# A new algorithm for identifying the flavour of $B_s^0$ mesons at LHCb

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## Abstract

A new algorithm for the determination of the initial flavour of $B_s^0$ mesons is presented. The algorithm is based on two neural networks and exploits the $b$ hadron production mechanism at a hadron collider. The first network is trained to select charged kaons produced in association with the $B_s^0$ meson. The second network combines the kaon charges to assign the $B_s^0$ flavour and estimates the probability of a wrong assignment. The algorithm is calibrated using data corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by the LHCb experiment in proton-proton collisions at 7 and 8 TeV centre-of-mass energies. The calibration is performed in two ways: by resolving the $B_s^0$-$\bar{B}_s^0$ flavour oscillations in $B_s^0 \to D_s^- \pi^+$ decays, and by analysing flavour-specific $B_{s 2}^{*}(5840)^0 \to B^+ K^-$ decays. The tagging power measured in $B_s^0 \to D_s^- \pi^+$ decays is found to be $(1.80 \pm 0.19({\rm stat}) \pm 0.18({\rm syst}))$%, which is an improvement of about 50% compared to a similar algorithm previously used in the LHCb experiment.

## Figures and captions

 (left) Distribution of the NN1 output, $o_1$, of signal (blue) and background (red) tracks. (right) Distribution of the NN2 output, $o_2$, of initially produced $B ^0_ s$ (blue) and $\overline{ B }{} {}^0_ s$ (red) mesons. Both distributions are obtained with simulated events. The markers represent the distributions obtained from the training samples; the solid histograms are the distributions obtained from the test samples. The good agreement between the distributions of the test and training samples shows that there is no overtraining of the classifiers. Fig1a.pdf [22 KiB] HiDef png [436 KiB] Thumbnail [299 KiB] *.C file Fig1b.pdf [23 KiB] HiDef png [425 KiB] Thumbnail [297 KiB] *.C file Mass distribution of $B ^0_ s \rightarrow D ^-_ s \pi ^+$ candidates with fit projections overlaid. Data points (black markers) correspond to the $B ^0_ s$ candidates selected in the 3 $fb^{-1}$ data sample. The total fit function and its components are overlaid with solid and dashed lines (see legend). Fig2.pdf [65 KiB] HiDef png [341 KiB] Thumbnail [279 KiB] *.C file (left) Background-subtracted $\eta$ distribution of $B ^0_ s \rightarrow D ^-_ s \pi ^+$ candidates in data; the vertical dotted lines show the binning used in the second method of the calibration. (right) Measured average mistag fraction $\omega$ in bins of mistag probability $\eta$ (black points), with the result of a linear fit superimposed (solid red line) and compared to the calibration obtained from the unbinned fit (dashed black line). The linear fit has $\chi^2/\mathrm{ndf} =1.3$. The shaded areas correspond to the 68% and 95% confidence level regions of the unbinned fit. Fig3a.pdf [19 KiB] HiDef png [236 KiB] Thumbnail [207 KiB] *.C file Fig3b.pdf [16 KiB] HiDef png [210 KiB] Thumbnail [153 KiB] *.C file Distribution of the mass difference, $Q$, of selected $B ^+ K ^-$ candidates, summing over four $B ^+$ decay modes (black points), and the function fitted to these data (solid blue line). From left to right, the three peaks are identified as being $B _{ s 1}(5830)^0\rightarrow B ^{*+} K ^-$, $B _{ s 2}^{*}(5840)^0 \rightarrow B ^{*+} K ^-$, and $B _{ s 2}^{*}(5840)^0 \rightarrow B ^+ K ^-$ . Same charge combinations $B ^\pm K ^\pm$ in data are superimposed (solid histogram) and contain no structure. Fig4.pdf [45 KiB] HiDef png [207 KiB] Thumbnail [168 KiB] *.C file (left) Background-subtracted $\eta$ distribution of $B _{ s 2}^{*}(5840)^0 \rightarrow B ^+ K ^-$ candidates in data; the vertical dotted lines show the binning used in the calibration. (right) Measured average mistag fraction $\omega$ in bins of mistag probability $\eta$ (black points), with the result of a linear fit superimposed (solid black line). The fit has $\chi^2/\mathrm{ndf} =0.8$. The shaded areas correspond to the 68% and 95% confidence level regions of the fit. Fig5a.pdf [18 KiB] HiDef png [222 KiB] Thumbnail [200 KiB] *.C file Fig5b.pdf [20 KiB] HiDef png [192 KiB] Thumbnail [148 KiB] *.C file Mass distribution of $D ^-_ s \rightarrow \phi(\rightarrow K ^+ K ^- )\pi ^-$ candidates with fit projections overlaid. Data points (black markers) correspond to the $D ^-_ s$ candidates selected in the 3 $fb^{-1}$ data sample. The total fit function and its components are overlaid (see legend). Fig6.pdf [25 KiB] HiDef png [216 KiB] Thumbnail [168 KiB] *.C file Animated gif made out of all figures. PAPER-2015-056.gif Thumbnail

## Tables and captions

 Systematic uncertainties of the parameters $p_0$ and $p_1$ obtained in the calibration with $B ^0_ s \rightarrow D ^-_ s \pi ^+$ decays. Table_1.pdf [59 KiB] HiDef png [115 KiB] Thumbnail [48 KiB] tex code Systematic uncertainties of the parameters $p_0$ and $p_1$ obtained in the calibration with $B _{ s 2}^{*}(5840)^0 \rightarrow B ^+ K ^-$ decays. Table_2.pdf [47 KiB] HiDef png [62 KiB] Thumbnail [28 KiB] tex code Systematic uncertainties of the parameters $p_0$ and $p_1$ related to the portability of the calibration to different decay modes. Table_3.pdf [44 KiB] HiDef png [50 KiB] Thumbnail [22 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf Supple[..].pdf [721 KiB] This ZIP file contains supplementary material for the publication LHCb-PAPER-2015-056. The files are: Supplementary.pdf: An overview of the extra figure *.pdf, *.png, *.eps, *.C: The figures in various formats. The *.C files contain the data on the figures. Fig1_S[..].pdf [697 KiB] HiDef png [464 KiB] Thumbnail [314 KiB] *C file Fig2a_[..].pdf [53 KiB] HiDef png [174 KiB] Thumbnail [171 KiB] *C file Fig2b_[..].pdf [52 KiB] HiDef png [188 KiB] Thumbnail [177 KiB] *C file Fig3a_[..].pdf [24 KiB] HiDef png [202 KiB] Thumbnail [153 KiB] *C file Fig3b_[..].pdf [23 KiB] HiDef png [197 KiB] Thumbnail [151 KiB] *C file Fig4_S[..].pdf [30 KiB] HiDef png [210 KiB] Thumbnail [161 KiB] *C file

Created on 27 February 2021.