Evidence for the decay $B^0 \to J/\psi \omega$ and measurement of the relative branching fractions of $B^0_s$ meson decays to $J/\psi \eta$ and $J/\psi \eta'$

First evidence of the $\mathrm{B}^0\to J/\psi\omega$ decay is found and the $\mathrm{B}_{s}^0\to J/\psi\eta$ and $\mathrm{B}_{s}^0\to J/\psi\eta^{\prime}$ decays are studied using a dataset corresponding to an integrated luminosity of 1.0~$\mathrm{fb}^{-1}$ collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 7$~TeV. The branching fractions of these decays are measured relative to that of the $\mathrm{B}^0\to J/\psi\rho^0$ decay: %The following ratios are measured \begin{equation} \begin{array}{lll} \frac{\mathcal{B}(\mathrm{B}^0\to J/\psi\omega)}{\mathcal{B}(\mathrm{B}^0\to J/\psi\rho^0)} $=$ \:0.89 \pm0.19\,(\mathrm{stat})\,^{+0.07}_{-0.13}\,(\mathrm{syst}),\nonumber \\ \frac{\mathcal{B}(\mathrm{B}^0_s\to J/\psi\eta)}{\mathcal{B}(\mathrm{B}^0\to J/\psi\rho^0)} $=$ \:14.0 \pm 1.2\,(\mathrm{stat})\,^{+1.1}_{-1.5}\,(\mathrm{syst})\,^{+1.1}_{-1.0}\left(\frac{f_\mathrm{d}}{f_\mathrm{s}}\right),\nonumber \\ \frac{\mathcal{B}(\mathrm{B}^0_s\to J/\psi\eta^{\prime})}{\mathcal{B}(\mathrm{B}^0\to J/\psi\rho^0)} $=$ \:12.7\pm1.1\,(\mathrm{stat})\,^{+0.5}_{-1.3}\,(\mathrm{syst})\,^{+1.0}_{-0.9}\left(\frac{f_\mathrm{d}}{f_\mathrm{s}}\right),\nonumber \end{array} \end{equation} where the last uncertainty is due to the knowledge of $f_\mathrm{d}/f_\mathrm{s}$, the ratio of b-quark hadronization factors that accounts for the different production rate of $\mathrm{B}^0$ and $\mathrm{B}^0_s$ mesons. The ratio of the branching fractions of $\mathrm{B}^0_s\to J/\psi\eta^{\prime}$ and $\mathrm{B}^0_s\to J/\psi\eta$ decays is measured to be \begin{equation} \frac{\mathcal{B}(\mathrm{B}^0_s\to J/\psi\eta^{\prime})}{\mathcal{B}(\mathrm{B}^0_s\to J/\psi\eta)} = 0.90\pm0.09\,(\mathrm{stat})\,^{+0.06}_{-0.02}\,(\mathrm{syst}).\nonumber \end{equation}