Exclusive Double Charmonium Production from $\Upsilon$ Decay

Understand

The exclusive decay of $\Upsilon$ to a vector plus pseudoscalar charmonium is studied in perturbative QCD.

• The corresponding branching ratios are predicted to be of order $10^{-6}$ for first three $\Upsilon$ resonances, and we expect these decay modes should be discovered in the prospective high-luminosity $e^+e^-$ facilities such as super $B$ experiment.
• As a manifestation of the short-distance loop contribution, the relative phases among strong, electromagnetic and radiative decay amplitudes can be deduced.
• It is particularly interesting to find that the relative phase between strong and electromagnetic amplitudes is nearly orthogonal.