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Measurement of the branching fractions of the decays $D^+\rightarrow K^-K^+K^+$, $D^+\rightarrow \pi^-\pi^+K^+$ and $D^+_s\rightarrow\pi^-K^+K^+$

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Abstract

The branching fractions of the doubly Cabibbo-suppressed decays $D^+\rightarrow K^-K^+K^+$, $D^+\rightarrow \pi^-\pi^+K^+$ and $D^+_s\rightarrow\pi^-K^+K^+$ are measured using the decays $D^+\rightarrow K^-\pi^+\pi^+$ and $D^+_s\rightarrow K^-K^+\pi^+$ as normalisation channels. The measurements are performed using proton-proton collision data collected with the LHCb detector at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2.0 fb$^{-1}$. The results are \begin{align} \frac {\mathcal{B}(D^+\rightarrow K^-K^+K^+)} {\mathcal{B}(D^+\rightarrow K^-\pi^+\pi^+)}& = (6.541 \pm 0.025 \pm 0.042) \times 10^{-4},\nonumber \frac {\mathcal{B}(D^+\rightarrow \pi^-\pi^+K^+)} {\mathcal{B}(D^+\rightarrow K^-\pi^+\pi^+)}& = (5.231 \pm 0.009 \pm 0.023) \times 10^{-3}, \nonumber \frac {\mathcal{B}(D^+_s\rightarrow\pi^-K^+K^+)} {\mathcal{B}(D^+_s\rightarrow K^-K^+\pi^+)}& = (2.372 \pm 0.024 \pm 0.025) \times 10^{-3},\nonumber \end{align} where the uncertainties are statistical and systematic, respectively. These are the most precise measurements up to date.

Figures and captions

Feynman diagrams for the DCS decays (a) $ D ^+ \!\rightarrow K ^- K ^+ K ^+ $ , (b) $ D ^+ \!\rightarrow \pi ^- \pi ^+ K ^+ $ and (c) $ D ^+_ s \!\rightarrow \pi ^- K ^+ K ^+ $ .

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Efficiency maps for (top left) $ D ^+ \!\rightarrow K ^- K ^+ K ^+ $ , (top right) $ D ^+ \!\rightarrow \pi ^- \pi ^+ K ^+ $ , (middle left) $ D ^+_ s \!\rightarrow \pi ^- K ^+ K ^+ $ , (middle right) $ D ^+ \!\rightarrow K ^- K ^+ \pi ^+ $ , (bottom left) $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ and (bottom right) $ D ^+_ s \!\rightarrow K ^- K ^+ \pi ^+ $ decays with PID efficiency, tracking, multiplicity and hardware trigger efficiency corrections, for MagDown polarity.

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Invariant-mass distributions of (top left) $ D ^+ \!\rightarrow K ^- K ^+ K ^+ $ , (top right) $ D ^+ \!\rightarrow \pi ^- \pi ^+ K ^+ $ , (bottom left) $ D ^+_ s \!\rightarrow \pi ^- K ^+ K ^+ $ and (bottom right) $ D ^+ \!\rightarrow K ^- K ^+ \pi ^+ $ with the corresponding fit result superimposed (red solid line). The blue dotted line corresponds to the signal PDF and the dashed grey line shows the background PDF.

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Invariant-mass distributions of candidates of the normalisation modes (left) $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ and (right) $ D ^+_ s \!\rightarrow K ^- K ^+ \pi ^+ $ with the corresponding fit result superimposed (red solid line). The blue dotted line corresponds to the signal PDF and the dashed grey line shows the background PDF.

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Dalitz plots of the (top left) $ D ^+ \!\rightarrow K ^- K ^+ K ^+ $ , (top right) $ D ^+ \!\rightarrow \pi ^- \pi ^+ K ^+ $ , where the $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ veto can be seen, (middle left) $ D ^+_ s \!\rightarrow \pi ^- K ^+ K ^+ $ , (middle right) $ D ^+ \!\rightarrow K ^- K ^+ \pi ^+ $ , (bottom left) $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ and (bottom right) $ D ^+_ s \!\rightarrow K ^- K ^+ \pi ^+ $ decays, with signal weights from sPlot . A logarithmic scale is used for the $ D ^+ \!\rightarrow K ^- K ^+ \pi ^+ $ and $ D ^+_ s \!\rightarrow K ^- K ^+ \pi ^+ $ channels.

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Animated gif made out of all figures.

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Tables and captions

World averages for the branching-fractions ratios under consideration [3].

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Ratios of average efficiencies for the full selection. The quoted uncertainty is due to the limited size of the simulated sample only (see Section 7).

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Observed yields for signal and normalisation modes with statistical uncertainties. The entry for the decay $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ $^{(\dagger)}$ corresponds to the yields obtained from the fit to $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ sample with cuts optimised for the $ D ^+ \!\rightarrow K ^- K ^+ K ^+ $ and $ D ^+ \!\rightarrow K ^- K ^+ \pi ^+ $ selections. The entry for the decay $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ $^{(\dagger\dagger)}$ is for fits to $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ samples with cuts optimised for the $ D ^+ \!\rightarrow \pi ^- \pi ^+ K ^+ $ selection.

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Produced yields for each decay mode with statistical uncertainties, shown separately for MagDown and MagUp samples. The numbers given for the decay $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ $^{(\dagger)}$ correspond to the sample with cuts optimised for the $ D ^+ \!\rightarrow K ^- K ^+ K ^+ $ and $ D ^+ \!\rightarrow K ^- K ^+ \pi ^+ $ and those for the decay $ D ^+ \!\rightarrow K ^- \pi ^+ \pi ^+ $ { $^{(\dagger\dagger)}$} to the sample with cuts optimised for the $ D ^+ \!\rightarrow \pi ^- \pi ^+ K ^+ $ selection.

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Relative systematic uncertainties for the MagDown and MagUp results (in %). The statistical uncertainties are also given for comparison.

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Ratios of branching fractions, shown separately for MagDown and MagUp samples. The first uncertainty is statistical and the second is systematic.

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Created on 17 December 2018.Citation count from INSPIRE on 18 December 2018.