We calculate the decay rate of bottomonium to two charm-quark jets ${\rm Y}\to c\overline{c}$ at the tree level and one-loop level including color-singlet and color-octet $b\overline{b}$ annihilations. We find that the short-distance coefficient of the color-octet piece is much larger than the color-singlet piece, and that the QCD correction will change the end point behavior of the charm quark jet. The color-singlet piece is strongly affected by the one-loop QCD correction. In contrast, the QCD correction to the color-octet piece is weak. Once the experiment can measure the branching ratio and energy distribution of the two charm-quark jets in the ${\rm Y}$ decay, the result can be used to test the color-octet mechanism or give a strong constraint on the color-octet matrix elements.

• Received 21 August 2008

DOI:https://doi.org/10.1103/PhysRevD.78.094017