GeV protons struck beryllium; collimators selected a neutral particle beam at 30 degrees. A downstream helium decay volume reduced interactions.^[ref]

The flight distance suppressed the short-lived kaon component. Each arm of a two-arm magnetic spectrometer had spark chambers before and after its magnet. Cherenkov detectors and scintillation counters triggered photographic recording in coincidence.^[ref]

The helium sample yielded $45\pm 9$ signal events; $(2.0\pm 0.4)\times 10^{-3}$ was the ratio to all charged decay channels.^[ref] That denominator must be retained when comparing this result with a total branching fraction.

The evidence was kinematic. Later regenerated-beam quantum interference established that the short- and long-lived states reached the same two-pion final state, excluding alternatives such as distinct pion-like particles.^[ref] The 1964 observation established evidence for CP violation; it did not determine every parameter of the CKM matrix. Inferring time-reversal symmetry violation from CP violation invokes CPT symmetry, rather than a direct comparison of time-reversed transitions in that experiment.

The final average table supplies the $K^{-}{\pi }^{+}$, ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ branching fractions, and the last paragraph supplies $K^{+}{\pi }^{-}$. This is a later experimental cross-check, not data provided in the 2012 paper.

For Ds meson spectator decays, $c\to s{W}^{+}$ followed by $W^{+}\to u\bar{d}$ carries CKM magnitude $|V_{cs}{V}_{ud}|$ and can form either $\varphi {\pi }^{+}$ or $K^{+}{\bar{K}}^0$. Replacing $c\to s$ by $c\to d$ carries $|V_{cd}{V}_{ud}|$ and can form $K^{+}{\pi }^0$ through the $-d\bar{d}/\sqrt{2}$ pion component. With otherwise equal reduced hadronic strengths, the last channel's rate is suppressed relative to the neutral-antikaon channel by $|V_{cd}/V_{cs}{|}^2/2$. Actual branching fractions also depend on phase space, colour contractions and strong final-state interactions; the CKM factors do not determine exact exclusive rates.

A search optimized for a specified production mode and decay topology. Reconstructing a resonance or a kinematic endpoint can reject backgrounds and constrain masses, while making sensitivity depend on branching fractions and intermediate states.

An interaction among outgoing hadrons that changes the observed channel amplitude or its phase after the short-distance production vertex. Rescattering can mix channels with the same conserved quantum numbers. Consequently identical CKM suppression orders do not imply equal branching fractions, and a free-quark spectator diagram need not determine the ordering of exclusive hadronic decay rates.

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.

An experimental averaging collaboration. The cited hadronic-decay average specifies its treatment of electromagnetic final-state radiation, which matters when comparing measured branching fractions.

The ATLAS experiment and CMS experiment searched proton-proton collisions at the Large Hadron Collider at collision energies of $7$ and $8\mathrm{TeV}$. The ATLAS experiment used silicon tracking, a $2\mathrm{T}$ solenoid, liquid-argon electromagnetic calorimeters and an external muon spectrometer. Its July 2012 paper reported a combined local statistical significance of $6.0$ standard deviations near $126.5\mathrm{GeV}$; this paper result is distinct from the initial 4 July announcement.^[ref]

The CMS experiment used silicon tracking in a $3.8\mathrm{T}$ solenoid, lead-tungstate electromagnetic calorimeters and external muon chambers. Electrons combine tracks and particle showers; muons combine tracking and chamber hits; photons supply shower energies and directions. Selected $H\to \gamma \gamma$ and $H\to Z{Z}^{\ast }\to 4\ell$ candidates, with $\ell =e,\mu$, yielded invariant mass peaks. It checked lepton efficiencies with Z boson decays, estimated fake-lepton backgrounds from control samples with relaxed identification, and fitted the smooth diphoton background from data. Its combined local statistical significance was $5.0$ standard deviations near $125\mathrm{GeV}$.^[ref]

The ATLAS experiment compared signal-plus-background and background-only hypotheses with a profile likelihood, accounting for systematic uncertainties and correlations between decay channels. Diphoton and four-lepton candidates gave precise invariant masses; $W{W}^{\ast }$ decays supplied additional evidence with poorer mass reconstruction because of escaping neutrinos. A local p-value concerns one specified mass; scanning masses requires a look-elsewhere effect correction.^[ref]

Two-photon decay excludes spin one under the usual assumptions, but does not prove spin zero. A mass peak does not determine every Higgs boson coupling. Production rates, branching fractions and angular correlations require additional tests.^[ref]

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.

Inclusive formation sums over all resonance decays and has exit branching fraction one. Selecting a particular final channel instead multiplies by that channel's branching fraction. Thus resonant elastic scattering contains the square of the entrance branching fraction, while inclusive formation contains only one power.

An inclusive branching fraction sums many exclusive final states. A clean reconstruction mode can be experimentally attractive without dominating the total decay rate. For example, the J/psi has useful electron-pair and muon-pair decays, but predominantly decays to hadrons inclusively. Detector acceptance, branching fraction and background rejection jointly determine the usefulness of a channel.^[ref]

A Majorana neutrino is its own antiparticle. A corresponding mass term can violate conventional lepton number by two. Observing a wrong-helicity charged-current process is nevertheless suppressed by the very small neutrino mass relative to its energy, rather than having the ordinary charge-conjugate branching fraction.

Physical Letters B 584, 251–259. doi.org/10.1016/j.physletb.2004.01.041

The collaboration selected 730 candidates with an estimated $58\pm 8$ background events and measured a branching fraction $(1.16\pm 0.05_{\mathrm{stat}}\pm 0.06_{\mathrm{syst}})\times 10^{-3}$. This is an observed weak radiative channel, not an electromagnetic flavour-conserving decay.

Use the kaon CP eigenstates convention $CP|K^0⟩=-|{\bar{K}}^0⟩$, matching kaon CP mixing parameter. Then $|K_1⟩=(|K^0⟩-|{\bar{K}}^0⟩)/\sqrt{2}$ is CP even, while $|K_2⟩=(|K^0⟩+|{\bar{K}}^0⟩)/\sqrt{2}$ is CP odd. With CPT symmetry and a common small mixing parameter, the physical states can be writtenHere $S,L$ mean short and long mean lifetimes; the kaon CP mixing parameter $ϵ$ depends on the flavor-state phase convention. A positive flavor-exchange convention instead makes the symmetric flavor combination CP even, as explained in exchange-positive CP convention for neutral kaon mixing. Mixing these conventions would reverse the interpretation of the written sums.

Why does the two-pion final state test CP symmetry? A spin-zero kaon decaying into two spin-zero pions has relative orbital angular momentum $\ell =0$ by angular momentum conservation. Two negative intrinsic parities multiply to plus, and $(-1{)}^{\ell }=1$. Charge conjugation exchanges ${\pi }^{+}$ and ${\pi }^{-}$; the $\ell =0$ state is even under this exchange. Hence this two-pion state has CP eigenvalue $+1$. If a decay transition operator $T$ preserves CP symmetry, inserting CP on both sides of $⟨\pi \pi |T|K_2⟩$ changes its sign without changing its value: that decay amplitude must vanish.

Assume for illustration that CP violation occurs only through the state admixture and the decay transition preserves CP symmetry. Put $A_1=⟨\pi \pi |T|K_1⟩$. ThenNeglecting the tiny difference in two-body Lorentz-invariant phase space between the physical masses gives ${\Gamma }_L^{\pi \pi }/{\Gamma }_S^{\pi \pi }\simeq |ϵ{|}^2$. A branching fraction, however, divides a partial decay width by the total decay width. With $\hslash =1$, ${\tau }_i=1/{\Gamma }_i$, soFor chosen values $|ϵ|=0.01$ and ${\tau }_L/{\tau }_S=100$, the branching fraction ratio is $0.01$, whereas the partial decay width ratio is $0.0001$. This is original arithmetic, not a historical fit. The longer observation time amplifies the integrated fraction relative to the instantaneous partial decay rate.

The contribution of a specified decay channel to the total decay width. In an exponential-decay description, its probability rate is ${\lambda }_i={\Gamma }_i/\hslash$, the total width is $\Gamma ={\sum }_i{\Gamma }_i=\hslash /\tau$, and its branching fraction is ${\Gamma }_i/\Gamma$. Channels must be specified consistently, including any inclusive treatment of unresolved radiation. A partial decay width has energy units rather than inverse-time units.