# Measurement of the CP-violating phase $\beta$ in $B^0\rightarrow J/\psi \pi^+\pi^-$ decays and limits on penguin effects

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## Abstract

Time-dependent 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 CP-violating 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 CP-violating 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.

## Figures and captions

 (a) Tree level and (b) penguin diagram for $\overline{ B }{} {}^0$ decays into $J/\psi \pi^+\pi^-$. feyn3.pdf [34 KiB] HiDef png [102 KiB] Thumbnail [23 KiB] *.C file Invariant mass of $J/\psi \pi^+\pi^-$ combinations with $K ^0_{\rm\scriptscriptstyle S}$ veto. The data have been fitted with double-Crystal 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) short-dashed shows the $B^-$ background, the (red) dot-dashed is $\overline{ B }{} {}^0_ s \rightarrow J/\psi \pi^+\pi^-$, the (light blue) long-dashed 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) dot-long dashed is the $\overline{ B }{} {}^0 \rightarrow J/\psi K^- \pi^+$ reflection and the (blue) solid line is the total. fitcut.pdf [17 KiB] HiDef png [313 KiB] Thumbnail [83 KiB] *.C file 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. plotea[..].pdf [93 KiB] HiDef png [370 KiB] Thumbnail [97 KiB] *.C file 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. timetest.pdf [12 KiB] HiDef png [263 KiB] Thumbnail [83 KiB] *.C file 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 egg-shaped contours. shift_sens.pdf [70 KiB] HiDef png [602 KiB] Thumbnail [126 KiB] *.C file 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 $a=a'$. Ubreaking.pdf [36 KiB] HiDef png [259 KiB] Thumbnail [54 KiB] *.C file Contours corresponding to 68% (dashed) and 95% (solid) confidence levels for ndf of two, respectively, for the penguin amplitude parameters $a^\prime$ and $\theta^\prime$. peng_c[..].pdf [32 KiB] HiDef png [247 KiB] Thumbnail [51 KiB] *.C file Animated gif made out of all figures. PAPER-2014-058.gif Thumbnail

## Tables and captions

 Parameter values and correlations for the acceptance function $\varepsilon_t(t)$ in Eq. (12). Table_1.pdf [43 KiB] HiDef png [65 KiB] Thumbnail [10 KiB] tex code Fit results for $2\beta_{i}^{\rm eff}$ and $\alpha_{ C\!P }^i$. Table_2.pdf [54 KiB] HiDef png [72 KiB] Thumbnail [13 KiB] tex code The correlation matrix for the $C\!P$ -violating parameters determined using Fit 2, where $\Delta 2\beta^{\rm eff}_i=2\beta^{\rm eff}_i-2\beta^{\rm eff}_{\rho_0}$. Table_3.pdf [55 KiB] HiDef png [69 KiB] Thumbnail [11 KiB] tex code Fit and transversity fractions of contributing resonances from Fit 1. Uncertainties are statistical only. These results are presented only as a cross-check. Table_4.pdf [53 KiB] HiDef png [76 KiB] Thumbnail [13 KiB] tex code Results allowing for different $C\!P$ -violating effects for resonances other than the $\rho$ in an extension of Fit 1. Table_5.pdf [52 KiB] HiDef png [56 KiB] Thumbnail [10 KiB] tex code Systematic uncertainties on $C\!P$ -violating phases $2\beta_{i}^{\rm eff}$ ($^\circ$). Statistical uncertainties are also shown. Table_6.pdf [56 KiB] HiDef png [142 KiB] Thumbnail [23 KiB] tex code Systematic uncertainties for the magnitude of the asymmetries $\alpha_{ C\!P }^i$ ($\times10^{-3}$). Statistical uncertainties are also shown. Table_7.pdf [56 KiB] HiDef png [133 KiB] Thumbnail [23 KiB] tex code Comparison of $S_f$ and $C_f$ between different measurements. Table_8.pdf [54 KiB] HiDef png [47 KiB] Thumbnail [8 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [200 KiB] asym-Bd.pdf [28 KiB] HiDef png [213 KiB] Thumbnail [48 KiB] *C file asym-mod.pdf [34 KiB] HiDef png [254 KiB] Thumbnail [56 KiB] *C file Fig7.pdf [28 KiB] HiDef png [213 KiB] Thumbnail [48 KiB] *C file Fig8.pdf [28 KiB] HiDef png [213 KiB] Thumbnail [48 KiB] *C file

Created on 15 February 2019.Citation count from INSPIRE on 15 February 2019.