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

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Abstract

A measurement of the time-dependent CP-violating asymmetry in $B_s^0\rightarrow\phi\phi$ decays is presented. Using a sample of proton-proton collision data corresponding to an integrated luminosity of $5.0$fb$^{-1}$ collected by the $ LHCb$ experiment at centre-of-mass energies $\sqrt{s} = 7$ TeV in 2011, 8 TeV in 2012 and 13 TeV in 2015 and 2016, a signal yield of around 9000 $B_s^0\rightarrow\phi\phi$ decays is obtained. The CP-violating phase $\phi_s^{s\bar{s}s}$ is measured to be $-0.073 \pm 0.115$(stat)$\pm 0.027$(syst) rad, under the assumption it is independent on the helicity of the $\phi\phi$ decay. In addition, the CP-violating phases of the transverse polarisations under the assumption of CP conservation of the longitudinal phase are measured. The helicity-independent direct CP-violation parameter is also measured, and is found to be $|\lambda|=0.99 \pm 0.05 $(stat)$ \pm 0.01 $(syst). In addition, $T$-odd triple-product asymmetries are measured. The results obtained are consistent with the hypothesis of CP conservation in $b\rightarrow\overline{s}s\overline{s}$ transitions. Finally, a limit on the branching fraction of the $B^0\rightarrow \phi\phi$ decay is determined to be $\mathcal{B}(B^0\rightarrow \phi\phi)<2.7\times 10^{-8}$ at 90% confidence level.

Figures and captions

A fit to the four-kaon mass for the (top left) 2011, (top right) 2012, (bottom left) 2015 and (bottom right) 2016 data sets, which are 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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Decay angles for the $ B ^0_ s \rightarrow \phi \phi$ decay, where $\theta_{1,2}$ is the angle between the $K^+$ momentum in the $\phi_{1,2}$ meson rest frame and the $\phi_{1,2}$ 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 normalised to the average obtained using 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 $\Phi$. Each figure includes the resulting fit curve.

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Decay-time acceptances calculated from (left) $ B ^0_ s \rightarrow D ^-_ s \pi ^+ $ decays to match Run 1 data and (right) $ B ^0 \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^{*0} $ decays to match Run 2 data. Superimposed is a parameterisation using cubic 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 fit. The $ C P$ -even $P$-wave, the $ C P$ -odd $P$-wave and the combined $S$-wave and 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 into 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 $\Lambda ^0_ b \rightarrow \phi p K$ contribution as a magenta long-dashed line and the combinatorial background as a blue short-dashed line.

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Results of the ${\rm CL}_s$ scan as a function of the $ B ^0 \rightarrow\phi\phi$ yield. 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 $90 \%$ CL limit is shown as a red line.

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Animated gif made out of all figures.

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Tables and captions

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 for the $ B ^0_ s \rightarrow \phi\phi$ decay.

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Results of the decay-time-dependent, polarisation-independent fit for the $ C P$ -violation fit. Uncertainties shown do not include systematic contributions.

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Results of the polarisation-dependent fit for the $ C P$ violation fit. Uncertainties shown do not include systematic contributions.

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Summary of systematic uncertainties (in units of $10^{-2}$) for parameters of interest in the decay-time-dependent measurement.

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

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Statistical correlation matrix of the time-dependent fit.

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Statistical correlation matrix of the time-dependent fit in which $ C P$ violation is polarisation dependent.

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Created on 19 October 2019.