Search for light tetraquark states in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays.

We search for the $J^{PC}=0^{--}$ and $1^{+-}$ light tetraquark states with masses up to 2.46~GeV/$c^2$ in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays with data samples of $(102\pm 2)$ million and $(158\pm 4)$ million events, respectively, collected with the Belle detector. No significant signals are observed in any of the studied production modes, and 90\% credibility level (C.L.) upper limits on their branching fractions in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays are obtained. The inclusive branching fractions of the $\Upsilon(1S)$ and $\Upsilon(2S)$ decays into final states with $f_1(1285)$ are measured to be ${\cal B}(\Upsilon(1S)\to f_1(1285)+anything)=(46\pm28({\rm stat.})\pm13({\rm syst.}))\times 10^{-4}$ and ${\cal B}(\Upsilon(2S)\to f_1(1285)+anything)=(22\pm15({\rm stat.})\pm6.3({\rm syst.}))\times 10^{-4}$. The measured $\chi_{b2} \to J/\psi + anything$ branching fraction is measured to be $(1.50\pm0.34({\rm stat.})\pm0.22({\rm syst.}))\times 10^{-3}$, and 90\% C.L. upper limits for the $\chi_{b0,b1} \to J/\psi + anything$ branching fractions are found to be $2.3\times 10^{-3}$ and $1.1\times 10^{-3}$, respectively. For ${\cal B}(\chi_{b1} \to \omega + anything)$, the branching fraction is measured to be $(4.9\pm1.3({\rm stat.})\pm0.6({\rm syst.}))\times 10^{-2}$. %(%CONTENT%lt;3.68\times 10^{-2}$ at 90\% C.L.). All results reported here are the first measurements for these modes.