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Measurement of $CP$ violation in $B^0\rightarrow J/\psi K^0_\mathrm{S}$ and $B^0\rightarrow\psi(2S) K^0_\mathrm{S}$ decays

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Abstract

A measurement is presented of decay-time-dependent $CP$ violation in the decays $B^0\rightarrow J/\psi K^0_\mathrm{S}$ and $B^0\rightarrow\psi(2S) K^0_\mathrm{S}$, where the $J/\psi$ is reconstructed from two electrons and the $\psi(2S)$ from two muons. The analysis uses a sample of $pp$ collision data recorded with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 $\mathrm{fb}^{-1}$. The $CP$-violation observables are measured to be \begin{equation*} \begin{aligned} C\left(B^0\rightarrow J/\psi K^0_\mathrm{S}\right)&=\phantom{+} 0.12 \pm 0.07\pm 0.02 , S\left(B^0\rightarrow J/\psi K^0_\mathrm{S}\right)&=\phantom{+} 0.83 \pm 0.08\pm 0.01 , C\left(B^0\rightarrow\psi(2S) K^0_\mathrm{S}\right)&=- 0.05 \pm 0.10\pm 0.01 , S\left(B^0\rightarrow\psi(2S) K^0_\mathrm{S}\right)&=\phantom{+} 0.84 \pm 0.10\pm 0.01 , \end{aligned} \end{equation*} where $C$ describes $CP$ violation in the direct decay, and $S$ describes $CP$ violation in the interference between the amplitudes for the direct decay and for the decay after $B^0$-$\overline{B}^0$ oscillation. The first uncertainties are statistical and the second are systematic. The two sets of results are compatible with the previous LHCb measurement using $B^0\rightarrow J/\psi K^0_\mathrm{S}$ decays, where the $J/\psi$ meson was reconstructed from two muons. The averages of all three sets of LHCb results are \begin{equation*} \begin{aligned} C\left(B^0\rightarrow[c\bar{c}]K^0_\mathrm{S}\right)&=-0.017 \pm 0.029 , S\left(B^0\rightarrow[c\bar{c}]K^0_\mathrm{S}\right)&=\phantom{+}0.760 \pm 0.034 , \end{aligned} \end{equation*} under the assumption that higher-order contributions to the decay amplitudes are negligible. The uncertainties include statistical and systematic contributions.

Figures and captions

Invariant mass of the $ B ^0 $ candidates for (left) the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and (right) the $\psi(2S)$ mode. The lines represent the result of the fit described in the text.

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Projections of the decay-time fit to weighted (left) $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^0_{\mathrm{ \scriptscriptstyle S}} $ and \hspace{\textwidth} (right) $ B ^0 \rightarrow \psi(2S) K ^0_{\mathrm{ \scriptscriptstyle S}} $ candidates.

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Signal yield asymmetries $(N_\overline{ B }{} {}^0 - N_ B ^0 )/(N_\overline{ B }{} {}^0 + N_ B ^0 )$ versus the decay time for \hspace{\textwidth} (left) $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^0_{\mathrm{ \scriptscriptstyle S}} $ and (right) $ B ^0 \rightarrow \psi(2S) K ^0_{\mathrm{ \scriptscriptstyle S}} $ decays. The symbol $N_ B ^0 $ ($N_\overline{ B }{} {}^0 $) is the number of decays with a $ B ^0 $ ($\overline{ B }{} {}^0 $) flavour tag. The solid curves are the projections of the PDF with the combined flavour tagging decision.

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Two-dimensional likelihood scans for the combination of the (left) $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^0_{\mathrm{ \scriptscriptstyle S}} $ modes and (right) all $ B ^0 \rightarrow [ c \overline c ] K ^0_{\mathrm{ \scriptscriptstyle S}} $ modes. The confidence level for the inner (outer) contour is $39\%$ ($87\%$).

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Animated gif made out of all figures.

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Tables and captions

Effective flavour-tagging efficiencies in per cent of the SS and OS taggers and their combination.

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Parameters used as external inputs in the decay-time-dependent fit. The production asymmetries are evaluated individually for both decay modes and separately for the different centre-of-mass energies of $7$ and $\SI{8}{\TeV}$. If two uncertainties are given the first is statistical and the second systematic. If one uncertainty is given it includes statistical and systematic contributions.

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Systematic uncertainties for the $ C P$ -violation observables $S$ and $C$.

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Created on 02 May 2024.