QCD Prediction for the Non-$D\overline{D}$ Annihilation Decay of $\psi (3770)$

To clarify the marked difference between BES and CLEO measurements on the non-$D\overline{D}$ decays of the $\psi (3770)$, a $1{}^{3}D_1$-dominated charmonium, we calculate the annihilation decay of $\psi (3770)$ in nonrelativistic QCD. By introducing the color-octet contributions, the results are free from infrared divergences. The color-octet matrix elements are estimated by solving the evolution equations. The $S\mathrm{\text{−}}D$ mixing effect is found to be very small. With $m_c=1.5\pm 0.1\mathrm{GeV}$, our result is $\Gamma \mathbf{(}\psi (3770)\to \mathrm{\text{light hadrons}}\mathbf{)}={467}_{+338}^{-187}\mathrm{keV}$. For $m_c=1.4\mathrm{GeV}$, together with the observed hadronic transitions and $E1$ transitions, the non-$D\overline{D}$ decay branching ratio of $\psi (3770)$ could reach about 5%. Our results do not favor the results of either the BES or the CLEO Collaborations, and further experimental tests are urged.

Figure 1

Renormalization scale $\mu$ dependence of the decay width of charmonium ${}^{3}D_1$ to light hadrons. Here NLO means LO $\mathrm{\text{contribution}}+\mathrm{\text{NLO}}$ correction.