Feynman diagrams for (a) $\overline{ B }{} ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $, and (b) $\overline{ B }{} ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$.

Distribution of the BDT classifier for both training and test samples of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ signal and background events. The signal samples are from simulation and the background samples are from data. The small difference between the background training and test samples is due to the fact that the sidebands used in the two cases are not identical.

Invariant mass of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ combinations. The data are fitted with a sum of two Gaussian functions for each signal peak and several background components. The (magenta) solid double-Gaussian function centered at 5280 MeV is the $\overline{ B }{} ^0 $ signal, the (black) dotted curve shows the combinatorial background, the (green) dashed-dot-dot curve shows the contribution of $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ decays, the (violet) dashed shape is the $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ \pi^0 K ^- $ background, $\Lambda ^0_ b \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p K ^- $ and $\overline{ B }{} ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^- \pi ^+ $ reflections are shown by (red) dot-dashed and (cyan) long dashed shapes, respectively and the (blue) solid curve is the total.

Fit to the invariant mass spectrum of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^- $ combinations. The (blue) solid curve is the total and the (black) dotted line shows the combinatorial background.

Distribution of $m^2( K ^+ K ^- )$ versus $m^2( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ )$ for $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ candidates with mass within $\pm 20$ MeV of the $\overline{ B }{} ^0 $ mass.

Exponential fit to the acceptance parameter $a(s_{23})$.

Parametrized detection efficiency as a function of $m^2( K ^+ K ^- )$ versus $ m^2( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ )$. The $z$-axis scale is arbitrary.

Projections of (a) $m^2( K ^+ K ^- )$ and (b) $ m^2( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ )$ of the simulated Dalitz plot used to measure the efficiency parameters. The points represent the simulated event distributions, and the curves the projections of the polynomial fit.

Invariant mass squared projections of (a) $K^+K^-$, and (b) $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^{+}$ from the Dalitz plot of candidates in the $\overline{ B }{} ^0$ mass sidebands, with fit projection overlaid.

Distribution of $\cos \theta_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ from the $\overline{ B }{} ^0$ mass sidebands, fitted with the function $1+\alpha \cos^{2} \theta_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$.

Projections of the reflection background in the variables (a) $ m^2(K^+K^-)$ and (b) $ m^2( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^{+})$.

Distribution of $\cos \theta_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ for the reflection background, fitted with the function $1+\beta \cos^{2} \theta_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$.

Dalitz plot fit projection of $m^2( K ^+ K ^- )$ in the signal region. The points with error bars are data, the (black) dotted curve shows the combinatorial background, the (red) dashed curve indicates the reflection from the misidentified $\Lambda ^0_ b \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p K ^- $ decays, the (green) dot-dashed curve is the signal, and the (blue) solid line represents the total.

Dalitz plot fit projections of (a) $m^2( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^{+})$ and (b) $\cos \theta_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ in the signal region. The points with error bars are data, the (black) dotted curve shows the combinatorial background, the (red) dashed curve indicates the reflection from the misidentified $\Lambda ^0_ b \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} p K ^- $ decays, the (green) dot-dashed curve is the signal, and the (blue) solid line represents the total.

Background-subtracted $m( K ^+ K ^- )$ distributions for (a) default and, (b) alternate fit models in the signal region. The points with error bars are data, the (magenta) dashed curve shows the $a_0(980)$ resonance, the nonresonant contribution is shown by (green) dot-dashed curve and the (blue) solid curve represents the sum of $a_0(980)$, nonresonant and the interference between the two. The (red) long-dashed curve in (a) shows the $f_0(980)$ contribution.

Background-subtracted and efficiency-corrected distribution of (a) $ \cos\theta_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ ($\chi^2/\rm ndf=5.3/10$) and (b) $\cos \theta_{KK}$ ($\chi^2/\rm ndf=12.8/10$). The points with error bars are data and the (blue) solid lines show the fit to the default model.

Animated gif made out of all figures.

Fit fractions and phases of the contributing components. The components of the form $\rm X+Y$ are the interference terms. Note that, in the default model the $f_0(980)$ amplitude strength is fixed to the expected value. Poisson likelihood $\chi^2$ [24] is used to calculate the $\chi^2$.

Relative systematic uncertainties on branching fractions (%).