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

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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]
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BstoJpsiKK.pdf

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]
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Bs_mass.pdf

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]
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reflection.pdf

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]
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Bs2JpsiKK2.pdf

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]
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Bu2JpsiK.pdf

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]
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dalitz.pdf

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]
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cosHacc.pdf

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]
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effmodel.pdf

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]
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eff.pdf

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]
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cosK_Phi.pdf

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]
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bkg.pdf

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]
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bkgcosH.pdf

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]
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ref.pdf

Distribution of $\cos \theta_{J/\psi}$ for the reflection fit with the function $1+\beta \cos^{2} \theta_{J/\psi}$.

refcosH.pdf [35 KiB]
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refcosH.pdf

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]
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ylog.pdf

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]
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x-cosH.pdf

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]
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mass-fix.pdf

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]
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swave3.pdf

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]
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interval.pdf

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]
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bgsubcosH_phi-f2.pdf

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]
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bgsubcosK_phi.pdf
bgsubc[..].pdf [34 KiB]
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bgsubcosK_f2.pdf

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]
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ang-mom-phi.pdf

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]
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ang-mom-hm.pdf

Animated gif made out of all figures.

PAPER-2012-040.gif
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Tables and captions

Possible resonance candidates in the $\overline{ B }{} ^0_ s \rightarrow J/\psi K^+K^-$ decay mode.

Table_0.pdf [45 KiB]
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Table_0.pdf

Breit-Wigner resonance parameters.

Table_1.pdf [55 KiB]
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Table_1.pdf

$\chi^2/\text{ndf}$ and $\rm -ln\mathcal{L}$ of different resonance models.

Table_2.pdf [37 KiB]
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Table_2.pdf

Fit fractions (%) and phases of contributing components. For P- and D-waves $\lambda$ represents the helicity.

Table_3.pdf [56 KiB]
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Table_3.pdf

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_4.pdf [48 KiB]
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Table_4.pdf

Absolute systematic uncertainties on the fit results.

Table_5.pdf [73 KiB]
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Table_5.pdf

Detector efficiencies determined from simulation and the correction factors.

Table_6.pdf [54 KiB]
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Table_6.pdf

Relative systematic uncertainties on branching fractions (%).

Table_7.pdf [59 KiB]
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Table_7.pdf

Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.