Measurement of branching fractions for B \to J/\psi \eta K decays and search for a narrow resonance in the J/\psi \eta final state

We report an observation of the $B^{\pm }\to J\mathrm{/}\psi \eta K^{\pm }$ and $B^0 \to J/\psi \eta K^0_S$decaysusing772$\times 10^{6}$ $B\bar{B}$ pairs collected at the $\mathrm{{\rm Y}}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We obtain the branching fractions ${\cal B}(B^{\pm}\rightarrow J/\psi\eta K^{\pm})=(1.27\pm 0.11{\rm (stat.)\pm 0.11{\rm (syst.)})}\times10^{-4}$and${\cal B}(B^0\to J/\psi \eta K^0_S)=(5.22 \pm 0.78 {\rm(stat.)} \pm 0.49{\rm(syst.)})\times10^{-5}$. We search for a new narrow charmonium(-like) state $X$ in the $J\mathrm{/}\psi \eta$ mass spectrum and find no significant excess. We set upper limits on the product of branching fractions, $\mathcal{B}(B^{\pm }\to X{K}^{\pm })\mathcal{B}(X\to J\mathrm{/}\psi \eta )$, at 3872 MeV$\mathrm{/}{c}^2$ where a $C$-odd partner of X(3872) may exist, at $\psi (4040)$ and $\psi (4160)$ assuming their known mass and width, and over a range from 3.8 to 4.8 GeV$\mathrm{/}{c}^2$. % at a 5 MeV$\mathrm{/}{c}^2$ step. The obtained upper limits at 90% confidence level for $X^{C-\mathrm{o}\mathrm{d}\mathrm{d}}(3872)$, $\psi (4040)$ and $\psi (4160)$ are 3.8$\times 10^{-6}$,15.5$\times 10^{-6}$and7.4$\times 10^{-6}$, respectively.