Υdecay to two charm-quark jets as a probe of the color-octet mechanism

Abstract

We calculate the decay rate of bottomonium to two charm-quark jets $\ensuremath{\Upsilon}\ensuremath{\rightarrow}c\overline{c}$ 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 $\ensuremath{\Upsilon}$ decay, the result can be used to test the color-octet mechanism or give a strong constraint on the color-octet matrix elements.