Definition of the angles in the helicity basis. The polar angle $\theta_K$ $(\theta_e)$ is the angle between the $ K ^+$ ( $ e ^+$ ) momentum and the direction opposite to the $ B ^0_ s $ momentum in the $ K ^+$ $ K ^-$ ( $ e ^+ e ^-$ ) centre-of-mass system, and the $\phi_h$ is the azimuthal angle between the $ K ^+$ $ K ^-$ and $ e ^+ e ^-$ decay planes.

Distribution of $m( e ^+ e ^- K ^+ K ^- )$ for selected $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } \phi $ candidates divided into three categories: (a) zero, (b) one and (c) both electrons with bremsstrahlung correction. The blue solid line shows the total fit which is composed of (red short-dashed line) the signal and the background contributions. The combinatorial background is indicated by the green long-dashed line while the partially reconstructed background from the $ B ^0_ s \rightarrow \psi {(2S)} \phi $ and $ B ^0_ s \rightarrow \chi _{ c 1} (1P)\phi $ decays are indicated by pink and purple dash-dotted lines, respectively.

Distribution of $m( e ^+ e ^- K ^+ \pi ^- )$ for selected $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi } K ^* (892)^0$ candidates divided into three categories: (a) zero, (b) one and (c) both electrons with bremsstrahlung correction. The blue solid line shows the total fit which is composed of (red short-dashed line) the signal and the background contributions. The combinatorial background is indicated by the green long-dashed line while the partially reconstructed background from the $ B ^0 \rightarrow \psi {(2S)} K ^* (892)^0$ , $ B ^0 \rightarrow \chi _{ c 1} (1P) K ^* (892)^0$ and $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi } K_1(1270)^0$ decays are indicated by pink, purple and yellow dash-dotted lines, respectively.

Signal efficiency as a function of the decay time, $\varepsilon ^{ B ^0_ s }_{\mathrm{data}}(t)$, scaled by the average efficiency.

Efficiency projected onto (left) $\cos\theta_K$, (middle) $\cos\theta_e$ and (right) $\phi_h$ obtained from a simulated $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } \phi $ sample, scaled by the average efficiency.

Decay time and helicity-angle distributions for (data points) $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } ($ { $ e ^+ e ^-$ ) $\phi $ } decays with the one-dimensional projections of the PDF extracted in the maximum-likelihood fit. The solid blue line shows the total signal contribution, which is composed of (long-dashed red) $ C P$ -even, (short-dashed green) $ C P$ -odd and (dash-dotted purple) S-wave contributions.

Animated gif made out of all figures.

Definition of angular and time-dependent functions for $ B ^0_ s $ and $\overline{ B } {}^0_ s $ mesons.

Angular acceptance integrals for the simulated sample. The $I_k$ integrals are normalised with respect to the $I_0$ integral.

Results of the maximum-likelihood fit, described in Sec. 6, to the $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } ($ { $ e ^+ e ^-$ ) $\phi $ } decays including all acceptance and resolution effects. The first uncertainty is statistical and the second is systematic.

Statistical and systematic uncertainties. A dash corresponds to systematic uncertainties that are negligible. Systematic uncertainties from different sources are added in quadrature.

Correlation matrix of statistical uncertainties.

Results of the maximum-likelihood fit described in Section 6 to the $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi } ($ { $ e ^+ e ^-$ ) $\phi $ } decays including all acceptance and resolution effects and with the mixing frequency fixed to the PDG value, $\Delta m_{ s } =17.757\text{ ps} ^{-1} $ [15]. The first uncertainty is statistical and the second is systematic, which is discussed in Section 7.

Correlation matrix of statistical uncertainties for a fit with fixed $\Delta m_{ s }$ .

Supplementary material full pdf