An angular analysis of the decay $B^0 \to \phi K^*(892)^0$ is reported based on a $pp$ collision data sample, corresponding to an integrated luminosity of 1.0 fb$^{1}$, collected at a centreofmass energy of $\sqrt{s} = 7$ TeV with the LHCb detector. The Pwave amplitudes and phases are measured with a greater precision than by previous experiments, and confirm about equal amounts of longitudinal and transverse polarization. The Swave $K^+ \pi^$ and $K^+K^$ contributions are taken into account and found to be significant. A comparison of the $B^0 \to \phi K^*(892)^0$ and $\bar{B}^0 \to \phi \bar{K}^*(892)^0$ results shows no evidence for direct CP violation in the rate asymmetry, in the tripleproduct asymmetries or in the polarization amplitudes and phases.
Leading Feynman diagram for the $ B ^0 \rightarrow \phi K ^{*0} $ decay. 
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The helicity angles $\theta_1$, $\theta_2$, $\Phi$ for the $ B ^0 \rightarrow \phi K ^{*0} $ decay. 
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Invariant mass distribution for selected $ K^+K^K^+\pi^ $ candidates. A fit to the model described in the text is superimposed (red solid line). The signal contribution is shown as the blue dotted line. The contribution from combinatorial background is shown in green (dotted line). A contribution from $\overline{ B }{} ^0_ s \rightarrow \phi K ^{*0} $ (purple dotdashed line) decays is visible around the known $B_s^0$ meson mass. 
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Binned projections of the detector acceptance for (a) $m_{K\pi}$, (b) $m_{KK}$ , (c) $\cos\theta_1$, (d) $\cos\theta_2$ and (e) $\Phi$. The acceptance for the TOS (filled crosses) and not TOS (open squares) are shown on each plot. 
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Data distribution for the helicity angles and of the intermediate resonance masses: (a) $m_{K\pi}$ and (b) $m_{KK}$, (c) $\cos \theta_1$, (d) $\cos\theta_2$ and (e) $\Phi$. The background has been subtracted using the sPlot technique. The results of the fit are superimposed. 
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Animated gif made out of all figures. 
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Definition of the $h_i$, $f_i$ and $\mathcal{M}_i$ terms in Eq. 3. Note that the Pwave interference terms $i=4$ and $i=6$ take the imaginary parts of $A_\perp A_\parallel^*$ and $A_\perp A_0^*$, while $i=5$ takes the real part of $A_\parallel A_0^*$. Similarly the Swave interference terms $i=9$ and $i=13$ take the imaginary parts of $A_\perp A_\textrm{S}^* M_1 M_0^*$, and the terms $i=8,10,12,14$ take the real parts of $A_\parallel A_\textrm{S}^* M_1 M_0^*$ and $A_0 A_\textrm{S}^* M_1 M_0^*$. 
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Parameters measured in the angular analysis. The first and second uncertainties are statistical and systematic, respectively. 
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Tripleproduct asymmetries. The first and second uncertainties on the measured values are statistical and systematic, respectively. 
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Systematic uncertainties on the measurement of the polarization amplitudes, relative strong phases and tripleproduct asymmetries. The column labelled `Total' is the quadratic sum of the individual contributions. 
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Comparison of measurements made by the LHCb , BaBar [8] and Belle [11] collaborations. The first uncertainty is statistical and the second systematic. 
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Supplementary material full pdf 
Supple[..].pdf [74 KiB] 
Created on 06 March 2021.