The first study of $C P$ violation in the decay mode $B^\pm\to[K^+K^-\pi^+\pi^-]_D h^\pm$, with $h=K,\pi$, is presented, exploiting a data sample of proton-proton collisions collected by the LHCb experiment that corresponds to an integrated luminosity of $9$ fb$^{-1}$. The analysis is performed in bins of phase space, which are optimised for sensitivity to local $C P$ asymmetries. $C P$-violating observables that are sensitive to the angle $\gamma$ of the Unitarity Triangle are determined. The analysis requires external information on charm-decay parameters, which are currently taken from an amplitude analysis of LHCb data, but can be updated in the future when direct measurements become available. Measurements are also performed of phase-space integrated observables for $B^\pm\to[K^+K^-\pi^+\pi^-]_D h^\pm$ and $B^\pm\to[\pi^+\pi^-\pi^+\pi^-]_D h^\pm$ decays.
Left: Optimised $2\times 8$ binning scheme in $\Delta \delta_D$-$\ln(r_D)$ space. Right: The associated $c_i$ and $s_i$ parameters calculated using the amplitude model (right). The numbers indicate the bin numbers. |
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Invariant-mass distributions for the (left) $ B ^\pm \rightarrow D K ^\pm $ and (right) $ B ^\pm \rightarrow D \pi ^\pm $ selections, for the $ D \rightarrow K ^+ K ^- \pi ^+ \pi ^- $ decay. The data are shown as black points and the blue curve is the fit result. The square brackets in the legend denote particles that are not reconstructed. |
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Graphical representation of the $ C P$ -violating observables for the (left) $ B ^\pm \rightarrow D K ^\pm $ and (right) $ B ^\pm \rightarrow D \pi ^\pm $ decay modes, assuming amplitude-model predictions of $c_i$ and $s_i$. The 1$\sigma$ and 2$\sigma$ contours shown represent the statistical uncertainties and correspond to $68.3\%$ ($\Delta\chi^2 = 2.30$) and $95.5\%$ ($\Delta\chi^2 = 6.18$) confidence intervals. |
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Fractional bin asymmetries for the (left) $ B ^\pm \rightarrow D K ^\pm $ and (right) $ B ^\pm \rightarrow D \pi ^\pm $ decays. The data are overlaid with the fit result and the prediction without $ C P$ violation. |
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Total bin yields for the (left) $ B ^\pm \rightarrow D K ^\pm $ and (right) $ B ^\pm \rightarrow D \pi ^\pm $ decays. The data are overlaid with the fit projections. |
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Invariant-mass distributions and fit projections of (top) $ B ^\pm \rightarrow [ K ^+ K ^- \pi ^+ \pi ^- ]_ D K ^\pm $ and (bottom) $ B ^\pm \rightarrow [ K ^+ K ^- \pi ^+ \pi ^- ]_ D \pi ^\pm $ candidates, for (left) $ B ^+ $ and (right) $ B ^- $ decays. The data are shown as black points and the blue curve is the fit result. |
d2kkpi[..].pdf [100 KiB] HiDef png [473 KiB] Thumbnail [331 KiB] *.C file |
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Invariant-mass distributions and fit projections of (top) $ B ^\pm \rightarrow [\pi ^+ \pi ^- \pi ^+ \pi ^- ]_ D K ^\pm $ and (bottom) $ B ^\pm \rightarrow [\pi ^+ \pi ^- \pi ^+ \pi ^- ]_ D \pi ^\pm $ candidates, for (left) $ B ^+ $ and (right) $ B ^- $ decays. The data are shown as black points and the blue curve is the fit result. |
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Interpretation of the binned and phase-space (`PS') integrated measurements in terms to the underlying physics parameters. The 1$\sigma$ and 2$\sigma$ contours are shown, which correspond to $68.3\%$ ($\Delta\chi^2 = 2.30$) and $95.5\%$ ($\Delta\chi^2 = 6.18$) confidence intervals, respectively. Also shown is the result from the analysis of other decay modes at LHCb (`LHCb 2021') [21]. |
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Left: Optimised $2\times 4$ binning scheme in $\Delta \delta_D$-$\ln(r_D)$ space. Right: The associated $c_i$ and $s_i$ parameters calculated using the amplitude model (right). The numbers indicate the bin numbers. |
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Animated gif made out of all figures. |
PAPER-2022-037.gif Thumbnail |
Values of $c_i$, $s_i$, $F_i$ and $V_i$ for the optimised $2\times 8$ binning scheme, as calculated from the amplitude model. The number of digits quoted reflects the uncertainty due to the sample size used in the Monte Carlo integration. |
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Yields of $ B ^\pm \rightarrow D K ^\pm $ and $ B ^\pm \rightarrow D \pi ^\pm $ candidates, partially reconstructed background, $ D \rightarrow K ^- \pi ^+ \pi ^- \pi ^+ \pi ^0 $ background, combinatorial background and charmless background in the region $m_ B \in[5249, 5309]\text{ Me V /}c^2 $, where the charm meson decays via $ D \rightarrow K ^+ K ^- \pi ^+ \pi ^- $ and $ D \rightarrow \pi ^+ \pi ^- \pi ^+ \pi ^- $. Charmless background in the $ B ^\pm \rightarrow D \pi ^\pm $ decay modes is known to be negligible, and is therefore not modelled. |
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Results of the binned fit. The first uncertainty is statistical, the second is systematic, and the third is associated with the model dependence of the strong-phase parameters. |
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Results of the phase-space integrated measurements. The first uncertainty is statistical and the second systematic. |
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Uncertainties on the results of the binned analysis. |
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Uncertainties on the results of the phase-space integrated analysis. |
Table_6.pdf [63 KiB] HiDef png [65 KiB] Thumbnail [27 KiB] tex code |
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Yields with the $2\times 8$ binning scheme. |
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Fit bias when using the bin yields for the $2\times 8$ binning scheme. |
Table_8.pdf [63 KiB] HiDef png [39 KiB] Thumbnail [17 KiB] tex code |
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Correlation matrix for systematic uncertainties of $ C P$ -violating observables for the binned measurement, with the $2\times 8$ binning scheme. The contribution from $c_i$ and $s_i$ is excluded. |
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Values of $c_i$, $s_i$, $F_i$ and $V_i$ for the optimised $2\times 4$ binning scheme, as calculated from the amplitude model. |
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Yields with the $2\times 4$ binning scheme. |
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Systematic uncertainties on the results of the binned analysis, with the $2\times 4$ binning scheme. |
Table_12.pdf [74 KiB] HiDef png [138 KiB] Thumbnail [54 KiB] tex code |
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Correlation matrix for systematic uncertainties of $ C P$ -violating observables for the binned measurement, with the $2\times 4$ binning scheme. The contribution from $c_i$ and $s_i$ is excluded. |
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Correlation matrix for statistical uncertainties of $ C P$ -violating observables for the binned measurement. |
Table_14.pdf [61 KiB] HiDef png [69 KiB] Thumbnail [34 KiB] tex code |
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Correlation matrix for systematic uncertainties of $ C P$ -violating observables for the binned measurement. |
Table_15.pdf [61 KiB] HiDef png [76 KiB] Thumbnail [37 KiB] tex code |
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Correlation matrix for statistical uncertainties of $ C P$ -violating observables for the phase-space integrated measurement. |
Table_16.pdf [53 KiB] HiDef png [81 KiB] Thumbnail [35 KiB] tex code |
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Correlation matrix for systematic uncertainties of $ C P$ -violating observables for the phase-space integrated measurement. |
Table_17.pdf [47 KiB] HiDef png [79 KiB] Thumbnail [35 KiB] tex code |
Supplementary material full pdf |
supple[..].pdf [354 KiB] |
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Fig1.pdf [35 KiB] HiDef png [250 KiB] Thumbnail [176 KiB] *C file |
Created on 02 May 2024.