Distributions of the BDT variable for both training and test samples of $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi\pi$ signal and background events. The signal samples are from simulation and the background samples derived from data.

Mass distribution of the selected $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ combinations in the $f_{\rm odd}$ region. The blue solid curve shows the result of a fit with a double Gaussian signal (red solid curve) and several background components: combinatorial background (brown dotted line), background from $B^-\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^-$ and $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^-$ (green short-dashed line), $\overline{ B }{} ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ (purple dot-dashed), $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \eta'$ and $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ when $\phi\rightarrow \pi^+\pi^-\pi^0$ (black dot-long-dashed), and $\overline{ B }{} ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K^- \pi^+$ (light-blue long-dashed).

Mass distribution of selected $\pi^+\pi^-$ combinations shown as the (solid black) histogram for events in the $\overline{ B }{} ^0_ s $ signal region. The (dashed red) line shows the background determined by fitting the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ mass in bins of $\pi^+\pi^-$ mass. The arrows designate the limits of the $f_{\rm odd}$ region.

Decay time distribution of prompt $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ candidates in the $f_0$ region. The dashed (red) line shows the long-lived component, and the solid curve the total.

Distribution of the estimated time resolution $\sigma_t$ for opposite-sign $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ signal events after background subtraction, and for like-sign background.

(a) Mass distribution of $\overline{ B }{} ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \overline{ K }{} ^{*0} $ candidates. The dashed (red) line shows the background, and the solid (blue) curve the total. (b) Decay time distribution, where the small background has been subtracted using the $\overline{ B }{} ^0 $ mass sidebands. The (blue) curve shows the lifetime fit.

Decay time distribution of $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} f_0$ candidates fitted with a single exponential function multiplied by the acceptance and convolved with the resolution. The dashed line is signal and the shaded area background.

Log-likelihood difference as a function of $\phi_s$ for $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} f_{\rm odd}$ events.

Decay time distribution of $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} f_{\rm odd}$ candidates. The solid line shows the result of the fit, the dashed line shows the signal, and the shaded region the background.

$ C P$ asymmetry as a function of decay time modulo $2\pi/\Delta m_s$. The curve shows the expectation for $\phi_s=-0.019$ rad.

Animated gif made out of all figures.

Resonance fractions in $\overline{ B }{} ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ over the full mass range [11]. The final-state helicity of the D-wave is denoted by $\Lambda$. Only statistical uncertainties are quoted.

Parameters of the decay time resolution function determined from fits to $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \pi^+\pi^-$ prompt data samples.

Parameters used in the functions for the invariant mass and decay time describing the signal and background. These parameters are fixed to their central values in the fit for $\phi_s$.

Summary of systematic uncertainties on $\phi_s$. Quantities fixed in the fit that are not included here give negligible uncertainties. The total uncertainty is found by adding in quadrature all the positive and negative contributions separately.