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Measurement of the branching fractions for $B^+\to D^{*+}D^-K^+$, $B^+\to D^{*-}D^+K^+$, and $B^0\to D^{*-}D^0K^+$ decays

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Abstract

A measurement of four branching-fraction ratios for three-body decays of $B$ mesons involving two open-charm hadrons in the final state is presented. Run 1 and Run 2 $pp$ collision data are used, recorded by the LHCb experiment at centre-of-mass energies $7$, $8$, and $13$ TeV and corresponding to an integrated luminosity of $9$ fb$^{-1}$. The measured branching-fraction ratios are \[ \begin{eqnarray} \frac{\mathcal{B} (B^+\to D^{*+}D^-K^+)}{\mathcal{B} (B^+\to \overline{ D}{}^0 D^0 K^+)} &=& 0.517 \pm 0.015 \pm 0.013 \pm 0.011 , \\ \frac{\mathcal{B} (B^+\to D^{*-}D^+K^+)}{\mathcal{B} (B^+\to \overline{ D}{}^0 D^0 K^+)} &=& 0.577 \pm 0.016 \pm 0.013 \pm 0.013 , \\ \frac{\mathcal{B} (B^0\to D^{*-}D^0K^+)}{\mathcal{B} (B^0\to D^- D^0 K^+)} &=& 1.754 \pm 0.028 \pm 0.016 \pm 0.035 , \\ \frac{\mathcal{B} (B^+\to D^{*+}D^-K^+)}{\mathcal{B} (B^+\to D^{*-}D^+K^+)} &=& 0.907 \pm 0.033 \pm 0.014 ,\end{eqnarray} \] where the first of the uncertainties is statistical, the second systematic, and the third is due to the uncertainties on the $D$-meson branching fractions. These are the most accurate measurements of these ratios to date.

Figures and captions

Top left: internal $ W $ -emission diagram for the decays $ B ^+ \rightarrow D ^{*-} D ^+ K ^+ $ and $ B ^+ \rightarrow D ^{*+} D ^- K ^+ $ . Top right: external $ W $ -emission diagram for the decays $ B ^0 \rightarrow D ^{*-} D ^0 K ^+ $ and $ B ^0 \rightarrow D ^- D ^0 K ^+ $ . Bottom row: (left) external and (right) internal $ W $ -emission diagrams contributing to the $ B ^+ \rightarrow \overline{ D }{} {}^0 D ^0 K ^+ $ decay.

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Fits to the invariant-mass distributions $m( D ^{(*)} \overline{ D }{} K )$ of (left) $ B \rightarrow D ^* \overline{ D }{} K $ and (right) $ B \rightarrow D \overline{ D }{} K $ for the combined Run 1 and Run 2 samples. The stacked components are (red) combinatorial background and (blue) signal shape.

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Selection and reconstruction efficiency, $\varepsilon^{\mathrm{sel}}$, as a function of position in the two-body squared invariant-mass plane for the seven $ B \rightarrow D ^* \overline{ D }{} K $ modes, obtained using Run 1 simulated samples. A KDE smoothing has been applied. The blue lines indicate the kinematic boundaries and the numbers indicate the value of the efficiency at several points in the phase space.

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Selection and reconstruction efficiency, $\varepsilon^{\mathrm{sel}}$, as a function of position in the two-body squared invariant-mass plane for the seven $ B \rightarrow D ^* \overline{ D }{} K $ modes, obtained using Run 2 simulated samples. A KDE smoothing has been applied. The blue lines indicate the kinematic boundaries and the numbers indicate the values of the efficiency at several points in the phase space.

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Animated gif made out of all figures.

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Tables and captions

Decays under study. In the first column no assumption about the $ D $ final state is made. In the second column, however, the particular $ D $ decays are specified.

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Table of all signal yields $N$ and efficiency and $ D $ -meson branching fraction corrected yields $ N^{\mathrm{corr}}$ with the residual peaking background subtracted. The values of corrected yields are rounded to the order of $10^6$. The uncertainties are statistical only.

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Systematic uncertainties on $ N^{\mathrm{corr}}$ from the signal PDF parameters ($\sigma_{\mathrm{PDF}}$), the finite simulation samples ($\sigma_{\mathrm{MC}}$), the PID resampling ($\sigma_{\mathrm{PID}}$), the residual peaking background ($\sigma_{\mathrm{bkg}}$), and the total systematic uncertainty ($\sigma_{\mathrm{tot.}}$). All values are given as a percentage of the central value of $ N^{\mathrm{corr}}$ .

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplemetary material for the publication LHCb-PAPER-2020-006. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps , *.C: The figures in variuous formats

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Created on 14 January 2021.