A first flavourtagged measurement of the timedependent CPviolating asymmetry in $B_s^0 \to \phi\phi$ decays is presented. In this decay channel, the CPviolating weak phase arises due to CP violation in the interference between $B_s^0$$\bar{B}_s^0$ mixing and the $b \to s \bar{s} s $ gluonic penguin decay amplitude. Using a sample of $pp$ collision data corresponding to an integrated luminosity of $1.0\; fb^{1}$ and collected at a centreofmass energy of $7 \rm TeV$ with the LHCb detector, $880\ \B_s^0 \to \phi\phi$ signal decays are obtained. The CPviolating phase is measured to be in the interval [2.46, 0.76] \rm rad$ at 68% confidence level. The pvalue of the Standard Model prediction is 16%.
Invariant $K^+K^K^+K^$ mass distribution for selected $ B ^0_ s \rightarrow \phi \phi$ candidates. The total fit (solid line) consists of a double Gaussian signal component together with an exponential background (dotted line). 
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Onedimensional projections of the $ B ^0_ s \rightarrow \phi\phi$ fit for (a) decay time, (b) helicity angle $\Phi$ and the cosine of the helicity angles (c) $\theta_1$ and (d) $\theta_2$. The data are marked as points, while the solid lines represent the projections of the best fit. The $ C P$ even $P$wave, the $ C P$ odd $P$wave and $S$wave components are shown by the long dashed, short dashed and dotted lines, respectively. 
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phi_pu[..].pdf [19 KiB] HiDef png [168 KiB] Thumbnail [139 KiB] *.C file 

ctheta[..].pdf [19 KiB] HiDef png [154 KiB] Thumbnail [132 KiB] *.C file 

ctheta[..].pdf [19 KiB] HiDef png [153 KiB] Thumbnail [133 KiB] *.C file 

Negative $\Delta$ln likelihood scan of $\phi_s$. Only the statistical uncertainty is included. 
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Animated gif made out of all figures. 
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Coefficients of the timedependent terms and angular functions defined in Eqs. 1 and 2. Amplitudes are defined at $t=0$. 
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Fit results with statistical and systematic uncertainties. A 68% statistical confidence interval is quoted for $\phi_{ s }$ . Amplitudes are defined at $t = 0$. 
Table_2.pdf [53 KiB] HiDef png [40 KiB] Thumbnail [18 KiB] tex code 
Created on 20 February 2021.