The decays of $B_s^0$ and $\overline{B}_s^0$ mesons into the $J/\psi K^+K^$ final state are studied in the $K^+K^$ mass region above the $\phi(1020)$ meson in order to determine the resonant substructure and measure the $CP$violating phase, $\phi_s$, the decay width, $\Gamma_s$, and the width difference between light and heavy mass eigenstates, $\Delta\Gamma_s$. A decaytime dependent amplitude analysis is employed. The data sample corresponds to an integrated luminosity of $3{\rm fb}^{1}$ produced in 7 and 8 Tev $pp$ collisions at the LHC, collected by the LHCb experiment. The measurement determines $\phi_s = 119\pm107\pm34 {\rm mrad}$. A combination with previous LHCb measurements using similar decays into the $J/\psi \pi^+\pi^$ and $J/\psi\phi(1020)$ final states gives $\phi_s=1\pm37 {\rm mrad}$, consistent with the Standard Model prediction.
Definition of the helicity angles. 
Fig1new.pdf [8 KiB] HiDef png [34 KiB] Thumbnail [19 KiB] *.C file 

Fits to invariant mass distributions of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+K^$ combinations after subtraction of the two reflection backgrounds for (a) $m_{KK}<1.05$ $\mathrm{ Ge V}$ and (b) $m_{KK}>1.05$ $\mathrm{ Ge V}$ . Total fits are shown by solid (blue) lines, the signal by dashed (black) lines, and the combinatorial background by darkened regions. Note that the combinatorial background in (a) is too small to be easily visible. 
Fig2a.pdf [22 KiB] HiDef png [175 KiB] Thumbnail [158 KiB] *.C file 

Fig2b.pdf [22 KiB] HiDef png [214 KiB] Thumbnail [203 KiB] *.C file 

Invariant mass squared of $K^+K^$ versus $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+$ for $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+K^$ candidates within $\pm15$ $\mathrm{ Me V}$ of the $ B ^0_ s $ mass peak. The high intensity $\phi(1020)$ resonance band is shown with a line (light green). 
Fig3.pdf [159 KiB] HiDef png [1 MiB] Thumbnail [588 KiB] *.C file 

Scaled decaytime efficiency $\varepsilon_{\rm data}^{ B ^0_ s }(t)$ in arbitrary units (a.u.) for (a) the $\phi(1020)$ region and (b) the highmass region. 
Fig4a.pdf [17 KiB] HiDef png [145 KiB] Thumbnail [145 KiB] *.C file 

Fig4b.pdf [17 KiB] HiDef png [145 KiB] Thumbnail [147 KiB] *.C file 

Efficiencies projected onto (a) $m_{KK}$, (b) $\cos \theta_{KK}$, (c) $\cos \theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ and (d) $\chi$ in arbitrary units (a.u.), obtained from simulation of $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ K ^ $ phasespace decays (points with error bars), while the curves show the parameterization from the efficiency model. 
Fig5a.pdf [17 KiB] HiDef png [132 KiB] Thumbnail [128 KiB] *.C file 

Fig5b.pdf [16 KiB] HiDef png [134 KiB] Thumbnail [130 KiB] *.C file 

Fig5c.pdf [16 KiB] HiDef png [131 KiB] Thumbnail [129 KiB] *.C file 

Fig5d.pdf [16 KiB] HiDef png [122 KiB] Thumbnail [119 KiB] *.C file 

Projections of the fitting variables in the (left) lowmass ($\phi(1020)$) and (right) highmass regions shown by the solid (blue) curves. The points with error bars are the data. At the bottom of each figure the differences between the data and the fit divided by the uncertainty in the data are shown. 
Fig6l1.pdf [23 KiB] HiDef png [224 KiB] Thumbnail [175 KiB] *.C file 

Fig6r1.pdf [24 KiB] HiDef png [249 KiB] Thumbnail [188 KiB] *.C file 

Fig6l2.pdf [23 KiB] HiDef png [195 KiB] Thumbnail [159 KiB] *.C file 

Fig6r2.pdf [23 KiB] HiDef png [190 KiB] Thumbnail [148 KiB] *.C file 

Fig6l3.pdf [22 KiB] HiDef png [187 KiB] Thumbnail [153 KiB] *.C file 

Fig6r3.pdf [21 KiB] HiDef png [184 KiB] Thumbnail [145 KiB] *.C file 

Fig6l4.pdf [22 KiB] HiDef png [181 KiB] Thumbnail [153 KiB] *.C file 

Fig6r4.pdf [22 KiB] HiDef png [188 KiB] Thumbnail [167 KiB] *.C file 

Fig6l5.pdf [25 KiB] HiDef png [213 KiB] Thumbnail [175 KiB] *.C file 

Fig6r5.pdf [26 KiB] HiDef png [228 KiB] Thumbnail [185 KiB] *.C file 

Fit projection of $m_{KK}$. The points represent the data; the resonances $\phi(1020)$, $f_2^\prime(1525)$, $\phi(1680)$ are shown by magenta, brown, and cyan longdashed curves, respectively; the Swave component is depicted by green longdashed curves; the other $f_2$ resonances are described by black solid curves; and the total fit by a blue solid curve. At the bottom the differences between the data and the fit divided by the uncertainty in the data are shown. 
Fig_7_new.pdf [28 KiB] HiDef png [369 KiB] Thumbnail [268 KiB] *.C file 

The $K^+K^$ mass dependence of the spherical harmonic moments of $\cos \theta_{KK}$ in the region of the $\phi(1020)$ resonance after efficiency corrections and background subtraction. The points with error bars are the data points and the (blue) lines are derived from the fit model. 
SPH_phi0.pdf [12 KiB] HiDef png [151 KiB] Thumbnail [148 KiB] *.C file 

SPH_phi2.pdf [13 KiB] HiDef png [137 KiB] Thumbnail [129 KiB] *.C file 

SPH_phi4.pdf [14 KiB] HiDef png [149 KiB] Thumbnail [149 KiB] *.C file 

The $K^+K^$ mass dependence of the spherical harmonic moments of $\cos \theta_{KK}$ above the $\phi(1020)$ resonance region after efficiency corrections and background subtraction. The points with error bars are the data points and the (blue) lines are derived from the fit model. 
SPH0.pdf [12 KiB] HiDef png [160 KiB] Thumbnail [139 KiB] *.C file 

SPH2.pdf [13 KiB] HiDef png [165 KiB] Thumbnail [149 KiB] *.C file 

SPH4.pdf [14 KiB] HiDef png [172 KiB] Thumbnail [166 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2017008.gif Thumbnail 
BreitWigner resonance parameters. 
Table_1.pdf [62 KiB] HiDef png [94 KiB] Thumbnail [48 KiB] tex code 

Fit results for the $ B ^0_ s $ decay observables in the high $m_{KK}$ region. 
Table_2.pdf [50 KiB] HiDef png [82 KiB] Thumbnail [38 KiB] tex code 

Fit results of the resonant structure. 
Table_3.pdf [54 KiB] HiDef png [94 KiB] Thumbnail [47 KiB] tex code 

Fitted phase differences between two transversity states (statistical uncertainty only). Here the symbol $\phi$ refers to the components of the $\phi(1020)$ meson. 
Table_4.pdf [45 KiB] HiDef png [313 KiB] Thumbnail [144 KiB] tex code 

Absolute systematic uncertainties for the physics parameters determined from the high $m_{KK}$ region compared to the corresponding statistical uncertainty. Here $M_0$ and $\Gamma_0$ refer to the uncertainties on the $f_2^\prime(1525)$ resonance mass and width. 
Table_5.pdf [74 KiB] HiDef png [103 KiB] Thumbnail [50 KiB] tex code 

Combined systematic and statistical uncertainties in the fit fractions using an absolute scale where the numbers are in units of %. "Res. modelling" refers to resonance modelling. 
Table_6.pdf [57 KiB] HiDef png [67 KiB] Thumbnail [32 KiB] tex code 

The correlation matrix from the highmass region fit, taking into account both statistical and systematic uncertainties. 
Table_7.pdf [32 KiB] HiDef png [54 KiB] Thumbnail [25 KiB] tex code 

The correlation matrix taking into account both statistical and systematic uncertainties for the combination of the three measurements $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^+K^$ for $m_{KK}>1.05$ GeV, $m_{KK}<1.05$ GeV, and $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$. 
Table_8.pdf [31 KiB] HiDef png [52 KiB] Thumbnail [24 KiB] tex code 
Created on 17 August 2019.Citation count from INSPIRE on 20 August 2019.