The decay Bs>J/\psi\pi+\pi can be exploited to study CP violation. A detailed understanding of its structure is imperative in order to optimize its usefulness. An analysis of this threebody final state is performed 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 of the final state is performed using both the invariant mass spectra and the decay angular distributions. The \pi+\pi system is shown to be dominantly in an Swave state, and the CPodd fraction in this Bs decay is shown to be greater than 0.977 at 95 confidence level. In addition, we report the first measurement of the J/\psi\pi+\pi branching fraction relative to J/\psi\phi of (19.79 +/ 0.47 +/ 0.52).
Leading order diagram for $\overline{ B }{} ^0_ s $ decays into $J/\psi \pi^+\pi^$. 
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(a) Invariant mass spectrum of $J/\psi K^+K^$ for candidates with $m(K^+K^)<1050$ MeV. The data has been fitted with a doubleGaussian signal and linear background functions shown as a dashed line. The solid curve shows the sum. (b) Background subtracted invariant mass spectrum of $K^+K^$ for events with $m(K^+K^)<1050$ MeV. The dashed line (barely visible along the $x$axis) shows the Swave contribution and the solid curve is the sum of the Swave and a Pwave BreitWigner functions, fitted to the data. 
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Invariant mass of $J/\psi \pi^+\pi^$ candidate combinations. The data have been fitted with doubleGaussian signal and several background functions. The (red) solid line shows the $\overline{ B }{} ^0_ s $ signal, the (brown) dotted line shows the combinatorial background, the (green) shortdashed shows the $B^$ background, the (purple) dotdashed is $\overline{ B }{} ^0 \rightarrow J/\psi \pi^+\pi^$, the (black) dotlong dashed is the sum of $\overline{ B }{} ^0_ s \rightarrow J/\psi\eta'$ and $\overline{ B }{} ^0_ s \rightarrow J/\psi\phi$ when $\phi\rightarrow \pi^+\pi^\pi^0$ backgrounds, the (light blue) longdashed is the $\overline{ B }{} ^0 \rightarrow J/\psi K^ \pi^+$ reflection, and the (blue) solid line is the total. 
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Background subtracted $\chi$ distribution from $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^$ candidates. 
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Distribution of $m(J/\psi \pi^+)$ for $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^$ candidate decays within $\pm20$ MeV of $\overline{ B }{} ^0_ s $ mass shown with the (blue) solid line; $m(J/\psi \pi^+)$ for wrongsign $J/\psi \pi^+\pi^+$ combinations is shown with the (red) dashed line, as an estimate of the background. 
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Distribution of $s_{23}\equiv m^2(\pi^+\pi^)$ versus $s_{12}\equiv m^2(J/\psi\pi^+)$ for $\overline{ B }{} ^0_ s $ candidate decays within $\pm20$ MeV of $\overline{ B }{} ^0_ s $ mass. 
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Parametrized detection efficiency as a function of $s_{23}\equiv m^2(\pi^+\pi^)$ versus $s_{12}\equiv m^2(J/\psi\pi^+)$. The scale is arbitrary. 
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Projections of invariant mass squared of (a) $s_{12}\equiv m^2(J/\psi \pi^+)$ and (b) $s_{23}\equiv m^2(\pi^+\pi^)$ of the MC Dalitz plot used to measure the efficiency parameters. The points represent the MC generated event distributions and the curves the polynomial fit. 
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Distributions of (a) $\cos\theta_{J/\psi}$, (b) $\cos\theta_{KK}$ for $J/\psi\phi$ background subtracted data (points) compared with the MC simulation (histogram). 
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Projections of invariant mass squared of (a) $s_{12}\equiv m^2(J/\psi \pi^+)$ and (b) $s_{23}\equiv m^2(\pi^{\pm}\pi^{\pm})$ of the background Dalitz plot. 
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The $\cos\theta_{J/\psi}$ distribution of the background and the fitted function $1+\alpha\cos\theta_{J/\psi}+\beta \cos^{2}\theta_{J/\psi}$. 
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Dalitz fit projections of $m^2(\pi^+ \pi^)$ fit with 3R+NR for the preferred 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. The normalized residuals in each bin are shown below, defined as the difference between the data and the fit divided by the error on the data. 
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Dalitz fit projections of (a) $s_{12}\equiv m^2(J/\psi \pi^{+})$ and (b) $\cos \theta_{J/\psi}$ fit with the 3R+NR preferred 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. 
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Background subtracted and acceptance corrected $\cos \theta_{J/\psi}$ helicity distributions fit with the preferred model: (a) in $f_0(980)$ mass region defined within $\pm90$ MeV of 980 MeV ($\chi^2$/ndf =39/40), (b) in $f_2(1270)$ mass region defined within one full width of $f_2(1270)$ mass ($\chi^2$/ndf =25/40), (c) in $f_0(1370)$ mass region defined within one full width of $f_2(1370)$ mass ($\chi^2$/ndf = 24/40). The points with error bars are data and the solid blue lines show the fit from the 3R+NR model. 
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Background subtracted and acceptance corrected $\cos \theta_{\pi\pi}$ helicity distributions fit the preferred model: (a) in $f_0(980)$ mass region defined within $\pm90$ MeV of 980 MeV ($\chi^2$/ndf =38/40), (b) in $f_2(1270)$ mass region defined within one full width of $f_2(1270)$ mass ($\chi^2$/ndf = 32/40), (c) in $f_0(1370)$ mass region defined within one full width of $f_2(1370)$ mass ($\chi^2$/ndf =37/40). The points with error bars are data and the solid blue lines show the fit from the 3R+NR model. 
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Background subtracted and acceptance corrected $\cos \theta_{\pi\pi}$ helicity distributions fit the preferred model: (a) in $[90,0]$ MeV of 980 MeV ($\chi^2$/ndf =41/40), (b) in $[0,90]$ MeV of 980 MeV ($\chi^2$/ndf =31/40) 
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The $\pi^+\pi^$ mass dependence of the spherical harmonic moments of $\cos \theta_{\pi\pi}$ after efficiency corrections and background subtraction: (a) $\langle Y^0_0\rangle$, (b) $\langle Y^0_1\rangle$, (c) $\langle Y^0_2\rangle$, (d) $\langle Y^0_3\rangle$, (e) $\langle Y^0_4\rangle$, (f) $\langle Y^0_5\rangle$, (g) $\langle Y^0_6\rangle$, and (h) $\langle Y^0_7\rangle$. The points with error bars are the data points and the solid curves are derived from the 3R+NR preferred model. 
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Detection efficiency of $\overline{ B }{} ^0_ s \rightarrow J/\psi\pi^+\pi^$ as a function of $s_{23}\equiv m^{2}(\pi^+\pi^)$. 
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Animated gif made out of all figures. 
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Possible resonance candidates in the $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^$ decay mode. 
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Models used in data fit. 
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BreitWigner resonance parameters. 
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$\chi^2/\text{ndf}$ and $\rm ln\mathcal{L}$ of different resonance models. 
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Fit fractions (%) of contributing components for the preferred model. For P and Dwaves $\lambda$ represents the final state helicity. Here $\rho$ refers to the $\rho(770)$ meson. 
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Fit fractions (%) of contributing components from different models for the alternate solution. For P and Dwaves $\lambda$ represents the final state helicity. Here $\rho$ refers to the $\rho(770)$ meson. 
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Fit fractions (%) of interference terms for both solutions of the 3R+NR model. 
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Fit results from the 3R+NR model for both the preferred and alternate solutions. $\phi$ indicates the phase with respect to the $f_0(980)$. For the $f_2(1270)$, $\lambda$ represents the final state helicity. 
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Normalized fit fractions (%) for alternate and preferred 3R+NR models and the ratio $R$ (%) relative to $\overline{ B }{} ^0_ s \rightarrow J/\psi\phi$. The numbers for the $f_2(1270)$ refer only to the $\lambda=0$ state. 
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Relative systematic uncertainties on $R$(%). 
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Changes due to modified acceptance function. 
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Created on 06 March 2021.