# Measurement of $CP$ violation in $B^0 \rightarrow J/\psi K^0_S$ decays

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## Abstract

Measurements are presented of the $CP$ violation observables $S$ and $C$ in the decays of $B^0$ and $\overline{B}{}^0$ mesons to the $J/\psi K^0_S$ final state. The data sample corresponds to an integrated luminosity of $3.0 \text{fb}^{-1}$ collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of $7$ and $8 \text{TeV}$. The analysis of the time evolution of $41500$ $B^0$ and $\overline{B}{}^0$ decays yields $S = 0.731 \pm 0.035 \text{(stat)} \pm 0.020 \text{(syst)}$ and $C = -0.038 \pm 0.032 \text{(stat)} \pm 0.005 \text{(syst)}$. In the Standard Model, $S$ equals $\sin(2\beta)$ to a good level of precision. The values are consistent with the current world averages and with the Standard Model expectations.

## Figures and captions

 Distribution of (a) the reconstructed mass and (b) logarithmic distribution of the decay time of tagged $B^0 \rightarrow {J\mskip -3mu/\mskip -2mu\psi\mskip 2mu} {K^0_{\rm\scriptscriptstyle S}}$ candidates. The solid black lines show the fit projections, while the dashed (dotted) lines show the projections for the signal (background) components only. Fig1a.pdf [43 KiB] HiDef png [288 KiB] Thumbnail [312 KiB] *.C file Fig1b.pdf [39 KiB] HiDef png [231 KiB] Thumbnail [254 KiB] *.C file Time-dependent signal-yield asymmetry $(N_{{\overline{ B}}{}^0} - N_{B^0})/(N_{{\overline{ B}}{}^0} + N_{B^0})$. Here, $N_{B^0}$ ($N_{{\overline{ B}}{}^0}$) is the number of $B^0 \rightarrow {J\mskip -3mu/\mskip -2mu\psi\mskip 2mu} {K^0_{\rm\scriptscriptstyle S}}$ decays with a $B^0$ (${\overline{ B}}{}^0$) flavor tag. The data points are obtained with the sPlot technique [37], assigning signal weights to the events based on a fit to the reconstructed mass distribution. The solid curve is the projection of the signal PDF. Fig2.pdf [32 KiB] HiDef png [195 KiB] Thumbnail [225 KiB] *.C file (a) Raw mixing asymmetry $(N_{\text{unmixed}} - N_{\text{mixed}})/(N_{\text{unmixed}} + N_{\text{mixed}})$ for all SS$\pi$ tagged $B^0 \rightarrow {J\mskip -3mu/\mskip -2mu\psi\mskip 2mu} K^{*0}$ decay candidates. Here, $N_{\text{unmixed}}$ ($N_{\text{mixed}}$) is the number of $B^0 \rightarrow {J\mskip -3mu/\mskip -2mu\psi\mskip 2mu} K^{*0}$ decays with a final state that does (not) correspond to the flavor tag. The black line shows the fit projection. (b) The linear calibration of the SS$\pi$ mistag probability with $B^0 \rightarrow {J\mskip -3mu/\mskip -2mu\psi\mskip 2mu} K^{*0}$ decays. FigA1a.pdf [33 KiB] HiDef png [221 KiB] Thumbnail [269 KiB] *.C file FigA1b.pdf [40 KiB] HiDef png [304 KiB] Thumbnail [281 KiB] *.C file Animated gif made out of all figures. PAPER-2015-004.gif Thumbnail

## Tables and captions

 Systematic uncertainties $\sigma_{S}$ and $\sigma_{C}$ on $S$ and $C$. Entries marked with a dash represent studies where no significant effect is observed. Table_1.pdf [50 KiB] HiDef png [118 KiB] Thumbnail [53 KiB] tex code

Created on 19 October 2019.