Problems of Double Charm Production in $e^+e^-$ Annihilation at $\sqrt{s}=10.6$ GeV

Abstract

Using the nonrelativistic QCD(NRQCD) factorization formalism, we calculate the color-singlet cross sections for exclusive production processes ${e^++e^-\to J/ψ+η_c}$~ and ~$e^++e^-\to J/ψ+ χ_{cJ}$~$(J=0,1,2)$ at the center-of-mass energy $\sqrt{s}$=10.6 GeV. The cross sections are estimated to be 5.5fb, 6.7fb, 1.1fb, and 1.6fb for $η_c, χ_{c0}, χ_{c1}$ and $χ_{c2}$, respectively. The calculated $J/ψ+η_c$ production rate is smaller than the recent Belle data by about an order of magnitude, which might indicate the failure of perturbative QCD calculation to explain the double-charmonium production data. The complete $\cal{O}$$(α^2_{s})$ color-singlet cross section for ${e^++e^-\to χ_{c0}+ c\bar {c}}$ is calculated. In addition, we also evaluate the ratio of exclusive to inclusive production cross sections. The ratio of $J/ψη_c$ production to $J/ψc\bar{c}$ production could be consistent with the experimental data.

Figures (4)

• Figure 1: Feynman diagrams for $e^+e^-\rightarrow J/\psi+\eta_c( \chi_{cJ} )$.
• Figure 2: Cross sections for $\sigma(e^+ + e^-\rightarrow J/\psi+ \eta_c)$(solid line) and $\sigma(e^+ + e^-\rightarrow J/\psi+ \chi_{cJ})$(dashed line for $J=1$, dotted line for $J=2$) plotted against the $e^+e^-$ center-of-mass energy $\sqrt{s}$ with z=$\sqrt{s/s_0}$ and $\sqrt{s_0}=10.6 {\rm GeV}$.
• Figure 3: Feynman diagrams for $e^++e^-\rightarrow \chi_{c0}+c\bar{c}$ process.
• Figure 4: cross sections for $\sigma(e^+ + e^-\rightarrow \chi_{c0}+ c\bar{c})$(solid line) and $\sigma(e^+ + e^-\rightarrow J/\psi+\chi_{c0})$(dotted line) plotted against the $e^+e^-$ center-of-mass energy $\sqrt{s}$ with z=$\sqrt{s/s_0}$ and $\sqrt{s_0}=10.6 {\rm GeV}$.