Radiative decays of bottomonia into charmonia and light mesons

In the framework of nonrelativistic QCD, we study the radiative decays of bottomonia into charmonia, including $\Upsilon\to \chi_{cJ}\gamma$, $\Upsilon\to \eta_c\gamma$, $\eta_b\to J/\psi\gamma$, and $\chi_{bJ}\to J/\psi\gamma$. We give predictions for their branching ratios with numerical calculations. E.g., we predict the branching ratio for $\eta_b\to J/\psi\gamma$ is about $1\times 10^{-7}$. As a phenomenological model study, we further extend our calculation to the radiative decays of bottomonia into light mesons by assuming the $f_2(1270)$, $f_2'(1525)$ and other light mesons to be described by nonrelativistic $q\bar q ~(q=u,d,s)$ bound states with constituent quark masses. The calculated branching ratios for $\Upsilon\to f_2(1270)\gamma$ and $\Upsilon\to f_2'(1525)\gamma$ are roughly consistent with the CLEO data. Comparisons with radiative decays of charmonium into light mesons such as $J/\psi\to f_2(1270)\gamma$ are also given. In all calculations the QED contributions are taken into account and found to be significant in some processes.