QCD prediction for the non-$D\bar{D}$ annihilation decay of $\psi (3770)$

Abstract

To clarify the marked difference between BES and CLEO measurements on the non-$D\bar{D}$ decays of the $\psi (3770)$, a $1^3{D}_1$-dominated charmonium, we calculate the annihilation decay of $\psi (3770)$ in NRQCD. 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-D mixing effect is found to be very small. With $m_c=1.5\pm 0.1\text{GeV}$ our result is $\Gamma (\psi (3770)\to \text{light hadrons})=467_{+338}^{-187}\text{KeV}$. For $m_c=1.4$ GeV, together with the observed hadronic transitions and E1 transitions, the non-$D\bar{D}$ decay branching ratio of $\psi (3770)$ could reach about 5%. Our results do not favor either of the results of BES and CLEO collaborations, and further experimental tests are urged.

Comments: Version published in PRL, errors and typos corrected, references added