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Updated branching fraction measurements of $B^0_{(s)} \to K_{\mathrm{\scriptscriptstyle S}}^0 h^+ h^{\prime -}$ decays

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Abstract

The charmless three-body decays $B^0_{(s)} \to K_{\mathrm{\scriptscriptstyle S}}^0 h^+ h^{\prime -}$ (where $h^{(\prime)} = \pi, K$) are analysed using a sample of $pp$ collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of $3 fb^{-1}$. The branching fractions are measured relative to that of the $B^0 \to K_{\mathrm{\scriptscriptstyle S}}^0 \pi^{+} \pi^{-}$ decay, and are determined to be: \begin{eqnarray*} \frac{{\cal B}(B^0\rightarrow K^0_{\rm S}K^{\pm}\pi^{\mp})}{{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 0.123 \pm 0.009 \; \mathrm{ (stat)}\; \pm 0.015 \; \mathrm{ (syst)} , \frac{{\cal B}(B^0\rightarrow K^0_{\rm S}K^{+}K^{-})} {{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 0.549 \pm 0.018 \; \mathrm{ (stat)}\; \pm 0.033 \; \mathrm{ (syst)} , \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})}{{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 0.191 \pm 0.027 \; \mathrm{ (stat)}\; \pm 0.031 \; \mathrm{ (syst)}\; \pm 0.011 \; (f_s/f_d) , \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}K^{\pm}\pi^{\mp})} {{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} = {} & 1.70\phantom{0} \pm 0.07\phantom{0} \; \mathrm{ (stat)} \; \pm 0.11\phantom{0} \; \mathrm{ (syst)}\; \pm 0.10\phantom{0} \; (f_s/f_d) , \frac{{\cal B}(B_{s}^0\rightarrow K^0_{\rm S}K^{+}K^{-})}{{\cal B}(B^0\rightarrow K^0_{\rm S}\pi^{+}\pi^{-})} \in {} & [0.008 - 0.051] \rm at 90\% confidence level, \end{eqnarray*} where $f_s/f_d$ represents the ratio of hadronisation fractions of the $B^0_s$ and $B^0$ mesons.

Figures and captions

Invariant mass distributions of, from top to bottom, $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^\pm \pi ^\mp $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ candidates, summing the three periods of data taking, with the selection optimisation chosen for the favoured decay modes for (left) downstream and (right) long $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction categories. In each plot, data are the black points with error bars and the total fit model is overlaid (solid blue line). The $ B ^0$ ( $ B ^0_ s $ ) signal components are the pink (orange) short-dashed (dotted) lines, while fully reconstructed misidentified decays are the green and dark blue dashed lines close to the $ B ^0$ and $ B ^0_ s $ peaks. The sum of the partially reconstructed contributions from $ B $ to open charm decays, charmless hadronic decays, $ B ^0 \rightarrow \eta ^{\prime} K ^0_{\mathrm{ \scriptscriptstyle S}} $ and charmless radiative decays are the red dash triple-dotted lines. The combinatorial background contribution is the gray long-dash dotted line.

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Invariant mass distributions of, from top to bottom, $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^\pm \pi ^\mp $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ candidates, summing the three periods of data taking, with the selection optimisation chosen for the favoured decay modes for (left) downstream and (right) long $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction categories. In each plot, data are the black points with error bars and the total fit model is overlaid (solid blue line). The $ B ^0$ ( $ B ^0_ s $ ) signal components are the pink (orange) short-dashed (dotted) lines, while fully reconstructed misidentified decays are the green and dark blue dashed lines close to the $ B ^0$ and $ B ^0_ s $ peaks. The sum of the partially reconstructed contributions from $ B $ to open charm decays, charmless hadronic decays, $ B ^0 \rightarrow \eta ^{\prime} K ^0_{\mathrm{ \scriptscriptstyle S}} $ and charmless radiative decays are the red dash triple-dotted lines. The combinatorial background contribution is the gray long-dash dotted line.

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Results of the simultaneous fit to data (downstream, 2011) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012a) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012b) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2011) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012a) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012b) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2011) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012a) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012b) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2011) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012a) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Results of the simultaneous fit to data (downstream, 2012b) with the BDT optimisation corresponding to the favoured decay modes. The modes $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ are shown from top to bottom. The left-hand side plots show the results with a logarithmic scale and the right-hand side with a linear scale. Legend is similar to that of plots shown in Fig. ???.

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Distribution of sPlot weights in data. The $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ K ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} K ^+ \pi ^- $ , $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ K ^- $ , and $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ final states are shown from top to bottom, with a $ B ^0$ parent on the left, and a $ B ^0_ s $ on the right. All data-taking periods and $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction categories are added.

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Animated gif made out of all figures.

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Tables and captions

Signal yields obtained from the simultaneous fit to the data. The yields are the sum of those obtained in the three data-taking periods when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in Sec. 5, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination.

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Summary of the systematic uncertainties on the ratio of branching fractions. A weighted average of the two $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction categories and three data-taking periods is performed. The values quoted for the individual contributions, which are illustrative of the hierarchy between sources of systematic uncertainty, each result from a weighted average in which the other systematic uncertainty contributions are disregarded. The total uncertainty is the weighted average including all contributions. All uncertainties are relative and are quoted as percentages.

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Signal yields obtained for the 2011 category from the simultaneous fit to the data. The yields shown are those obtained when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in Sec. ???, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination.

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Signal yields obtained for the 2011 category from the simultaneous fit to the data. The yields shown are those obtained when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in Sec. ???, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination.

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Signal yields obtained for the 2011 category from the simultaneous fit to the data. The yields shown are those obtained when fitting the data sample selected using the BDT optimisation chosen for the given decay mode. The uncertainties are statistical only. The average selection efficiencies, described in Sec. ???, are also shown for each decay mode together with the corresponding total uncertainty due to the limited simulation sample size and systematic effects in their determination.

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Systematic uncertainties on the ratios of branching fractions for downstream $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction. All uncertainties are relative and are quoted as percentages.

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Systematic uncertainties on the ratios of branching fractions for long $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction. All uncertainties are relative and are quoted as percentages.

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Created on 11 July 2020.