An amplitude analysis of the final state structure in the Bs>J/\psi K+K decay mode is performed using 1.0/fb of data collected by the LHCb experiment in 7 TeV centerofmass energy pp collisions produced by the LHC. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. Resonant structures are observed in the K+K mass spectrum as well as a significant nonresonant Swave contribution. The largest resonant component is the \phi(1020), accompanied by f0(980), f'2(1525), and four additional resonances. The overall branching fraction is measured to be B(Bs>J/\psi K+K)=(7.70 +/0.08 +/ 0.39 +/ 0.60)x 10^(4), where the first uncertainty is statistical, the second systematic, and the third due to the ratio of the number of Bs to B mesons produced. The mass and width of the f'2(1525) are measured to be 1522.2 +/ 2.8^{+5.3}_{2.0} MeV and 84 +/ 6^{+10}_{5} MeV, respectively. The final state fractions of the other resonant states are also reported.
Leading order diagram for $\overline{ B }{} ^0_ s \rightarrow J/\psi K ^+ K ^ $. 
BstoJpsiKK.pdf [75 KiB] HiDef png [139 KiB] Thumbnail [194 KiB] *.C file 

Invariant mass spectrum of $J/\psi K^+K^$ combinations. The vertical lines indicate the signal (blackdotted) and sideband (reddashed) regions. 
Bs_mass.pdf [37 KiB] HiDef png [357 KiB] Thumbnail [201 KiB] *.C file 

Invariant mass distribution for $J/\psi K ^+ K ^ $ candidates $25200$ MeV above the $\overline{ B }{} ^0_ s $ mass, reinterpreted as $\overline{ B }{} ^0 \rightarrow J/\psi K^{\mp} \pi^{\pm}$ events. The fit is to a signal Gaussian whose mass and width are allowed to vary as well as the polynomial background. 
reflection.pdf [38 KiB] HiDef png [172 KiB] Thumbnail [155 KiB] *.C file 

Fit to the invariant mass spectrum of $J/\psi K^+K^$ combinations. The dotted (black) line is the combinatorial background, the dashed (red) shape shows the misidentified $\overline{ B }{} ^0 \rightarrow J/\psi K ^ \pi ^+ $decays, and the solid (blue) curve shows the total. The vertical dashed lines indicate the signal region. 
Bs2JpsiKK2.pdf [39 KiB] HiDef png [224 KiB] Thumbnail [182 KiB] *.C file 

Fit to the invariant mass spectrum of $J/\psi K ^ $ candidates. The dotted line shows the combinatorial background and the solid (blue) curve is the total. 
Bu2JpsiK.pdf [35 KiB] HiDef png [185 KiB] Thumbnail [155 KiB] *.C file 

Distribution of $m^2(K^+K^)$ versus $m^2(J/\psi K^+)$ for $\overline{ B }{} ^0_ s $ candidate decays within $\pm 20$ MeV of the $\overline{ B }{} ^0_ s $ mass. The horizontal bands result from the $\phi(1020)$ and $f_2'(1525)$ resonances. 
dalitz.pdf [162 KiB] HiDef png [611 KiB] Thumbnail [508 KiB] *.C file 

Exponential fit to the efficiency parameter $a(s_{23})$. The point near the $\phi(1020)$ meson mass is determined more precisely due to the use of a large simulation sample. 
cosHacc.pdf [34 KiB] HiDef png [146 KiB] Thumbnail [125 KiB] *.C file 

Parametrized detection efficiency as a function of $m^2(K^+K^)$ versus $m^2(J/\psi K^+)$. The zaxis scale is arbitrary. 
effmodel.pdf [4 MiB] HiDef png [2 MiB] Thumbnail [573 KiB] *.C file 

Projections of the invariant mass squared (a) $K^+K^$ and (b) $J/\psi K^{+}$ from the simulation used to measure the efficiency parameters. The points represent the generated event distributions and the curves the polynomial fit. 
eff.pdf [36 KiB] HiDef png [172 KiB] Thumbnail [124 KiB] *.C file 

Distribution of $\cos \theta_{KK}$ for the $J/\psi \phi$ simulated sample fitted with $\varepsilon_1(x,y )\times A(\theta_{KK})$, within $\pm 20$ MeV of the $\phi(1020)$ mass. 
cosK_Phi.pdf [34 KiB] HiDef png [224 KiB] Thumbnail [128 KiB] *.C file 

Invariant mass squared projections of (a) $K^+K^$ and (b) $J/\psi K^{+}$ from the background Dalitz plot of candidates in the $\overline{ B }{} ^0_ s $ mass sidebands. 
bkg.pdf [36 KiB] HiDef png [166 KiB] Thumbnail [131 KiB] *.C file 

Distribution of $\cos \theta_{J/\psi}$ from the background sample fit with the function $1+\alpha \cos^{2} \theta_{J/\psi}$. 
bkgcosH.pdf [34 KiB] HiDef png [171 KiB] Thumbnail [113 KiB] *.C file 

Projections of the reflection background in the variables (a) $ m^2(K^+K^)$ and (b) $ m^2(J/\psi K^{+})$, obtained from $\overline{ B }{} ^0 \rightarrow J/\psi \overline{ K }{} ^{*0} (892)$ and $\overline{ B }{} ^0 \rightarrow J/\psi \overline{ K }{} ^* _2(1430)$ simulations. 
ref.pdf [28 KiB] HiDef png [50 KiB] Thumbnail [74 KiB] *.C file 

Distribution of $\cos \theta_{J/\psi}$ for the reflection fit with the function $1+\beta \cos^{2} \theta_{J/\psi}$. 
refcosH.pdf [35 KiB] HiDef png [237 KiB] Thumbnail [141 KiB] *.C file 

Dalitz plot fit projection of $ m^2(K^+ K^)$ using a logarithmic scale. 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 $\overline{ B }{} ^0 \rightarrow J/\psi K ^ \pi ^+ $ decays, and the (blue) solid line represents the total. 
ylog.pdf [39 KiB] HiDef png [168 KiB] Thumbnail [132 KiB] *.C file 

Dalitz plot fit projections of (a) $ m^2(J/\psi K^{+})$ and (b) $\cos \theta_{J/\psi}$. 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 $\overline{ B }{} ^0 \rightarrow J/\psi K ^ \pi ^+ $ decays, and the (blue) solid line represents the total fit results. 
xcosH.pdf [35 KiB] HiDef png [204 KiB] Thumbnail [133 KiB] *.C file 

Dalitz fit projection of $m(K^+ K^)$. The points represent the data, the dotted (black) curve shows the combinatorial background, and the dashed (red) curve indicates the reflection from misidentified $\overline{ B }{} ^0 \rightarrow J/\psi K ^ \pi ^+ $ decays. The largest three resonances $\phi(1020)$, $f_2'(1525)$ and $f_0(980)$ are shown by magenta, brown and green longdashed curves, respectively; all other resonances are shown by thin black curves. The dashed (cyan) curve is the nonresonant contribution. The dotdashed (black) curve is the contribution from the interferences, and the solid (blue) curve represents the total fit result. 
massfix.pdf [51 KiB] HiDef png [287 KiB] Thumbnail [209 KiB] *.C file 

Swave fraction as a function of $m( K ^+ K ^ )$ starting from 990 MeV up to 1050 MeV in 4 MeV mass intervals. The squares (blue), triangles (red), and circles (green) represent the LHCb , BES and BaBar parameterizations of $f_0(980)$, respectively. The experimental statistical uncertainties are only shown for the LHCb model; they are almost identical for the other cases. The experimental mass resolution is not unfolded. 
swave3.pdf [29 KiB] HiDef png [143 KiB] Thumbnail [83 KiB] *.C file 

Swave fractions in different $m( K ^+ K ^ )$ intervals centered on the $\phi$ meson mass. The squares (blue), triangles (red), and circles (green) represent the LHCb , BES and BaBar parameterizations of $f_0(980)$, respectively. The experimental statistical uncertainties are only shown for the LHCb model; they are almost identical for the other cases. The experimental mass resolution is not unfolded. 
interval.pdf [31 KiB] HiDef png [160 KiB] Thumbnail [93 KiB] *.C file 

Backgroundsubtracted efficiencycorrected $\cos \theta_{J/\psi}$ helicity distributions: (a) in $\phi(1020)$ mass region ($\chi^2/\rm ndf =54.4/40$), (b) in $f_2'(1525)$ mass region ($\chi^2/\rm ndf =34.4/40$). 
bgsubc[..].pdf [32 KiB] HiDef png [142 KiB] Thumbnail [116 KiB] *.C file 

Backgroundsubtracted efficiencycorrected $\cos \theta_{KK}$ helicity distributions: (a) in $\phi(1020)$ mass region ($\chi^2/\rm ndf =57.4/40$), (b) in $f_2'(1525)$ mass region ($\chi^2/\rm ndf =43.4/40$). The distributions are compatible with expectations for spin1 and spin2, respectively. 
bgsubc[..].pdf [34 KiB] HiDef png [221 KiB] Thumbnail [134 KiB] *.C file 

bgsubc[..].pdf [34 KiB] HiDef png [213 KiB] Thumbnail [133 KiB] *.C file 

Dependence of the spherical harmonic moments of $\cos \theta_{KK}$ as a function of the $K^+K^$ mass around the $\phi(1020)$ mass peak after efficiency corrections and background subtraction. The points with error bars are the data and the solid curves are derived from the fit model. 
angmo[..].pdf [70 KiB] HiDef png [329 KiB] Thumbnail [221 KiB] *.C file 

Dependence of the spherical harmonic moments of $\cos \theta_{KK}$ as a function of the $K^+K^$ mass above 1050 MeV, after efficiency corrections and background subtraction. The points with error bars are the data and the solid curves are derived from the fit model. 
angmomhm.pdf [60 KiB] HiDef png [279 KiB] Thumbnail [204 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2012040.gif Thumbnail 
Possible resonance candidates in the $\overline{ B }{} ^0_ s \rightarrow J/\psi K^+K^$ decay mode. 
Table_1.pdf [45 KiB] HiDef png [56 KiB] Thumbnail [27 KiB] tex code 

BreitWigner resonance parameters. 
Table_2.pdf [55 KiB] HiDef png [128 KiB] Thumbnail [64 KiB] tex code 

$\chi^2/\text{ndf}$ and $\rm ln\mathcal{L}$ of different resonance models. 
Table_3.pdf [37 KiB] HiDef png [59 KiB] Thumbnail [28 KiB] tex code 

Fit fractions (%) and phases of contributing components. For P and Dwaves $\lambda$ represents the helicity. 
Table_4.pdf [56 KiB] HiDef png [185 KiB] Thumbnail [95 KiB] tex code 

Fit fractions matrix for the best fit in units of %. The diagonal elements correspond to the decay fractions in Table ???. The offdiagonal elements give the fit fractions of the interference. The null values originate from the fact that any interference contribution between different spin$J$ state integrates to zero. Here the resonances are labeled by their masses in MeV and the subscripts denote the helicities. 
Table_5.pdf [20 KiB] HiDef png [49 KiB] Thumbnail [20 KiB] tex code 

Comparison of the fit fractions (%) with the LHCb, BES and BaBar $f_0(980)$ parameterizations described in the text. For P and Dwaves, $\lambda$ represents the helicity. 
Table_6.pdf [48 KiB] HiDef png [150 KiB] Thumbnail [76 KiB] tex code 

Absolute systematic uncertainties on the fit results. 
Table_7.pdf [73 KiB] HiDef png [182 KiB] Thumbnail [91 KiB] tex code 

Detector efficiencies determined from simulation and the correction factors. 
Table_8.pdf [54 KiB] HiDef png [66 KiB] Thumbnail [31 KiB] tex code 

Relative systematic uncertainties on branching fractions (%). 
Table_9.pdf [59 KiB] HiDef png [102 KiB] Thumbnail [47 KiB] tex code 
Created on 20 February 2021.