Improved measurement of $\eta / \eta^{\prime}$ mixing in $B^{0}_{(s)} \rightarrow J/\psi \eta^{(\prime)}$ decays

Abstract

Branching fraction ratios between the decays $B^{0}_{(s)} \rightarrow J/\psi \eta^{(\prime)}$ are measured using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of $7$, $8$ and $13~\textrm{TeV}$, corresponding to an integrated luminosity of $9~ \textrm{fb}^{-1}$. The measured ratios of these branching fractions are $\frac{BF(B^{0} \rightarrow J/\psi \eta^{\prime})}{BF(B^{0} \rightarrow J/\psi \eta)} = 0.48 \pm 0.06 \pm 0.02 \pm 0.01$ and $\frac{BF(B^{0}_{s} \rightarrow J/\psi \eta^{\prime})}{BF(B^{0}_{s} \rightarrow J/\psi \eta)} = 0.80 \pm 0.02 \pm 0.02 \pm 0.01$, where the uncertainties are statistical, systematic and related to the precision of the $\eta^{(\prime)}$ branching fractions, respectively. They are used to constrain the $\eta/\eta^{\prime}$ mixing angle, $\phi_{P}$, and to probe the presence of a possible glueball component in the $\eta^{\prime}$ meson, described by the gluonic mixing angle $\phi_{G}$. The obtained results are $\phi_{P} = (41.6^{+1.0}_{-1.2})^\circ$ and $\phi_{G} = (28.1^{+3.9}_{-4.0})^\circ$, where the uncertainties are statistically dominated. While the value of $\phi_{P}$ is compatible with existing experimental determinations and theoretical calculations, the angle $\phi_{G}$ differs from zero by more than four standard deviations, which points to a substantial glueball component in the $\eta^{\prime}$ meson and/or unexpectedly large contributions from gluon-mediated processes in these decays. The absolute branching fractions are also measured relative to that of the well-established $B^{0}_{s} \rightarrow J/\psi\phi$ decay, which serves as the normalisation channel. These results supersede the previous LHCb measurements and are the most precise to date.