# Study of $\eta-\eta'$ mixing from measurement of $B^0_{(s)}\to J/\psi\eta^{(')}$ decay rates

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## Abstract

A study of $B^0$ and $B^0_s$ meson decays into $J/\psi\eta$ and $J/\psi\eta^{\prime}$ 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: $$\frac{\mathcal{B}(B^0 \rightarrow J/\psi \eta^{\prime})}{\mathcal{B}(B^0_s \rightarrow J/\psi \eta^{\prime})} = (2.28\pm0.65\,(stat)\,\pm0.10\,(syst)\,\pm0.13\,(f_{s}/f_{d}))\times10^{-2},$$ $$\frac{\mathcal{B}(B^0 \rightarrow J/\psi \eta)}{\mathcal{B}(B^0_s \rightarrow J/\psi \eta)} = (1.85\pm0.61\,(stat)\,\pm0.09\,(syst)\,\pm0.11\,(f_{s}/f_{d}))\times10^{-2},$$ 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 $\eta-\eta^{\prime}$ 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, $$\frac{\mathcal{B}(B^0_s \rightarrow \psi(2S) \eta^{\prime})}{\mathcal{B}(B^0_s \rightarrow J/\psi \eta^{\prime})} = (38.7\pm9.0\,(stat)\,\pm1.3\,(syst)\,\pm0.9(\mathcal{B}))\times10^{-2},$$ where the third uncertainty is due to the limited knowledge of the branching fractions of $J/\psi$ and $\psi(2S)$ mesons.

## Figures and captions

 Leading-order Feynman diagrams for the decays $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta ^{(\prime)}$. Fig_1.pdf [55 KiB] HiDef png [75 KiB] Thumbnail [15 KiB] *.C file tex code Mass distributions of (a) $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta ^{\prime}$ and (b) $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta$ candidates. The decays $\eta ^{\prime} \!\rightarrow \eta \pi ^+ \pi ^-$ and $\eta \!\rightarrow \pi ^+ \pi ^- \pi ^0$ are used in the reconstruction of ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta ^{\prime}$ and ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta$ candidates, respectively. The total fit function (solid blue) and the combinatorial background contribution (dashed black) are shown. The long-dashed red line represents the signal $B ^0_ s$ contribution and the yellow shaded area shows the $B ^0$ contribution. Fig_2.pdf [94 KiB] HiDef png [184 KiB] Thumbnail [42 KiB] *.C file tex code Background subtracted ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow \mu ^+\mu ^-$ (a,b), $\eta ^{\prime} \!\rightarrow \eta \pi ^+ \pi ^-$ (c,d) and $\eta \!\rightarrow \gamma \gamma$ (e,f) mass distributions in $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta ^{\prime}$ decays. The figures (a,c,e) correspond to $B ^0_ s$ decays and the figures (b,d,f) correspond to $B ^0$ decays. The solid curves represent the total fit functions. Fig_3.pdf [133 KiB] HiDef png [498 KiB] Thumbnail [155 KiB] *.C file tex code Background subtracted ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \rightarrow \mu ^+\mu ^-$ (a,b), $\eta \!\rightarrow \pi ^+ \pi ^- \pi ^0$ (c,d) and $\pi ^0 \!\rightarrow \gamma \gamma$ (e,f) mass distributions in $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta$ decays. The figures (a,c,d) correspond to $B ^0_ s$ decays and the figures (b,d,f) correspond to $B ^0$ decays. The solid curves represent the total fit functions. Fig_4.pdf [128 KiB] HiDef png [461 KiB] Thumbnail [143 KiB] *.C file tex code Mass distributions of (a) $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta ^{\prime}$ and (b) $B ^{0}_{(\mathrm{s})} \!\rightarrow \psi {\mathrm{(2S)}} \eta ^{\prime}$ candidates, where the $\eta ^{\prime}$ state is reconstructed using the $\eta ^{\prime} \!\rightarrow \rho ^0 \gamma$ decay. The total fit function (solid blue) and the combinatorial background contribution (short-dashed black) are shown. The long-dashed red line shows the signal $B ^0_ s$ contribution and the yellow shaded area corresponds to the $B ^0$ contribution. The contribution of the reflection from $B ^0 \rightarrow \psi K ^{*0}$ decays is shown by the green dash-dotted line. Fig_5.pdf [108 KiB] HiDef png [242 KiB] Thumbnail [57 KiB] *.C file tex code Background subtracted $\psi \rightarrow \mu ^+\mu ^-$ (a,b) and $\eta ^{\prime} \rightarrow \pi ^+ \pi ^- \gamma$ (c,d) mass distributions in $B ^0_ s \!\rightarrow \psi \eta ^{\prime}$ decays. The figures (a,c) correspond to the ${ J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ channel, and the figures (b,d) correspond to the $\psi {\mathrm{(2S)}}$ channel. The solid curves represent the total fit functions. Fig_6.pdf [106 KiB] HiDef png [320 KiB] Thumbnail [101 KiB] *.C file tex code Confidence regions derived from the likelihood function $\mathcal{L}\left(\varphi_{\rm{P}} ,\left|\varphi_{\rm{G}} \right|\right)$. The contours corresponding to $-2\Delta\ln\mathcal{L}=2.3,\,6.2$ and $11.8$ are shown with dotted\,green, dashed\,blue and solid\,red lines. Fig_7.pdf [74 KiB] HiDef png [185 KiB] Thumbnail [50 KiB] *.C file tex code Animated gif made out of all figures. PAPER-2014-056.gif Thumbnail

## Tables and captions

 Mixing angles $\varphi_{\rm{G}}$ and $\varphi_{\rm{P}}$ (in degrees). The third column corresponds to measurements where the gluonic component is neglected. Total uncertainties are quoted. Table_1.pdf [51 KiB] HiDef png [46 KiB] Thumbnail [8 KiB] tex code Fit results for the numbers of signal events ($N_{ B ^{0}_{(\mathrm{s})} }$), $B ^0_ s$ signal peak position (${m_0}$) and mass resolution ($\sigma$) in $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta ^{\prime}$ and $B ^{0}_{(\mathrm{s})} \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta$ decays, followed by $\eta ^{\prime} \!\rightarrow \eta \pi ^+ \pi ^-$ and $\eta \!\rightarrow \pi ^+ \pi ^- \pi ^0$ decays, respectively. The quoted uncertainties are statistical only. Table_2.pdf [57 KiB] HiDef png [38 KiB] Thumbnail [7 KiB] tex code Fitted values of the number of signal events ($N_{ B ^{0}_{(\mathrm{s})} }$), $B ^0_ s$ signal peak position (${m_0}$) and mass resolution ($\sigma$) in $B ^{0}_{(\mathrm{s})} \!\rightarrow \psi \eta ^{\prime}$ decays, followed by the $\eta ^{\prime} \!\rightarrow \rho ^0 \gamma$ decay. The quoted uncertainties are statistical only. Table_3.pdf [72 KiB] HiDef png [37 KiB] Thumbnail [6 KiB] tex code Ratios of the total efficiencies as defined in Eqs. 5--7. The quoted uncertainties are statistical only and reflect the sizes of the simulated samples. Table_4.pdf [51 KiB] HiDef png [107 KiB] Thumbnail [15 KiB] tex code Systematic uncertainties (in %) of the ratios of the branching fractions. Table_5.pdf [46 KiB] HiDef png [69 KiB] Thumbnail [11 KiB] tex code

Created on 23 February 2019.Citation count from INSPIRE on 23 February 2019.