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.

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

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Cited by in corpus (8)

• Weak productions of new charmonium in semi-leptonic decays of B_c
• The mass spectrum and wave functions of the $B_c$ system
• Modeling Charmonium-$\eta$ Decays of $J^{PC}=1^{--}$ Higher Charmonia
• Possible large branching fraction of psi(3770) decays to charmless final states
• ${\alpha }_s{v}^2$ corrections to ${\eta }_c$ and ${\chi }_{cJ}$ production recoiled with a photon at $e^{+}{e}^{-}$ colliders
• $\psi (3770)$ and $B$ meson exclusive decay $B\to \psi (3770)K$ in QCD factorization
• $B_u$ $\to$ $\psi M$ decays and $S$-$D$ wave mixing effects
• Observation of the decay $\psi (3686)\to {\Sigma }^{-}{\bar{\Sigma }}^{+}$ and measurement of its angular distribution