Study of $η-η^{\prime}$ mixing from measurement of $B^0_{(s)} \rightarrow J/ψη^{(\prime)}$~decay rates

A study of $B^0$~and $B^0_s$ meson decays into $J/ψη$~and $J/ψη^{\prime}$ 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 $B^0 \rightarrow J/ψη^{\prime}$ is observed for thefirst time. The following ratios of branching fractions are measured: $$ \frac{\mathcal{B}(B^0 \rightarrow J/ψη^{\prime})}{\mathcal{B}(B^0_s \rightarrow J/ψη^{\prime})} = (2.28\pm0.65\,(stat)\,\pm0.10\,(syst)\,\pm0.13\,(f_{s}/f_{d}))\times10^{-2},$$ $$ \frac{\mathcal{B}(B^0 \rightarrow J/ψη)}{\mathcal{B}(B^0_s \rightarrow J/ψη)} = (1.85\pm0.61\,(stat)\,\pm0.09\,(syst)\,\pm0.11\,(f_{s}/f_{d}))\times10^{-2},$$ 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 $η-η^{\prime}$ meson mixing. In addition, the first evidence for the decay $B^0_s \rightarrow ψ(2S) η^{\prime}$ is reported, and the relative branching fraction is measured, $$\frac{\mathcal{B}(B^0_s \rightarrow ψ(2S) η^{\prime})}{\mathcal{B}(B^0_s \rightarrow J/ψη^{\prime})} = (38.7\pm9.0\,(stat)\,\pm1.3\,(syst)\,\pm0.9(\mathcal{B}))\times10^{-2},$$ where the third uncertainty is due to the limited knowledge of the branching fractions of $J/ψ$ and $ψ(2S)$~mesons.