Electromagnetic annihilation of e+e− into quarkonium states with even charge conjugation

We calculate the production of narrow resonances with even charge conjugation ${}^3\text{P}{}_{\mathrm{J}}\text{=1,2}$ in e⁺e^? annihilation in the quarkonium and vectordominance models. We give unitarity bounds for $\text{Γ(}{}^3\text{P}{}_{\mathrm{J}}\text{→ e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)}$ in terms of $\text{Γ(}{}^3\text{P}{}_{\mathrm{J}}\text{→ γγ)}$ and $\text{Γ(}{}^3\text{P}{}_{\mathrm{J}}\text{→ e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)}$. The electromagnetic production dominates through the neutral current at low energies independent of details of the model. For masses above 10 GeV the situation is reversed.