S-D mixing and $ψ(3770)$ production in $e^+e^-$ annihilation and B decay and its radiative transitions

Abstract

The large decay rate observed by Belle for $B^+\toψ(3770)K^+$, which is comparable to $B^+\toψ(3686)K^+$, might indicate either an unexpectedly large S-D mixing angle $|θ|\approx 40^o$ or the leading role of the color-octet mechanism in D-wave charmonium production in B decay. By calculating the production rate of $ψ(3770)$ in the continuum $e^+e^-$ annihilation at $\sqrt{s}=10.6$ GeV with these two possible approaches (i.e. the large S-D mixing and the color-octet mechanism), we show that the measurement for this process at Belle and BaBar may provide a clear cut clarification for the two approaches. In addition, the radiative E1 transition ratio $Γ(ψ(3770)\to γχ_{c2})/Γ(ψ(3770)\to γχ_{c1})$ may dramatically change from $\sim$ 0.04 (for $θ\approx 0^o$) to $\sim$ 200 (for $θ\approx -40^o$) due to the large S-D interference effect, thus the E1 transition measurement of $ψ(3770)$ at BES and CLEO-c will also be very useful in clarifying this issue.