Inclusive decays of ${\eta }_b$ into $S$- and $P$-wave charmonium states

Abstract

Inclusive S- and P-wave charmonium productions in the bottomonium ground state ${\eta }_b$ decay are calculated at the leading order in the strong coupling constant ${\alpha }_s$ and quarkonium internal relative velocity $v$ in the framework of the NRQCD factorization approach. We find the contribution of ${\eta }_b\to {\chi }_{c_J}+gg$ followed by ${\chi }_{c_J}\to J/\psi +\gamma$ is also very important to the inclusive $J/\psi$ production in the ${\eta }_b$ decays, which maybe helpful to the investigation of the color-octet mechanism in the inclusive $J/\psi$ production in the ${\eta }_b$ decays in the forthcoming LHCb and SuperB. As a complementary work, we also study the inclusive production of ${\eta }_c$, and ${\chi }_{cJ}$ in the ${\eta }_b$ decays, which may help us understand the X(3940) and X(3872) states.

Comments: 7 pages, 2 figures