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

Abstract

The large decay rate observed by Belle for $B^{+}\to \psi (3770)K^{+}$, which is comparable to $B^{+}\to \psi (3686)K^{+}$, might indicate either an unexpectedly large S-D mixing angle $|\theta |\approx 40^o$ or the leading role of the color-octet mechanism in D-wave charmonium production in B decay. By calculating the production rate of $\psi (3770)$ 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 $\Gamma (\psi (3770)\to \gamma {\chi }_{c2})/\Gamma (\psi (3770)\to \gamma {\chi }_{c1})$ may dramatically change from $\sim$ 0.04 (for $\theta \approx 0^o$) to $\sim$ 200 (for $\theta \approx -40^o$) due to the large S-D interference effect, thus the E1 transition measurement of $\psi (3770)$ at BES and CLEO-c will also be very useful in clarifying this issue.

Comments: final version to appear in Phys.Rev.D, discussion on uncertainties associated with the color-octet matrix elements is added, 16 pages, 2 figures