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Measurement of CP violation in the $B_s^0 \to \phi \phi$ decay and search for the $B^0 \to \phi\phi$ decay

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Abstract

A measurement of the time-dependent $ C\!P$ -violating asymmetry in $ B ^0_ s \rightarrow \phi\phi$ decays is presented, along with measurements of the $ T$ -odd triple-product asymmetries. Using a sample of proton-proton collision data corresponding to an integrated luminosity of $5.0\,fb^{-1} $ collected with the LHCb detector, a signal yield of approximately 8500 $ B ^0_ s \!\rightarrow \phi\phi$ decays is obtained. The $ C\!P$ -violating phase is measured to be ${\phi_{ s }^{ s \overline s s } =-0.07\pm0.13\mathrm{\,(stat)} \pm0.03\mathrm{\,(syst)} }\rm \,rad $. The triple-product asymmetries are measured to be ${A_U=0.000\pm0.012\mathrm{\,(stat)} \pm0.004\mathrm{\,(syst)} }$ and ${A_V=-0.003\pm0.012\mathrm{\,(stat)} \pm0.004\mathrm{\,(syst)} }$. The results obtained are consistent with the hypothesis of $ C\!P$ conservation in $ b \rightarrow s \overline s s $ transitions. In addition, an improved limit on the branching fraction of the $ B ^0 \rightarrow \phi\phi$ decay is set, $\mathcal{B}( B ^0 \rightarrow \phi\phi)<2.4\times 10^{-8}$ at 90\,% confidence level.

Figures and captions

A fit to the 2011 (top left), 2012 (top right), 2015 (bottom left) and 2016 (bottom right) data, represented by the black points. Also shown are the results of the total fit (blue solid line), with the $ B ^0_ s \!\rightarrow \phi\phi$ (red dashed), the $\Lambda ^0_ b \rightarrow \phi p K ^- $ (magenta long dashed), and the combinatorial (blue short dashed) fit components.

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2015Da[..].pdf [72 KiB]
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2015Data_Fixed3.pdf
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2016Data_Fixed3.pdf

Decay angles for the $ B ^0_ s \rightarrow \phi \phi$ decay, where $\theta_{1,2}$ is the angle between the $K^+$ track momentum in the $\phi_{1,2}$ meson rest frame and the parent $\phi_{1,2}$ momentum in the $ B ^0_ s $ rest frame, $\Phi$ is the angle between the two $\phi$ meson decay planes and $\hat{n}_{V_{1,2}}$ is the unit vector normal to the decay plane of the $\phi_{1,2}$ meson.

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Angular acceptance found from simulated $ B ^0_ s \!\rightarrow \phi\phi$ decays (top-left) integrated over $\cos\theta_2$ and $\Phi$ as a function of $\cos\theta_1$, (top-right) integrated over $\cos\theta_1$ and $\Phi$ as a function of $\cos\theta_2$, and (bottom) integrated over $\cos\theta_1$ and $\cos\theta_2$ as a function of $\Phi$.

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Decay-time acceptances calculated from (left) $ B ^0_ s \rightarrow D ^-_ s \pi ^+ $ and (right) $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*0} $ decays. Superimposed are calculated analytical splines.

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One-dimensional projections of the $ B ^0_ s \rightarrow \phi\phi$ fit for (top-left) decay time with binned acceptance, (top-right) helicity angle $\Phi$ and (bottom-left and bottom-right) cosine of the helicity angles $\theta_1$ and $\theta_2$. The background-subtracted data are marked as black points, while the blue solid lines represent the projections of the best fit. The $ C\!P$ -even $P$-wave, the $ C\!P$ -odd $P$-wave and $S$-wave combined with double $S$-wave components are shown by the red long dashed, green short dashed and purple dot-dashed lines, respectively. Fitted components are plotted taking in to account efficiencies in the time and angular observables.

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Fit to the four-kaon invariant mass. The total PDF as described in the text is shown as a blue solid line, $ B ^0_ s \!\rightarrow \phi\phi$ as a red dashed line, $ B ^0 \rightarrow \phi \phi$ as a green dotted line, the $\Lambda ^0_ b \rightarrow \phi p K$ as a magenta long-dashed line and the combinatorial background as a blue short-dashed line.

DataFi[..].pdf [68 KiB]
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DataFit_Fixed2.pdf

Results of the ${\rm CL}_s$ scan as a function of $N_{ B ^0 }$. The solid black line shows the observed ${\rm CL}_s$ distribution, while the dotted black line indicates the expected distribution. The green (yellow) band marks the $1\sigma$ ($2\sigma$) confidence region on the expected ${\rm CL}_s$. The $90\,(95)\,\%$ CL limit is indicated as a solid (dashed) red line.

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CLplot_Fixed.pdf

Animated gif made out of all figures.

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Tables and captions

Coefficients of the time-dependent terms and angular functions used in Eq. 2. Amplitudes are defined at $t=0$.

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Angular coefficients, written in the same basis as the efficiency parameterisation.

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Tagging performance of the opposite side (OS) and same side kaon (SSK) flavour taggers.

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Results of the time-dependent fit. Uncertainties shown do not include systematic contributions.

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Correlation matrix associated with the result of the time-dependent fit and relate to the statistical uncertainties.

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Summary of systematic uncertainties for physics parameters in the time-dependent measurement, where AA denotes angular acceptance, TA denotes time acceptance, and TR time resolution.

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Summary of systematic uncertainties on $A_U$ and $A_V$.

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Created on 18 December 2018.Citation count from INSPIRE on 18 December 2018.