Richter-Ting independent J/psi discovery experiments

In 1974, Samuel Chao Chung Ting's Brookhaven team and Burton Richter's SPEAR team independently found the narrow state now called the J/psi meson. Each discovery paper notes learning of the other result during manuscript preparation.^[ref][ref]

The common question was whether the observed excess represented a new particle resonance, rather than a peculiarity of particle identification, acceptance or calibration. The important difference was the horizontal coordinate of the search: Brookhaven reconstructed a final-state invariant mass; SPEAR scanned an initial-state center-of-mass energy. The invariant-mass selection of bubble-chamber events uses the first kind of reasoning, despite a very different recording medium.

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 SPEAR, counterrotating Electron and Positron beams collided inside a magnetic particle detector. Finer steps in stored-beam energy resolved a sharp production peak. A magnetometer and measured orbit positions monitored the energy settings; Bhabha scattering normalized the cross sections. The paper attributed the observed width to beam-energy spread and radiation effects, reporting an upper limit on intrinsic width. Its muon identification system was not functioning: the non-electron two-body excess was not conclusively a muon pair.^[ref]

A scan must compare normalized production rates, since more selected events can result from more beam encounters or different detection efficiency. A proposed diagnostic is to revisit energies on either side of the peak while monitoring the energy calibration and event selection. Such neighboring settings test the local production background; their event totals alone are not an independent measurement of the intrinsic decay width.

For a reconstructed Electron–Positron pair, four-momentum conservation givesNeglecting the electron mass compared with the daughter energies, and calling the opening angle $\theta$, this becomesAs an original example, choose $E_{+}=2\mathrm{GeV}$, $E_{-}=3\mathrm{GeV}$ and $\theta =60^{\circ }$. Then $M_{ee}{c}^2=\sqrt{6}\mathrm{GeV}\simeq 2.449\mathrm{GeV}$, although the pair's laboratory energy is $5\mathrm{GeV}$. The pair carries net momentum. Neither its laboratory energy nor the original proton beam energy is its invariant mass; unobserved products carry additional four-momentum.

For equal, oppositely directed incoming beams with equal total energy $E_b$, their total momentum vanishes. Thus the incoming center-of-mass energy isStipulated $1.50\mathrm{GeV}$ beams therefore provide $3.00\mathrm{GeV}$ of incoming center-of-mass energy. This identity is exact for the stated equal-beam geometry. Radiation before annihilation can reduce the energy forming the final state; the apparatus also has a distribution of beam energies. A nominal machine setting is therefore not an exact event-by-event final-state invariant mass.

A simple isolated particle resonance model starts with a survival amplitude proportional toIts survival probability is $|a(t){|}^2=e^{-\Gamma t/\hslash }$, giving mean rest-frame lifetime $\tau =\hslash /\Gamma$. The Fourier transform of this one-sided amplitude is proportional to $(\Gamma /2-i(E-E_0){)}^{-1}$; its squared modulus gives a Lorentzian line shape. Write its normalized density asAt $E-E_0=\pm \Gamma /2$ the density is half its peak, so its intrinsic full width at half maximum is $\Gamma$. This is a local isolated-line approximation, extending the offset coordinate over the real line; physical production thresholds, interference and energy-dependent decay widths can require a richer quantum scattering model.

Now stipulate a centered normal distribution for the measurement response, with standard deviation $\sigma$. A measured coordinate $x$ has densityThis convolution describes the smearing of an underlying line, with constant acceptance and no background. For a pair spectrometer the response summarizes invariant-mass resolution; for an idealized collider scan it summarizes incoming center-of-mass energy spread. These are different experimental sources of uncertainty even when the same mathematical response is useful.

Choose an arbitrary scale $E_{\ast }$, intrinsic decay width $\Gamma =0.20E_{\ast }$ and response standard deviations $0.40E_{\ast }$ and $1.20E_{\ast }$. Numerical integration gives apparent full width at half maximum values of approximately $1.05E_{\ast }$ and $2.93E_{\ast }$, respectively. The state and its rest-frame lifetime are identical in both cases. The normal distribution's width alone is $2\sqrt{2\ln 2}\sigma$; adding that width to $\Gamma$ in quadrature is not an exact rule for this convolution.

For a purely illustrative $E_{\ast }=1\mathrm{MeV}$, taking $\hslash \simeq 6.5821\times 10^{-22}\mathrm{MeV}\mathrm{s}$ gives $\tau \simeq 3.2911\times 10^{-21}\mathrm{s}$. These are invented line parameters, not J/psi meson measurements. Substituting the larger apparent width into $\hslash /\Gamma$ would incorrectly shorten the inferred lifetime by nearly a factor of fifteen. An unresolved width can support an upper bound on intrinsic decay width, and consequently a lower bound on lifetime, only after the instrumental response and model assumptions have been assessed.

The discovery peak and its later interpretation answer different questions. The J/psi meson is understood as charmonium, a bound charm quark–charm antiquark system. Richter's 1976 lecture distinguishes the initial discovery from subsequent tests of competing explanations, including the related level structure and later evidence for particles carrying uncancelled charm. A narrow peak alone did not establish all these properties in 1974.^[ref]