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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.

Differential pumping maintains different gas pressures in connected regions by restricting the connecting gas flow and pumping each region separately. A small aperture or narrow tube limits the vacuum conductance between stages.

In the molecular flow regime, a connection with conductance $C$ carries throughput $Q=C(p_1-p_2)$. A downstream stage pumped at effective speed $S$ has $S{p}_2=C(p_1-p_2)$ in steady state, giving $p_2/p_1=C/(S+C)$. This lets a source operate at a higher pressure while an adjacent particle beam travels in a better vacuum.^[ref]

An ion source produces ions for a beam or another experiment. Ionization changes the charge state of an atom or molecule; an applied electric field can then extract charged particles into a transport region. The resulting particle beam depends on the ionization mechanism, extraction geometry and the distribution of initial positions and velocities.

One arrangement uses an electron beam to ionize a gas and an electrode voltage to extract the products. Surface ionization is another mechanism: suitable atoms can leave a hot surface as ions, as in the surface ionization detector. Producing an ion and identifying its species are separate operations, so a source may need downstream mass spectrometry or other selection when several charged species are present.

A particle beam dominated by neutrinos. Accelerator beams can use particle decay of focused charged pions and kaons, followed by shielding that suppresses other beam components.

A particle beam is a directed stream of particles prepared for transport, interaction or detection. A molecular beam can contain neutral chemical atoms or molecules; an accelerator beam can contain charged electrons, protons or ions. Its direction, energy spread, spatial distribution and particle flux describe different aspects of the preparation.

A source, direction-selecting apertures or focusing elements, a transport region and a detector perform separate tasks. For a charged beam, electric fields can change its energy and magnetic fields can bend its trajectory through the Lorentz force. A neutral atomic beam requires interactions appropriate to its neutral constituents. A vacuum reduces unwanted collisions along either transport path, but it does not itself make every particle's speed equal.

Here particle flux means the number of particles crossing a surface per unit area and unit time, with the area taken perpendicular to the incident particle beam. Multiplying by the target interaction cross section gives an event rate per target particle in the ideal independent-target model.

A two-track invariant mass and a direction test answer different questions. In units $c=1$, assign each track the pion mass $m_{\pi }$ and reconstruct its momentum before magnetic deflection. With $p_{\pm }=|{\mathbf{p}}_{\pm }|$ and opening angle $\alpha$,This follows by expanding the squared sum of the two four-momenta. The angle $\theta$ between the reconstructed parent momentum $\mathbf{P}={\mathbf{p}}_{+}+{\mathbf{p}}_{-}$ and the neutral particle beam direction $\hat{\mathbf{n}}$ satisfiesA fully reconstructed two-body decay channel gives the parent mass and $\theta \simeq 0$, within experimental resolution. A three-body decay channel with an unseen neutrino generally misses both constraints; an accidental correct invariant mass alone is insufficient. Notice that the track opening angle $\alpha$ need not be small even when the parent direction angle $\theta$ vanishes.

The 1964 analysis selected $490<M_{\pi \pi }<510$ MeV and remeasured events with $\cos \theta >0.9995$, comparing adjacent mass bands.^[ref]

For an original dimensionless example, take $m_{\pi }=1$, $\hat{\mathbf{n}}=(0,0,1)$ and ${\mathbf{p}}_{\pm }=(\pm \sqrt{3},0,3)$. Each energy is $\sqrt{13}$; the opening angle is $60$ degrees since $\cos \alpha =(9-3)/(9+3)=1/2$. Yet $\mathbf{P}=(0,0,6)$ points exactly along the beam, and $M_{\pi \pi }^2=4(13)-36=16$. Thus a parent of mass $4$ passes both ideal tests. These chosen numbers illustrate four-momentum conservation, not detector performance.

An encounter of charged particle beams at an impact parameter large enough to suppress direct overlap of the atomic nuclei, while their electromagnetic fields still interact.