A study of $B^0$~and $B^0_s$ meson decays into $J/psieta$~and $J/psieta^{prime}$ final states is performed using a data set of proton-proton collisions at centre-of-mass energies of 7 and 8TeV, collected by the LHCb experiment and corresponding to 3.0fb$^{-1}$ of integrated luminosity. The decay $B^0 rightarrow J/psi eta^{prime}$ is observed for thefirst time. The following ratios of branching fractions are measured: $$ frac{mathcal{B}(B^0 rightarrow J/psi eta^{prime})}{mathcal{B}(B^0_s rightarrow J/psi eta^{prime})} = (2.28pm0.65,(stat),pm0.10,(syst),pm0.13,(f_{s}/f_{d}))times10^{-2},$$ $$ frac{mathcal{B}(B^0 rightarrow J/psi eta)}{mathcal{B}(B^0_s rightarrow J/psi eta)} = (1.85pm0.61,(stat),pm0.09,(syst),pm0.11,(f_{s}/f_{d}))times10^{-2},$$ where the third uncertainty is related to the present knowledge of $f_{s}/f_{d}$, the ratio between the probabilities for a $b$ quark to form a $B^0_s$ or $B^0$ meson. The branching fraction ratios are used to determine the parameters of $eta-eta^{prime}$ meson mixing. In addition, the first evidence for the decay $B^0_s rightarrow psi(2S) eta^{prime}$ is reported, and the relative branching fraction is measured, $$frac{mathcal{B}(B^0_s rightarrow psi(2S) eta^{prime})}{mathcal{B}(B^0_s rightarrow J/psi eta^{prime})} = (38.7pm9.0,(stat),pm1.3,(syst),pm0.9(mathcal{B}))times10^{-2},$$ where the third uncertainty is due to the limited knowledge of the branching fractions of $J/psi$ and $psi(2S)$~mesons.
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