A study of $C P$ violation in the decays $B^\pm\to[K^+K^-\pi^+\pi^-]_D h^{\pm}$ ($h = K, \pi$) and $B^\pm\to[\pi^+\pi^-\pi^+\pi^-]_D h^{\pm}$

Information

LHCb-PAPER-2022-037
CERN-EP-2022-285
arXiv:2301.10328 [PDF]

(Submitted on 24 Jan 2023)
Eur. Phys. J. C83 547 (2023)
Inspire 2626410

Tools

Abstract

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.

Figures and captions

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.	Binnin[..].pdf [20 KiB] HiDef png [113 KiB] Thumbnail [169 KiB] *.C file
	Strong[..].pdf [14 KiB] HiDef png [95 KiB] Thumbnail [55 KiB] *.C file
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.	d2kkpi[..].pdf [59 KiB] HiDef png [278 KiB] Thumbnail [200 KiB] *.C file
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.	B2DK_C[..].pdf [16 KiB] HiDef png [272 KiB] Thumbnail [188 KiB] *.C file
	B2Dpi_[..].pdf [16 KiB] HiDef png [212 KiB] Thumbnail [146 KiB] *.C file
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.	BinAsy[..].pdf [15 KiB] HiDef png [104 KiB] Thumbnail [62 KiB] *.C file
	BinAsy[..].pdf [15 KiB] HiDef png [103 KiB] Thumbnail [61 KiB] *.C file
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.	TotalB[..].pdf [15 KiB] HiDef png [120 KiB] Thumbnail [71 KiB] *.C file
	TotalB[..].pdf [14 KiB] HiDef png [114 KiB] Thumbnail [65 KiB] *.C file
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
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.	d2pipi[..].pdf [100 KiB] HiDef png [480 KiB] Thumbnail [339 KiB] *.C file
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].	gammac[..].pdf [17 KiB] HiDef png [659 KiB] Thumbnail [343 KiB] *.C file
	gammac[..].pdf [21 KiB] HiDef png [969 KiB] Thumbnail [463 KiB] *.C file
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.	Binnin[..].pdf [19 KiB] HiDef png [85 KiB] Thumbnail [161 KiB] *.C file
	Strong[..].pdf [14 KiB] HiDef png [88 KiB] Thumbnail [51 KiB] *.C file
Animated gif made out of all figures.	PAPER-2022-037.gif Thumbnail

Tables and captions

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.	Table_1.pdf [57 KiB] HiDef png [93 KiB] Thumbnail [42 KiB] tex code
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.	Table_2.pdf [62 KiB] HiDef png [79 KiB] Thumbnail [35 KiB] tex code
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.	Table_3.pdf [66 KiB] HiDef png [61 KiB] Thumbnail [31 KiB] tex code
Results of the phase-space integrated measurements. The first uncertainty is statistical and the second systematic.	Table_4.pdf [52 KiB] HiDef png [71 KiB] Thumbnail [34 KiB] tex code
Uncertainties on the results of the binned analysis.	Table_5.pdf [75 KiB] HiDef png [162 KiB] Thumbnail [65 KiB] tex code
Uncertainties on the results of the phase-space integrated analysis.	Table_6.pdf [63 KiB] HiDef png [65 KiB] Thumbnail [27 KiB] tex code
Yields with the $2\times 8$ binning scheme.	Table_7.pdf [56 KiB] HiDef png [144 KiB] Thumbnail [75 KiB] tex code
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
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.	Table_9.pdf [61 KiB] HiDef png [71 KiB] Thumbnail [35 KiB] tex code
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.	Table_10.pdf [57 KiB] HiDef png [50 KiB] Thumbnail [23 KiB] tex code
Yields with the $2\times 4$ binning scheme.	Table_11.pdf [56 KiB] HiDef png [84 KiB] Thumbnail [43 KiB] tex code
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
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.	Table_13.pdf [61 KiB] HiDef png [76 KiB] Thumbnail [36 KiB] tex code
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
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
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
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