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 $J/\psi \pi^+\pi^$. 
feyn1.pdf [87 KiB] HiDef png [94 KiB] Thumbnail [24 KiB] *.C file 

(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. 
JpsiKK.pdf [39 KiB] HiDef png [221 KiB] Thumbnail [39 KiB] *.C file 

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. 
fitmass.pdf [41 KiB] HiDef png [475 KiB] Thumbnail [85 KiB] *.C file 

Background subtracted $\chi$ distribution from $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^$ candidates. 
bkgsubchi.pdf [77 KiB] HiDef png [174 KiB] Thumbnail [48 KiB] *.C file 

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. 
mjpsipi.pdf [35 KiB] HiDef png [209 KiB] Thumbnail [56 KiB] *.C file 

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. 
dalitz1.pdf [129 KiB] HiDef png [1 MiB] Thumbnail [217 KiB] *.C file 

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. 
effmod[..].pdf [582 KiB] HiDef png [1 MiB] Thumbnail [141 KiB] *.C file 

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. 
eff.pdf [38 KiB] HiDef png [264 KiB] Thumbnail [47 KiB] *.C file 

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). 
cos_theta.pdf [31 KiB] HiDef png [187 KiB] Thumbnail [40 KiB] *.C file 

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. 
xy_bkgnew.pdf [40 KiB] HiDef png [225 KiB] Thumbnail [51 KiB] *.C file 

The $\cos\theta_{J/\psi}$ distribution of the background and the fitted function $1+\alpha\cos\theta_{J/\psi}+\beta \cos^{2}\theta_{J/\psi}$. 
bkg_cosH.pdf [37 KiB] HiDef png [261 KiB] Thumbnail [65 KiB] *.C file 

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. 
mpipi[..].pdf [82 KiB] HiDef png [445 KiB] Thumbnail [77 KiB] *.C file 

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. 
8R1R3.pdf [37 KiB] HiDef png [274 KiB] Thumbnail [55 KiB] *.C file 

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. 
2JPsi2_all.pdf [32 KiB] HiDef png [230 KiB] Thumbnail [49 KiB] *.C file 

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. 
2PP2_all.pdf [32 KiB] HiDef png [213 KiB] Thumbnail [50 KiB] *.C file 

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) 
2sol2_all.pdf [33 KiB] HiDef png [220 KiB] Thumbnail [55 KiB] *.C file 

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. 
2SPH.pdf [102 KiB] HiDef png [753 KiB] Thumbnail [190 KiB] *.C file 

Detection efficiency of $\overline{ B }{} ^0_ s \rightarrow J/\psi\pi^+\pi^$ as a function of $s_{23}\equiv m^{2}(\pi^+\pi^)$. 
jpsipi[..].pdf [34 KiB] HiDef png [204 KiB] Thumbnail [51 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2012005.gif Thumbnail 
Possible resonance candidates in the $\overline{ B }{} ^0_ s \rightarrow J/\psi \pi^+\pi^$ decay mode. 
Table_1.pdf [38 KiB] HiDef png [106 KiB] Thumbnail [16 KiB] tex code 

Models used in data fit. 
Table_2.pdf [30 KiB] HiDef png [84 KiB] Thumbnail [13 KiB] tex code 

BreitWigner resonance parameters. 
Table_3.pdf [39 KiB] HiDef png [82 KiB] Thumbnail [14 KiB] tex code 

$\chi^2/\text{ndf}$ and $\rm ln\mathcal{L}$ of different resonance models. 
Table_4.pdf [39 KiB] HiDef png [145 KiB] Thumbnail [22 KiB] tex code 

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. 
Table_5.pdf [49 KiB] HiDef png [111 KiB] Thumbnail [18 KiB] tex code 

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. 
Table_6.pdf [49 KiB] HiDef png [109 KiB] Thumbnail [18 KiB] tex code 

Fit fractions (%) of interference terms for both solutions of the 3R+NR model. 
Table_7.pdf [37 KiB] HiDef png [76 KiB] Thumbnail [13 KiB] tex code 

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. 
Table_8.pdf [56 KiB] HiDef png [187 KiB] Thumbnail [30 KiB] tex code 

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. 
Table_9.pdf [53 KiB] HiDef png [60 KiB] Thumbnail [10 KiB] tex code 

Relative systematic uncertainties on $R$(%). 
Table_10.pdf [60 KiB] HiDef png [86 KiB] Thumbnail [13 KiB] tex code 

Changes due to modified acceptance function. 
Table_11.pdf [55 KiB] HiDef png [136 KiB] Thumbnail [21 KiB] tex code 
Created on 15 February 2019.Citation count from INSPIRE on 15 February 2019.