# Amplitude analysis and the branching fraction measurement of $\bar{B}^0_s \to J/\psi K^+K^-$

[to restricted-access page]

## Abstract

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 center-of-mass 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 non-resonant S-wave 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.

## Figures and captions

 Leading order diagram for $\overline{ B }{} ^0_ s \rightarrow J/\psi K ^+ K ^-$. BstoJpsiKK.pdf [75 KiB] HiDef png [137 KiB] Thumbnail [35 KiB] *.C file Invariant mass spectrum of $J/\psi K^+K^-$ combinations. The vertical lines indicate the signal (black-dotted) and sideband (red-dashed) regions. Bs_mass.pdf [37 KiB] HiDef png [365 KiB] Thumbnail [75 KiB] *.C file Invariant mass distribution for $J/\psi K ^+ K ^-$ candidates $25-200$ 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 [205 KiB] Thumbnail [54 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 [232 KiB] Thumbnail [51 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 [193 KiB] Thumbnail [49 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 [615 KiB] Thumbnail [171 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 [145 KiB] Thumbnail [44 KiB] *.C file Parametrized detection efficiency as a function of $m^2(K^+K^-)$ versus $m^2(J/\psi K^+)$. The z-axis scale is arbitrary. effmodel.pdf [4 MiB] HiDef png [2 MiB] Thumbnail [177 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 [173 KiB] Thumbnail [39 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 [226 KiB] Thumbnail [52 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 [168 KiB] Thumbnail [47 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 [177 KiB] Thumbnail [49 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 [22 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 [239 KiB] Thumbnail [49 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 [170 KiB] Thumbnail [41 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. x-cosH.pdf [35 KiB] HiDef png [204 KiB] Thumbnail [47 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 long-dashed curves, respectively; all other resonances are shown by thin black curves. The dashed (cyan) curve is the non-resonant contribution. The dot-dashed (black) curve is the contribution from the interferences, and the solid (blue) curve represents the total fit result. mass-fix.pdf [51 KiB] HiDef png [303 KiB] Thumbnail [65 KiB] *.C file S-wave 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 [142 KiB] Thumbnail [36 KiB] *.C file S-wave 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 [159 KiB] Thumbnail [41 KiB] *.C file Background-subtracted efficiency-corrected $\cos \theta_{J/\psi}$ 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 [144 KiB] Thumbnail [45 KiB] *.C file Background-subtracted efficiency-corrected $\cos \theta_{KK}$ 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 spin-1 and spin-2, respectively. bgsubc[..].pdf [34 KiB] HiDef png [228 KiB] Thumbnail [54 KiB] *.C file bgsubc[..].pdf [34 KiB] HiDef png [223 KiB] Thumbnail [55 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. ang-mo[..].pdf [70 KiB] HiDef png [334 KiB] Thumbnail [75 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. ang-mom-hm.pdf [60 KiB] HiDef png [288 KiB] Thumbnail [71 KiB] *.C file Animated gif made out of all figures. PAPER-2012-040.gif Thumbnail

## Tables and captions

 Possible resonance candidates in the $\overline{ B }{} ^0_ s \rightarrow J/\psi K^+K^-$ decay mode. Table_1.pdf [45 KiB] HiDef png [67 KiB] Thumbnail [11 KiB] tex code Breit-Wigner resonance parameters. Table_2.pdf [55 KiB] HiDef png [151 KiB] Thumbnail [26 KiB] tex code $\chi^2/\text{ndf}$ and $\rm -ln\mathcal{L}$ of different resonance models. Table_3.pdf [37 KiB] HiDef png [68 KiB] Thumbnail [11 KiB] tex code Fit fractions (%) and phases of contributing components. For P- and D-waves $\lambda$ represents the helicity. Table_4.pdf [56 KiB] HiDef png [221 KiB] Thumbnail [39 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 D-waves, $\lambda$ represents the helicity. Table_5.pdf [48 KiB] HiDef png [180 KiB] Thumbnail [30 KiB] tex code Absolute systematic uncertainties on the fit results. Table_6.pdf [73 KiB] HiDef png [230 KiB] Thumbnail [39 KiB] tex code Detector efficiencies determined from simulation and the correction factors. Table_7.pdf [54 KiB] HiDef png [79 KiB] Thumbnail [13 KiB] tex code Relative systematic uncertainties on branching fractions (%). Table_8.pdf [59 KiB] HiDef png [124 KiB] Thumbnail [19 KiB] tex code

Created on 20 April 2019.Citation count from INSPIRE on 24 April 2019.