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Measurement of $C P$ observables in the process $B^0 \to DK^{*0}$ with two- and four-body $D$ decays

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Abstract

Measurements of $C P$ observables in $B^0 \to DK^{*0}$ decays are presented, where $D$ represents a superposition of $D^0$ and $\bar{D}^0$ states. The $D$ meson is reconstructed in the two-body final states $K^+\pi^-$, $\pi^+ K^-$, $K^+K^-$ and $\pi^+\pi^-$, and, for the first time, in the four-body final states $K^+\pi^-\pi^+\pi^-$, $\pi^+ K^-\pi^+\pi^-$ and $\pi^+\pi^-\pi^+\pi^-$. The analysis uses a sample of neutral $B$ mesons produced in proton-proton collisions, corresponding to an integrated luminosity of 1.0, 2.0 and 1.8 $\rm fb^{-1}$ collected with the LHCb detector at centre-of-mass energies of $\sqrt{s} = $ 7, 8 and 13 TeV, respectively. First observations of the decays $B^0 \to D(\pi^+ K^-)K^{*0}$ and $B^0 \to D(\pi^+\pi^-\pi^+\pi^-)K^{*0}$ are obtained. The measured observables are interpreted in terms of the $C P$-violating weak phase $\gamma$.

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Feynman diagrams of (left) $ B ^0 \rightarrow D ^0 K ^{*0} $ and (right) $ B ^0 \rightarrow \overline{ D } {}^0 K ^{*0} $.

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Invariant-mass distributions (data points with error bars) and results of the fit (lines and coloured areas) for the two-body GLW modes (top left) $\overline{ B } {}^0 \rightarrow D( K ^+ K ^- )\overline{ K } {}^{*0} $, (top right) $ B ^0 \rightarrow D( K ^+ K ^- ) K ^{*0} $, (bottom left) $\overline{ B } {}^0 \rightarrow D(\pi ^+ \pi ^- )\overline{ K } {}^{*0} $ and (bottom right) $ B ^0 \rightarrow D(\pi ^+ \pi ^- ) K ^{*0} $.

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Invariant-mass distributions (data points with error bars) and results of the fit (lines and coloured areas) for the two-body ADS modes (top left) $\overline{ B } {}^0 \rightarrow D( K ^- \pi ^+ )\overline{ K } {}^{*0} $, (top right) $ B ^0 \rightarrow D( K ^+ \pi ^- ) K ^{*0} $, (bottom left) $\overline{ B } {}^0 \rightarrow D(\pi ^- K ^+ )\overline{ K } {}^{*0} $ and (bottom right) $ B ^0 \rightarrow D(\pi ^+ K ^- ) K ^{*0} $. The bottom distributions are shown on a logarithmic scale.

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Invariant-mass distributions (data points with error bars) and results of the fit (lines and coloured areas) for the four-body GLW mode (left) $\overline{ B } {}^0 \rightarrow D(\pi ^+ \pi ^- \pi ^+ \pi ^- )\overline{ K } {}^{*0} $, (right) $ B ^0 \rightarrow D(\pi ^+ \pi ^- \pi ^+ \pi ^- ) K ^{*0} $.

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Invariant-mass distributions (data points with error bars) and results of the fit (lines and coloured areas) for the four-body ADS modes (top left) $\overline{ B } {}^0 \rightarrow D( K ^- \pi ^+ \pi ^- \pi ^+ )\overline{ K } {}^{*0} $, (top right) $ B ^0 \rightarrow D( K ^+ \pi ^- \pi ^+ \pi ^- ) K ^{*0} $, (bottom left) $\overline{ B } {}^0 \rightarrow D(\pi ^- K ^+ \pi ^+ \pi ^- )\overline{ K } {}^{*0} $ and (bottom right) $ B ^0 \rightarrow D(\pi ^+ K ^- \pi ^- \pi ^+ ) K ^{*0} $. The bottom distributions are shown on a logarithmic scale.

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Contour plots showing 2D scans of (left) $\delta_B^{D K ^{*0} }$ versus $\gamma$ and (right) $\delta_B^{D K ^{*0} }$ versus $r_B^{D K ^{*0} }$. The lines represent the $\Delta\chi^2 =$ 2.30, 6.18 and 11.8 contours, corresponding to 68.6%, 95.5% and 99.7% confidence levels (C.L.), respectively.

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Animated gif made out of all figures.

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Tables and captions

Summary of signal yields. The uncertainties are statistical.

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Measured observables split by LHC running period. Observables relating to $ B ^0 \rightarrow D(\pi ^+ \pi ^- \pi ^+ \pi ^- ) K ^{*0} $ decays are not presented for Run 1, as this decay channel was not selected in the Run 1 data.

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Combined statistical and systematic correlation matrix for the principal observables.

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Combined statistical and systematic correlation matrix for the principal observables in Run 1 data only.

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Combined statistical and systematic correlation matrix for the principal observables in Run 2 data only.

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Correlation matrix for the principal observables between Run 1 and Run 2 data.

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Supplementary Material [file]

Supplementary material full pdf

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Supplementary material full pdf

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This ZIP file contains supplementary material for the publication LHCb-PAPER-2019-021. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in various formats

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Created on 13 September 2019.