Interpretation of CP violation measurements using charmonium decays, in both the B0 and Bs systems, can be subject to changes due to "penguin" type diagrams. These effects can be investigated using measurements of the Cabibbosuppressed B0>J/\psi pi+pi decays. The final state composition of this channel is investigated using a 1.0/fb sample of data produced in 7 TeV pp collisions at the LHC and collected by the LHCb experiment. A modified Dalitz plot analysis is performed using both the invariant mass spectra and the decay angular distributions. An improved measurement of the B0>J/\psi pi+pi branching fraction of (3.97 +/0.09+/ 0.11 +/ 0.16)x10^{5} is reported where the first uncertainty is statistical, the second is systematic and the third is due to the uncertainty of the branching fraction of the decay B > J/\psi K used as a normalization channel. In the J/\psi pi+pi final state significant production of f0(500) and rho(770) resonances is found, both of which can be used for CP violation studies. In contrast evidence for the f0(980) resonance is not found, thus establishing the first upper limit on the branching fraction product B(B0>J/\psi f0(980) x B(f0(980)> pi+ pi) < 1.1x10^{6}, leading to an upper limit on the absolute value of the mixing angle of the f0(980)$ with the f0(500) of <31 degrees, both at 90% confidence level.
(a) Tree level and (b) penguin diagram examples for $\overline{ B }{} ^0 $ decays into $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^0_{\rm\scriptscriptstyle S} $. 
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(a) Tree level and (b) penguin diagram for $\overline{ B }{} ^0 $ decays into $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$. 
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Distributions of the BDT classifier 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 are from data. 
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Invariant mass of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$ combinations. The data are fitted with a doubleGaussian signal and several background functions. The (red) solid doubleGaussian function centered at 5280 $\mathrm{ Me V}$ is the $\overline{ B }{} ^0 $ signal, the (brown) dotted line shows the combinatorial background, the (green) shortdashed shows the $B^$ background, the (purple) dotdashed line shows the contribution of $\overline{ B }{} ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$ decays, the (black) dotlong dashed is the sum of $\overline{ B }{} ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \eta'(\rightarrow \rho \gamma)$ and $\overline{ B }{} ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \phi(\rightarrow \pi^+\pi^\pi^0)$ backgrounds, the (light blue) longdashed is the $\overline{ B }{} ^0 \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^ \pi^+$ reflection, and the (blue) solid line is the total. 
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Invariant mass of $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^$ combinations. The data points are fitted with a doubleGaussian function for signal and a linear function for background. The dotted line shows the background, and the (blue) solid line is the total. 
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Distribution of $m^2(\pi^+\pi^)$ versus $m^2( { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+)$ for $\overline{ B }{} ^0 $ candidate decays within $\pm20$ $\mathrm{ Me V}$ of the $\overline{ B }{} ^0 $ mass. 
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Distribution of (a) $m( { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+)$ and (b) $m(\pi^+\pi^)$ for $\overline{ B }{} ^0 \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$ candidate decays within $\pm20$ $\mathrm{ Me V}$ of $\overline{ B }{} ^0 $ mass shown with the solid line. The (red) points with error bars show the background contribution determined from $m( { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^)$ fits performed in each bin. 
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mpipi.pdf [39 KiB] HiDef png [281 KiB] Thumbnail [164 KiB] *.C file 

Distributions of $\cos\theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ for the $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$ simulated sample in (a) the entire dipion mass region and (b) $\rho(770)$ region. 
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cosH_e[..].pdf [36 KiB] HiDef png [259 KiB] Thumbnail [158 KiB] *.C file 

Exponential fit to the acceptance parameter $a(s_{12})$ used in Eq. 18. 
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Parametrized detection efficiency as a function of $m^2(\pi^+\pi^)$ versus $m^2( { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+)$ determined from simulation. The $z$axis scale is arbitrary. 
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Projections onto (a) $m^2( { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+)$ and (b) $m^2(\pi^+\pi^)$ of the simulated Dalitz plot used to determine the efficiency parameters. The points represent the simulated event distributions and the curves the projections of the polynomial fits. 
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effy.pdf [38 KiB] HiDef png [200 KiB] Thumbnail [163 KiB] *.C file 

The $m^2(\pi\pi)$ distribution of background. The (black) histogram with error bars shows the samesign data combinations with additional background from simulation, the (blue) points with error bars show the background obtained from the mass fits, the (black) dashed line is the partially reconstructed $\overline{ B }{} ^0_ s $ background, and the (red) dotted is the misidentified $\overline{ B }{} ^0 \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^ \pi^+$ contribution. 
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Projections of invariant mass squared of (a) $m^2( { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+)$ and (b) $m^2(\pi^+\pi^)$ of the background Dalitz plot. The points with error bars show the samesign combinations with additional background from simulation. 
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y_bkgnew.pdf [38 KiB] HiDef png [202 KiB] Thumbnail [174 KiB] *.C file 

distribution of the background in $\cos\theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ resulting from $ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$ candidate mass fits in each bin of $\cos\theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$. The curve represents the fitted function $1+\alpha\cos^2\theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$. 
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Dalitz fit projections of (a) $m^2(\pi^+\pi^)$, (b) $m^2( { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^{+})$, (c) $\cos \theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ and (d) $m(\pi^+\pi^)$ for the best model. The points with error bars are data, the signal fit is shown with a (red) dashed line, the background with a (black) dotted line, and the (blue) solid line represents the total. In (a) and (d), the shape variations near the $\rho(770)$ mass is due to $\rho(770)\omega(782)$ interference, and the dip at the $ K ^0_{\rm\scriptscriptstyle S} $ mass [31] is due to the $ K ^0_{\rm\scriptscriptstyle S} $ veto. 
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x.pdf [40 KiB] HiDef png [210 KiB] Thumbnail [195 KiB] *.C file 

cosH.pdf [37 KiB] HiDef png [242 KiB] Thumbnail [165 KiB] *.C file 

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Helicity angle distributions of (a) $\cos \theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ ($\chi^2$/ndf =15/20) and (b) $\cos\theta_{\pi\pi}$ ($\chi^2$/ndf =14/20) in the $\rho(770)$ mass region defined within one full width of the $\rho(770)$ mass. The points with error bars are data, the signal fit to the best model is shown with a (red) dashed line, the background with a (black) dotted line, and the (blue) solid line represents the total. 
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cospp_rho.pdf [36 KiB] HiDef png [229 KiB] Thumbnail [150 KiB] *.C file 

Background subtracted and efficiency corrected helicity distributions of (a) $\cos \theta_{ { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} }$ ($\chi^2$/ndf =20/20) and (b) $\cos\theta_{\pi\pi}$ ($\chi^2$/ndf =13/20) in the $\rho(770)$ mass region defined within one full width of the $\rho(770)$ mass. The points with error bars are data and the solid blue lines show the fit to the best model. 
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cospp_[..].pdf [35 KiB] HiDef png [271 KiB] Thumbnail [159 KiB] *.C file 

Animated gif made out of all figures. 
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Efficiency parameters to describe the acceptance on the signal Dalitzplot. 
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Parameters for the background model used in Eq. 23. 
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Possible resonances in the $\overline{ B }{} ^0 \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$ decay mode. 
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BreitWigner resonance parameters. 
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Values of $\chi^2/\text{ndf}$ and $\rm ln\mathcal{L}$ of different resonance models. 
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Fit fractions and significances of contributing components for the best model, as well as the fractions of the helicity $\lambda=0$ part. The significance takes into account both statistical and systematic uncertainties. 
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Interference fractions ${\cal{F}}_{\lambda}^{RR'}$ (%) computed using Eq 25. Note that the diagonal elements are fit fractions defined in Eq 24. 
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Resonant phases from the best fit. 
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Fit fractions (%) of contributing components for the best model with adding one additional resonance. 
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Branching fractions for each channel. The upper limit at 90% CL is also quoted for the $f_0(980)$ resonance which has a significance smaller than 3$\sigma$. The first uncertainty is statistical and the second the total systematic. 
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Relative systematic uncertainties on branching fractions (%). 
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Absolute systematic uncertainties on the results of the Dalitz analysis. 
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Masses of light vector and scalar resonances. All values are taken from [31], except for the $f_0(500)$ [43]. 
Table_13.pdf [38 KiB] HiDef png [32 KiB] Thumbnail [14 KiB] tex code 
Created on 18 January 2020.