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Charmonium is a family of bound states of a charm quark and its antiquark, with zero net charm. It differs from open-charm D mesons, which carry a charm quark together with a light antiquark.

The constituent spins and relative orbital angular momentum distinguish states such as the J/psi meson, eta c meson and chi c mesons. Their level separations and radiative transitions test the interaction between heavy quarks. Decay can proceed through annihilation of the charm–anticharm pair, so net charm conservation does not imply that a charmonium state is stable. A valence quark label organizes the spectrum while additional gluonic and quark-pair contributions remain part of the interacting state.

Coauthored the discovery of the J/psi meson in electron-positron annihilation. Scanning the collision energy revealed a sharp enhancement in production of hadrons and electron-Positron pairs near $3.105\mathrm{GeV}$, with a reported full-width upper limit of $1.3\mathrm{MeV}$.^[ref]

Coauthored the observation of the J/psi meson through a narrow peak near $3.1\mathrm{GeV}$ in the invariant mass of electron-Positron pairs. The experiment used a precise pair spectrometer to analyze products of protons striking a beryllium target.^[ref]

The J/psi meson is the ground spin-triplet S-wave vector state of charmonium, with leading valence content $c\bar{c}$ and quantum numbers $J^{PC}=1^{--}$. It has zero net charm and can decay into hadrons or charged-lepton pairs.^[ref]

Its comparatively narrow decay width makes it a conspicuous resonance in reconstructed mass distributions. An electron–Positron mass peak in a fixed-target experiment and an enhanced event rate during an energy scan in an electron-positron collider were complementary observations in the Richter-Ting independent J/psi discovery experiments of 1974.^[ref][ref] A peak's measured width also includes detector resolution or beam-energy spread, so it must not automatically be identified with the intrinsic lifetime width.

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]

Neutral B meson mixing converts the flavor eigenstates $B^0=\bar{b}d$ and ${\bar{B}}^0=b\bar{d}$ into one another through the weak interaction. The propagating mass eigenstates are $|B_L⟩=p|B^0⟩+q|{\bar{B}}^0⟩$ and $|B_H⟩=p|B^0⟩-q|{\bar{B}}^0⟩$, with $|p{|}^2+|q{|}^2=1$.

In units $\hslash =c=1$, neglect their width difference and take $|q/p|=1$. Evolution of an initial $B^0$ at proper time $t$ gives the undecayed flavour probabilitieswhere $\Delta m=m_H-m_L$ and $\Gamma$ is the common decay width. Their sum is the survival probability, not one.

For a common final state, mixing and direct decay interfere through ${\lambda }_f=(q/p)({\bar{A}}_f/A_f)$. In the Standard Model, $f=J/\psi K_S$ combines a J/psi meson with a short-lived neutral kaon. Neglecting subleading weak amplitudes and small kaon CP violation,Here the $V_{ij}$ are CKM matrix elements; the minus sign reflects the approximate negative CP parity of this specified final state. A different charmonium-kaon final state need not have that same sign.^[ref]

For the neutral strange B meson, a charged-current tree amplitude has $\bar{b}\to \bar{c}{W}^{+}$ followed by $W^{+}\to c\bar{s}$, while the initial $s$ is a spectator. The $c\bar{c}$ pair forms the J/psi meson and the $s\bar{s}$ pair forms the phi meson. Charge and quark flavour flow are conserved at each vertex except for the permitted weak flavour change. antiquark arrows point opposite their physical propagation direction.

Useful reconstruction modes are $J/\psi \to {\mu }^{+}{\mu }^{-}$ or $e^{+}{e}^{-}$, through a virtual photon, and $\varphi \to K^{+}{K}^{-}$, a strong decay. The latter is the largest individual $\varphi$ mode, with $K_L^0{K}_S^0$ also important. For the $J/\psi$, the inclusive branching fraction versus reconstruction mode distinction matters: hadronic decays dominate inclusively, principally through three gluons; each charged-lepton pair accounts for about 6%, not most decays. The charm pair lies below open-charm threshold. These distinctions are confirmed by the official particle listings.^[ref]

The dominant interaction is electromagnetic. The color singlet charm-anticharm component of the J/psi meson annihilates through a virtual photon, which creates a muon and an antimuon:Panel (i) shows the two electromagnetic vertices. Vector quantum numbers allow the one-photon channel. A Z boson contribution is negligible at this mass scale; a single gluon cannot connect a color singlet initial state to colorless leptons. The dominant interaction for this specified final state need not dominate the meson's total decay width.

TODO: the numerical resonance-area reading is unavailable from the retained source. Page 6 retains the upper data panels but loses the lower part of the scanned data image, including the numerical horizontal energy calibration. A vertical cross section scale and an apparent peak cannot supply $\int \sigma dE$ without that calibration. The decoded image contains 2,834,898 of 4,437,216 required RGB bytes; the archived bundle has the same truncation. No horizontal scale or natural decay width is inferred from the display width.

The recoverable numerical conversion is nevertheless definite. With $M\simeq 3.1\mathrm{GeV}$, $B_{ee}=0.060$, $ϵ=0.50$, and $1{\mathrm{GeV}}^{-2}=389400\mathrm{nb}$, b givesThis coefficient assumes the plotted exclusive electronic sample has not already been corrected for acceptance. A restored area, with continuum subtraction and acceptance convention checked, would complete the estimate. A tabulated modern J/psi meson width would be external information rather than a reading of these data.

The narrow scattering resonance indicates suppressed strong interaction decay. In the quark model, $c\bar{c}$ is below the open-charm quark $D\bar{D}$ threshold, so its constituents cannot simply emerge in separate charmed mesons. The OZI rule suppresses annihilation into light hadrons; for a $1^{--}$ color-singlet state the leading purely gluonic channel needs three gluons. The observed leptonic channels remain competitive. Its mass and $I=0$ fit charmonium; the small width alone would not uniquely identify the new quark flavour without the wider spectrum and threshold evidence.

The four allowed two-real-photon states are ${\eta }_c$, ${\eta }_c(2S)$, ${\chi }_{c0}$ and ${\chi }_{c2}$. Two photons have $C=+1$, excluding $J/\psi$, $\psi (2S)$ and $h_c$; the Landau-Yang theorem excludes ${\chi }_{c1}$ because $J=1$. Both scalar and pseudoscalar two-photon amplitudes exist, so $0^{++}$ and $0^{-+}$ are allowed. The J/psi meson was discovered first because its $1^{--}$ assignment permits direct, resonantly enhanced single-photon formation in $e^{+}{e}^{-}$ and a clean dilepton peak in hadron production. The lighter ${\eta }_c$ cannot be formed by one photon; it needs less favorable production channels and has a broader two-gluon decay.

A spin-zero ${\eta }_c$ at rest has no preferred axis, so $d\Gamma /d{\Omega }_p$ is isotropic after summing final spins. A J/psi meson formed in unpolarized high-energy $e^{+}{e}^{-}$ has transverse $m=\pm 1$ alignment. Its $p\bar{p}$ distribution can be writtenwhere $a,b$ contain the two independent helicity amplitudes. It is generally anisotropic; the approximate massless, helicity-conserving limit has $b\to 0$. The tabulated branching fraction does not fix $a/b$. An ensemble equally populated in all three spin projections would instead be isotropic: alignment of the production ensemble matters.

The three structures are the radiative cascadesIn the quark model, the J/psi meson and $\psi (2S)$ are respectively $1{}^3{S}_1$ and $2{}^3{S}_1$ charmonium states. Thus $L=0$, $S=1$, $J=1$, and meson parity and charge conjugation gives $J^{PC}=1^{--}$. The intermediate chi c mesons are $1{}^3{P}_J$: $L=1$, $S=1$, and addition of angular momentum permits $J=0,1,2$. ConsequentlyThese are electric dipole transitions, changing $L$ by one and preserving $S$ to leading order. A singlet $1{}^1{P}_1$ state has $J^{PC}=1^{+-}$ and is not another member of these spin-triplet cascades.

The primary photon energy is $(M_{2S}^2-M_{{\chi }_J}^2)/(2M_{2S})$, about $261$, $171$ and $128\mathrm{MeV}$ for $J=0,1,2$. The secondary photon remains more energetic even after its boost into the parent rest frame. Hence $m^2(J/\psi {\gamma }_h)=M_{{\chi }_J}^2$: with this quantity on the vertical axis, each resonance gives a horizontal band. A finite decay width and detector measurement resolution broaden each band; photon ordering removes the mirrored duplication of an unordered Dalitz plot.

The faint band beside the negative-slope diagonal boundary is $\psi (2S)\to J/\psi {\pi }^0$, followed by ${\pi }^0\to \gamma \gamma$. The neutral pion is predominantly $(u\bar{u}-d\bar{d})/\sqrt{2}$, a ${}^1{S}_0$ pseudoscalar meson with $J^{PC}=0^{-+}$. This production transition violates isospin, accounting for its small rate. To locate the band, set $X=m^2(J/\psi {\gamma }_l)$ and $Y=m^2(J/\psi {\gamma }_h)$. Four-momentum conservation givesFor the neutral pion, $m_{\gamma \gamma }^2=m_{{\pi }^0}^2$ is small, putting the line just inside the $m_{\gamma \gamma }^2=0$ boundary. The allowed $J/\psi \eta$ channel, with the eta meson also $0^{-+}$, produces a parallel line further inside, at $m_{\gamma \gamma }^2=m_{\eta }^2$. The positive-slope edge $X=Y$ instead comes from ordering the two photon energies; proximity to that edge alone would not identify the two-photon state.

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.