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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]
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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 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.

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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 egg-shaped 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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Tables and captions

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 $\Delta 2\beta^{\rm eff}_i=2\beta^{\rm eff}_i-2\beta^{\rm eff}_{\rho_0}$.

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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 cross-check.

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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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Supplementary Material [file]

Supplementary material full pdf

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supplementary.pdf
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Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.