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

TL;DR

The annihilation decay of psi(3770) in nonrelativistic QCD is calculated by introducing the color-octet contributions, and the results do not favor the results of either the BES or the CLEO Collaborations.

Abstract

To clarify the marked difference between BES and CLEO measurements on the non-$D\bar D$ decays of the $ψ(3770)$, a $1^{3}D_{1}$-dominated charmonium, we calculate the annihilation decay of $ψ(3770)$ 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 $m_{c}=1.5\pm0.1\textrm{GeV}$ our result is $Γ(ψ(3770)\to \textrm{light hadrons})=467^{-187}_{+338}\textrm{KeV}$. For $m_c=1.4$ GeV, together with the observed hadronic transitions and E1 transitions, the non-$D\bar D$ decay branching ratio of $ψ(3770)$ could reach about 5%. Our results do not favor either of the results of BES and CLEO collaborations, and further experimental tests are urged.

Figures (1)

• Figure 1: Renormalization scale $\mu$-dependence of the decay width of charmonium $^{3}D_{1}$ to light hadrons. Here NLO means LO contribution+NLO correction