= Electromagnetic production and decay of vector quarkonium
{title2=$J^{PC}=1^{--},\quad\Gamma_{ee}\propto\alpha^2Q_q^2|\psi(0)|^2/M^2$}
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 $\alpha^2Q_q^2|\psi(0)|^2/M^2$, 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.
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