Timedependent CP violation is measured in the $B^0\rightarrow J/\psi\pi^+\pi^$ channel for each $\pi^+\pi^$ resonant final state using data collected with an integrated luminosity of 3.0 fb$^{1}$ in $pp$ collisions using the LHCb detector. The final state with the largest rate, $J/\psi\rho^0(770)$, is used to measure the CPviolating angle $2\beta^{\rm eff}$ to be $(41.7\pm 9.6_{6.3}^{+2.8})^{\circ}$. This result can be used to limit the size of penguin amplitude contributions to CP violation measurements in, for example, $B_s^0\rightarrow J/\psi\phi$ decays. Assuming approximate SU(3) flavour symmetry and neglecting higher order diagrams, the shift in the CPviolating phase $\phi_s$ is limited to be within the interval [$1.05^\circ$, +$1.18^\circ$] at 95 confidence level. Changes to the limit due to SU(3) symmetry breaking effects are also discussed.
(a) Tree level and (b) penguin diagram for $\overline{ B }{} {}^0 $ decays into $J/\psi \pi^+\pi^$. 
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Invariant mass of $J/\psi \pi^+\pi^$ combinations with $ K ^0_{\rm\scriptscriptstyle S} $ veto. The data have been fitted with doubleCrystal ball signal and several background functions. The (purple) solid line shows the $\overline{ B }{} {}^0 $ signal, the (brown) dotted line shows the combinatorial background, the (green) shortdashed shows the $B^$ background, the (red) dotdashed is $\overline{ B }{} {}^0_ s \rightarrow J/\psi \pi^+\pi^$, the (light blue) longdashed is the sum of $\overline{ B }{} {}^0_ s \rightarrow J/\psi\eta'$, $\overline{ B }{} {}^0_ s \rightarrow J/\psi\phi$ when $\phi\rightarrow \pi^+\pi^\pi^0$ backgrounds and the $\Lambda ^0_ b \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K^ p$ reflection, the (black) dotlong dashed is the $\overline{ B }{} {}^0 \rightarrow J/\psi K^ \pi^+$ reflection and the (blue) solid line is the total. 
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Fit projection of $m(\pi^+\pi^)$ showing the different resonant contributions in the "Best model" [7]. The $ K ^0_{\rm\scriptscriptstyle S}$ veto causes the absence of events near 500 MeV. The shape variation near 780 MeV is due to interference between the $\rho(770)$ and $\omega(782)$ states. The total fit is the sum of the individual components plus their interferences. 
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Decay time distribution of $\optbar{ B}{} ^0\rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \pi^+\pi^$ candidates. The signal component is shown with a (red) dashed line, the background with a (black) dotted line, and the (blue) solid line represents the total. The lower plot shows the normalized residual distribution. 
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The magnitude of the penguin induced shift $\delta_P$ on the $ C P$ violating phase in favoured decays, assuming SU(3) flavour symmetry, shown in grey or colour scale in degrees, as a function of the measured difference $\Delta2\beta_f$ ($x$axis) and $\alpha_{ C P }=\frac{1\lambda_f}{1+\lambda_f}$ ($y$axis). Here we use fixed values for $\gamma=70^{\circ}$ and $\epsilon=0.0534$. The projected 68% (solid) and 95% (dashed) confidence levels on $\delta_P$ are shown by the eggshaped contours. 
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The limit on the penguin induced phase change $\delta_P$ as a function of the difference in the penguin amplitude strong phases in $b\rightarrow c\bar{c}s$ and $b\rightarrow c\bar{c}d$ transitions $\theta\theta'$, for $a=a'$. 
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Contours corresponding to 68% (dashed) and 95% (solid) confidence levels for ndf of two, respectively, for the penguin amplitude parameters $a^\prime$ and $\theta^\prime$. 
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Animated gif made out of all figures. 
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Parameter values and correlations for the acceptance function $\varepsilon_t(t)$ in Eq. (12). 
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Fit results for $2\beta_{i}^{\rm eff}$ and $\alpha_{ C P }^i$. 
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The correlation matrix for the $ C P$ violating parameters determined using Fit 2, where $\Delta 2\beta^{\rm eff}_i=2\beta^{\rm eff}_i2\beta^{\rm eff}_{\rho_0}$. 
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Fit and transversity fractions of contributing resonances from Fit 1. Uncertainties are statistical only. These results are presented only as a crosscheck. 
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Results allowing for different $ C P$ violating effects for resonances other than the $\rho$ in an extension of Fit 1. 
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Systematic uncertainties on $ C P$ violating phases $2\beta_{i}^{\rm eff}$ ($^\circ$). Statistical uncertainties are also shown. 
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Systematic uncertainties for the magnitude of the asymmetries $\alpha_{ C P }^i$ ($\times10^{3}$). Statistical uncertainties are also shown. 
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Comparison of $S_f$ and $C_f$ between different measurements. 
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Created on 20 February 2021.